US20170093430A1 - Data processing device and data processing method - Google Patents

Data processing device and data processing method Download PDF

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US20170093430A1
US20170093430A1 US15/310,930 US201515310930A US2017093430A1 US 20170093430 A1 US20170093430 A1 US 20170093430A1 US 201515310930 A US201515310930 A US 201515310930A US 2017093430 A1 US2017093430 A1 US 2017093430A1
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ldpc code
bit
parity check
bits
check matrix
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Ryoji IKEGAYA
Makiko YAMAMOTO
Yuji Shinohara
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Sony Corp
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Sony Corp
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Assigned to SONY CORPORATION reassignment SONY CORPORATION ASSIGNMENT OF ASSIGNORS INTEREST (SEE DOCUMENT FOR DETAILS). Assignors: IKEGA, RYOJI, SHINOHARA, YUJI, YAMAMOTO, MAKIKO
Publication of US20170093430A1 publication Critical patent/US20170093430A1/en
Priority to US15/935,439 priority Critical patent/US10333550B2/en
Assigned to SONY CORPORATION reassignment SONY CORPORATION CORRECTIVE ASSIGNMENT TO CORRECT THE FIRST INVENTOR'S NAME PREVIOUSLY RECORDED ON REEL 040652 FRAME 0281. ASSIGNOR(S) HEREBY CONFIRMS THE ASSIGNMENT. Assignors: IKEGAYA, RYOJI, SHINOHARA, YUJI, YAMAMOTO, MAKIKO
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    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
    • H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
    • H03M13/03—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words
    • H03M13/05—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits
    • H03M13/11—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits using multiple parity bits
    • H03M13/1102—Codes on graphs and decoding on graphs, e.g. low-density parity check [LDPC] codes
    • H03M13/1148—Structural properties of the code parity-check or generator matrix
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F11/00—Error detection; Error correction; Monitoring
    • G06F11/07—Responding to the occurrence of a fault, e.g. fault tolerance
    • G06F11/08—Error detection or correction by redundancy in data representation, e.g. by using checking codes
    • G06F11/10—Adding special bits or symbols to the coded information, e.g. parity check, casting out 9's or 11's
    • H—ELECTRICITY
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    • H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
    • H03M13/03—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words
    • H03M13/033—Theoretical methods to calculate these checking codes
    • H03M13/036—Heuristic code construction methods, i.e. code construction or code search based on using trial-and-error
    • H—ELECTRICITY
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    • H03M13/03—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words
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    • H03M13/11—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits using multiple parity bits
    • H03M13/1102—Codes on graphs and decoding on graphs, e.g. low-density parity check [LDPC] codes
    • H03M13/1105—Decoding
    • H03M13/1131—Scheduling of bit node or check node processing
    • H03M13/1137—Partly parallel processing, i.e. sub-blocks or sub-groups of nodes being processed in parallel
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    • H03M13/03—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words
    • H03M13/05—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits
    • H03M13/11—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits using multiple parity bits
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    • H03M13/1148—Structural properties of the code parity-check or generator matrix
    • H03M13/116—Quasi-cyclic LDPC [QC-LDPC] codes, i.e. the parity-check matrix being composed of permutation or circulant sub-matrices
    • H03M13/1165—QC-LDPC codes as defined for the digital video broadcasting [DVB] specifications, e.g. DVB-Satellite [DVB-S2]
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    • H03M13/25—Error detection or forward error correction by signal space coding, i.e. adding redundancy in the signal constellation, e.g. Trellis Coded Modulation [TCM]
    • H03M13/255—Error detection or forward error correction by signal space coding, i.e. adding redundancy in the signal constellation, e.g. Trellis Coded Modulation [TCM] with Low Density Parity Check [LDPC] codes
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    • H03M13/27—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes using interleaving techniques
    • H03M13/2703—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes using interleaving techniques the interleaver involving at least two directions
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    • H03M13/27—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes using interleaving techniques
    • H03M13/2757—Interleaver with an interleaving rule not provided for in the subgroups H03M13/2703 - H03M13/2753
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    • H03M13/27—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes using interleaving techniques
    • H03M13/2778—Interleaver using block-wise interleaving, e.g. the interleaving matrix is sub-divided into sub-matrices and the permutation is performed in blocks of sub-matrices
    • H—ELECTRICITY
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    • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
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    • H03M13/27—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes using interleaving techniques
    • H03M13/2792—Interleaver wherein interleaving is performed jointly with another technique such as puncturing, multiplexing or routing
    • H—ELECTRICITY
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    • H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
    • H03M13/29—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes combining two or more codes or code structures, e.g. product codes, generalised product codes, concatenated codes, inner and outer codes
    • H03M13/2906—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes combining two or more codes or code structures, e.g. product codes, generalised product codes, concatenated codes, inner and outer codes using block codes
    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
    • H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
    • H03M13/35—Unequal or adaptive error protection, e.g. by providing a different level of protection according to significance of source information or by adapting the coding according to the change of transmission channel characteristics
    • H03M13/356—Unequal error protection [UEP]
    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
    • H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
    • H03M13/61—Aspects and characteristics of methods and arrangements for error correction or error detection, not provided for otherwise
    • H03M13/615—Use of computational or mathematical techniques
    • H03M13/616—Matrix operations, especially for generator matrices or check matrices, e.g. column or row permutations
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L1/00—Arrangements for detecting or preventing errors in the information received
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L1/00—Arrangements for detecting or preventing errors in the information received
    • H04L1/004—Arrangements for detecting or preventing errors in the information received by using forward error control
    • H04L1/0041—Arrangements at the transmitter end
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L1/00—Arrangements for detecting or preventing errors in the information received
    • H04L1/004—Arrangements for detecting or preventing errors in the information received by using forward error control
    • H04L1/0056—Systems characterized by the type of code used
    • H04L1/0057—Block codes
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L1/00—Arrangements for detecting or preventing errors in the information received
    • H04L1/004—Arrangements for detecting or preventing errors in the information received by using forward error control
    • H04L1/0056—Systems characterized by the type of code used
    • H04L1/0057—Block codes
    • H04L1/0058—Block-coded modulation
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L1/00—Arrangements for detecting or preventing errors in the information received
    • H04L1/004—Arrangements for detecting or preventing errors in the information received by using forward error control
    • H04L1/0056—Systems characterized by the type of code used
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    • H03M13/03—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words
    • H03M13/05—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits
    • H03M13/13—Linear codes
    • H03M13/15—Cyclic codes, i.e. cyclic shifts of codewords produce other codewords, e.g. codes defined by a generator polynomial, Bose-Chaudhuri-Hocquenghem [BCH] codes
    • H03M13/151—Cyclic codes, i.e. cyclic shifts of codewords produce other codewords, e.g. codes defined by a generator polynomial, Bose-Chaudhuri-Hocquenghem [BCH] codes using error location or error correction polynomials
    • H03M13/152—Bose-Chaudhuri-Hocquenghem [BCH] codes

Definitions

  • the present technology relates to a data processing device and a data processing method, and more particularly, a data processing device and a data processing method, which are capable of securing excellent communication quality in data transmission using an LDPC code, for example.
  • a low density parity check (LDPC) code has a high error correction capability, and in recent years, the LDPC code has widely been employed in transmission schemes of digital broadcasting such as Digital Video Broadcasting (DVB)-S.2, DVB-T.2, and DVB-C.2 of Europe and the like, or Advanced Television Systems Committee (ATSC) 3.0 of the USA and the like (for example, see Non-Patent Literature 1).
  • DVD Digital Video Broadcasting
  • DVB-T.2 DVB-T.2
  • DVB-C.2 Advanced Television Systems Committee
  • the LDPC code has a property that a shortest distance is proportional to the code length, the LDPC code has advantages of a block error probability characteristic being superior and a so-called error floor phenomenon observed in a decoding characteristic of the turbo code being rarely generated, as characteristics thereof.
  • the LDPC code is converted into a symbol of an orthogonal modulation (digital modulation) such as Quadrature Phase Shift Keying (QPSK), and the symbol is mapped to a signal point of the orthogonal modulation and transmitted.
  • orthogonal modulation digital modulation
  • QPSK Quadrature Phase Shift Keying
  • the data transmission using the LDPC code has spread worldwide, and there is a demand to secure excellent communication (transmission) quality.
  • the present technology was made in light of the foregoing, and it is desirable to secure excellent communication quality in data transmission using the LDPC code.
  • a first data processing device/method is a data processing device/method including: an encoding unit/step configured to perform LDPC encoding based on a parity check matrix of an LDPC code in which a code length N is 16200 bits and an encoding rate r is 6/15; a group-wise interleaving unit/step configured to perform group-wise interleave of interleaving the LDPC code in units of bit groups of 360 bits; and a mapping unit/step configured to map the LDPC code to any of 64 signal points decided in a modulation scheme in units of 6 bits.
  • bit group i when an (i+1)-th bit group from a head of the LDPC code is indicated by a bit group i, a sequence of bit groups 0 to 44 of the LDPC code of 16200 bits is interleaved into a sequence of bit groups
  • the LDPC code includes an information bit and a parity bit.
  • the parity check matrix includes an information matrix portion corresponding to the information bit and a parity matrix portion corresponding to the parity bit.
  • the information matrix portion is represented by a parity check matrix initial value table.
  • the parity check matrix initial value table is a table in which a position of a 1 element of the information matrix portion is indicated for every 360 columns, and includes
  • LDPC encoding is performed based on a parity check matrix of an
  • LDPC code in which a code length N is 16200 bits and an encoding rate r is 6/15.
  • Group-wise interleave of interleaving the LDPC code in units of bit groups of 360 bits is performed.
  • the LDPC code is mapped to any of 64 signal points decided in a modulation scheme in units of 6 bits.
  • a sequence of bit groups 0 to 44 of the LDPC code of 16200 bits is interleaved into a sequence of bit groups
  • the LDPC code includes an information bit and a parity bit.
  • the parity check matrix includes an information matrix portion corresponding to the information bit and a parity matrix portion corresponding to the parity bit.
  • the information matrix portion is represented by a parity check matrix initial value table.
  • the parity check matrix initial value table is a table in which a position of a 1 element of the information matrix portion is indicated for every 360 columns, and includes
  • a second data processing device/method is a data processing device/method including: a group-wise deinterleaving unit/step configured to restore a sequence of an LDPC code that has undergone group-wise interleave and has been obtained from data transmitted from a transmitting device to an original sequence, the transmitting device including an encoding unit configured to perform LDPC encoding based on a parity check matrix of the LDPC code in which a code length N is 16200 bits and an encoding rate r is 6/15, a group-wise interleaving unit configured to perform the group-wise interleave of interleaving the LDPC code in units of bit groups of 360 bits, and a mapping unit configured to map the LDPC code to any of 64 signal points decided in a modulation scheme in units of 6 bits.
  • bit group i when an (i+1)-th bit group from a head of the LDPC code is indicated by a bit group i, a sequence of bit groups 0 to 44 of the LDPC code of 16200 bits is interleaved into a sequence of bit groups
  • the LDPC code includes an information bit and a parity bit.
  • the parity check matrix includes an information matrix portion corresponding to the information bit and a parity matrix portion corresponding to the parity bit.
  • the information matrix portion is represented by a parity check matrix initial value table.
  • the parity check matrix initial value table is a table in which a position of a 1 element of the information matrix portion is indicated for every 360 columns, and includes
  • a sequence of an LDPC code that has undergone group-wise interleave and has been obtained from data transmitted from a transmitting device is restored to an original sequence
  • the transmitting device including an encoding unit configured to perform LDPC encoding based on a parity check matrix of the LDPC code in which a code length N is 16200 bits and an encoding rate r is 6/15, a group-wise interleaving unit configured to perform the group-wise interleave of interleaving the LDPC code in units of bit groups of 360 bits, and a mapping unit configured to map the LDPC code to any of 64 signal points decided in a modulation scheme in units of 6 bits.
  • bit group i when an (i+1)-th bit group from a head of the LDPC code is indicated by a bit group i, a sequence of bit groups 0 to 44 of the LDPC code of 16200 bits is interleaved into a sequence of bit groups
  • the LDPC code includes an information bit and a parity bit.
  • the parity check matrix includes an information matrix portion corresponding to the information bit and a parity matrix portion corresponding to the parity bit.
  • the information matrix portion is represented by a parity check matrix initial value table.
  • the parity check matrix initial value table is a table in which a position of a 1 element of the information matrix portion is indicated for every 360 columns, and includes
  • a third data processing device/method is a data processing device/method including: an encoding unit/step configured to perform LDPC encoding based on a parity check matrix of an LDPC code in which a code length N is 16200 bits and an encoding rate r is 8/15; a group-wise interleaving unit/step configured to perform group-wise interleave of interleaving the LDPC code in units of bit groups of 360 bits; and a mapping unit/step configured to map the LDPC code to any of 64 signal points decided in a modulation scheme in units of 6 bits.
  • bit group i when an (i+1)-th bit group from a head of the LDPC code is indicated by a bit group i, a sequence of bit groups 0 to 44 of the LDPC code of 16200 bits is interleaved into a sequence of bit groups
  • the LDPC code includes an information bit and a parity bit.
  • the parity check matrix includes an information matrix portion corresponding to the information bit and a parity matrix portion corresponding to the parity bit.
  • the information matrix portion is represented by a parity check matrix initial value table.
  • the parity check matrix initial value table is a table in which a position of a 1 element of the information matrix portion is indicated for every 360 columns, and includes
  • LDPC encoding is performed based on a parity check matrix of an LDPC code in which a code length N is 16200 bits and an encoding rate r is 8/15.
  • Group-wise interleave of interleaving the LDPC code in units of bit groups of 360 bits is performed.
  • the LDPC code is mapped to any of 64 signal points decided in a modulation scheme in units of 6 bits.
  • a sequence of bit groups 0 to 44 of the LDPC code of 16200 bits is interleaved into a sequence of bit groups
  • the LDPC code includes an information bit and a parity bit.
  • the parity check matrix includes an information matrix portion corresponding to the information bit and a parity matrix portion corresponding to the parity bit.
  • the information matrix portion is represented by a parity check matrix initial value table.
  • the parity check matrix initial value table is a table in which a position of a 1 element of the information matrix portion is indicated for every 360 columns, and includes
  • a fourth data processing device/method is a data processing device/method including: a group-wise deinterleaving unit/step configured to restore a sequence of an LDPC code that has undergone group-wise interleave and has been obtained from data transmitted from a transmitting device to an original sequence, the transmitting device including an encoding unit configured to perform LDPC encoding based on a parity check matrix of the LDPC code in which a code length N is 16200 bits and an encoding rate r is 8/15, a group-wise interleaving unit configured to perform the group-wise interleave of interleaving the LDPC code in units of bit groups of 360 bits, and a mapping unit configured to map the LDPC code to any of 64 signal points decided in a modulation scheme in units of 6 bits.
  • bit group i when an (i+1)-th bit group from a head of the LDPC code is indicated by a bit group i, a sequence of bit groups 0 to 44 of the LDPC code of 16200 bits is interleaved into a sequence of bit groups
  • the LDPC code includes an information bit and a parity bit.
  • the parity check matrix includes an information matrix portion corresponding to the information bit and a parity matrix portion corresponding to the parity bit.
  • the information matrix portion is represented by a parity check matrix initial value table.
  • the parity check matrix initial value table is a table in which a position of a 1 element of the information matrix portion is indicated for every 360 columns, and includes
  • a sequence of an LDPC code that has undergone group-wise interleave and has been obtained from data transmitted from a transmitting device is restored to an original sequence
  • the transmitting device including an encoding unit configured to perform LDPC encoding based on a parity check matrix of the LDPC code in which a code length N is 16200 bits and an encoding rate r is 8/15, a group-wise interleaving unit configured to perform the group-wise interleave of interleaving the LDPC code in units of bit groups of 360 bits, and a mapping unit configured to map the LDPC code to any of 64 signal points decided in a modulation scheme in units of 6 bits.
  • bit group i when an (i+1)-th bit group from a head of the LDPC code is indicated by a bit group i, a sequence of bit groups 0 to 44 of the LDPC code of 16200 bits is interleaved into a sequence of bit groups
  • the LDPC code includes an information bit and a parity bit.
  • the parity check matrix includes an information matrix portion corresponding to the information bit and a parity matrix portion corresponding to the parity bit.
  • the information matrix portion is represented by a parity check matrix initial value table.
  • the parity check matrix initial value table is a table in which a position of a 1 element of the information matrix portion is indicated for every 360 columns, and includes
  • a fifth data processing device/method is a data processing device/method including: an encoding unit/step configured to perform LDPC encoding based on a parity check matrix of an LDPC code in which a code length N is 16200 bits and an encoding rate r is 10/15; a group-wise interleaving unit/step configured to perform group-wise interleave of interleaving the LDPC code in units of bit groups of 360 bits; and a mapping unit/step configured to map the LDPC code to any of 64 signal points decided in a modulation scheme in units of 6 bits.
  • bit group i when an (i+1)-th bit group from a head of the LDPC code is indicated by a bit group i, a sequence of bit groups 0 to 44 of the LDPC code of 16200 bits is interleaved into a sequence of bit groups
  • the LDPC code includes an information bit and a parity bit.
  • the parity check matrix includes an information matrix portion corresponding to the information bit and a parity matrix portion corresponding to the parity bit.
  • the information matrix portion is represented by a parity check matrix initial value table.
  • the parity check matrix initial value table is a table in which a position of a 1 element of the information matrix portion is indicated for every 360 columns, and includes
  • LDPC encoding is performed based on a parity check matrix of an LDPC code in which a code length N is 16200 bits and an encoding rate r is 10/15.
  • Group-wise interleave of interleaving the LDPC code in units of bit groups of 360 bits is performed.
  • the LDPC code is mapped to any of 64 signal points decided in a modulation scheme in units of 6 bits.
  • a sequence of bit groups 0 to 44 of the LDPC code of 16200 bits is interleaved into a sequence of bit groups
  • the LDPC code includes an information bit and a parity bit.
  • the parity check matrix includes an information matrix portion corresponding to the information bit and a parity matrix portion corresponding to the parity bit.
  • the information matrix portion is represented by a parity check matrix initial value table.
  • the parity check matrix initial value table is a table in which a position of a 1 element of the information matrix portion is indicated for every 360 columns, and includes
  • a sixth data processing device/method is a data processing device/method including: a group-wise deinterleaving unit/step configured to restore a sequence of an LDPC code that has undergone group-wise interleave and has been obtained from data transmitted from a transmitting device to an original sequence, the transmitting device including an encoding unit configured to perform LDPC encoding based on a parity check matrix of the LDPC code in which a code length N is 16200 bits and an encoding rate r is 10/15, a group-wise interleaving unit configured to perform the group-wise interleave of interleaving the LDPC code in units of bit groups of 360 bits, and a mapping unit configured to map the LDPC code to any of 64 signal points decided in a modulation scheme in units of 6 bits.
  • bit group i when an (i+1)-th bit group from a head of the LDPC code is indicated by a bit group i, a sequence of bit groups 0 to 44 of the LDPC code of 16200 bits is interleaved into a sequence of bit groups
  • the LDPC code includes an information bit and a parity bit.
  • the parity check matrix includes an information matrix portion corresponding to the information bit and a parity matrix portion corresponding to the parity bit.
  • the information matrix portion is represented by a parity check matrix initial value table.
  • the parity check matrix initial value table is a table in which a position of a 1 element of the information matrix portion is indicated for every 360 columns, and includes
  • a sequence of an LDPC code that has undergone group-wise interleave and has been obtained from data transmitted from a transmitting device is restored to an original sequence
  • the transmitting device including an encoding unit configured to perform LDPC encoding based on a parity check matrix of the LDPC code in which a code length N is 16200 bits and an encoding rate r is 10/15, a group-wise interleaving unit configured to perform the group-wise interleave of interleaving the LDPC code in units of bit groups of 360 bits, and a mapping unit configured to map the LDPC code to any of 64 signal points decided in a modulation scheme in units of 6 bits.
  • bit group i when an (i+1)-th bit group from a head of the LDPC code is indicated by a bit group i, a sequence of bit groups 0 to 44 of the LDPC code of 16200 bits is interleaved into a sequence of bit groups
  • the LDPC code includes an information bit and a parity bit.
  • the parity check matrix includes an information matrix portion corresponding to the information bit and a parity matrix portion corresponding to the parity bit.
  • the information matrix portion is represented by a parity check matrix initial value table.
  • the parity check matrix initial value table is a table in which a position of a 1 element of the information matrix portion is indicated for every 360 columns, and includes
  • the data processing device may be an independent device and may be an internal block constituting one device.
  • FIG. 1 is an illustration of a parity check matrix H of an LDPC code.
  • FIG. 2 is a flowchart illustrating a decoding sequence of an LDPC code.
  • FIG. 3 is an illustration of an example of a parity check matrix of an LDPC code.
  • FIG. 4 is an illustration of an example of a Tanner graph of a parity check matrix.
  • FIG. 5 is an illustration of an example of a variable node.
  • FIG. 6 is an illustration of an example of a check node.
  • FIG. 7 is an illustration of a configuration example of an embodiment of a transmission system to which the present invention is applied.
  • FIG. 8 is a block diagram illustrating a configuration example of a transmitting device 11 .
  • FIG. 9 is a block diagram illustrating a configuration example of a bit interleaver 116 .
  • FIG. 10 is an illustration of an example of a parity check matrix.
  • FIG. 11 is an illustration of an example of a parity matrix.
  • FIG. 12 is an illustration of the parity check matrix of the LDPC code that is defined in the standard of the DVB-T.2.
  • FIG. 13 is an illustration of the parity check matrix of the LDPC code that is defined in the standard of the DVB-T.2.
  • FIG. 14 is an illustration of an example of a Tanner graph for decoding of an LDPC code.
  • FIG. 15 is an illustration of an example of a parity matrix H T becoming a staircase structure and a Tanner graph corresponding to the parity matrix H T .
  • FIG. 16 is an illustration of an example of a parity matrix H T of a parity check matrix H corresponding to an LDPC code after parity interleave.
  • FIG. 17 is a flowchart illustrating an example of a process performed by a bit interleaver 116 and a mapper 117 .
  • FIG. 18 is a block diagram illustrating a configuration example of an LDPC encoder 115 .
  • FIG. 19 is a flowchart illustrating processing of an example of an LDPC encoder 115 .
  • FIG. 20 is an illustration of an example of a parity check matrix initial value table in which an encoding rate is 1/4 and a code length is 16200.
  • FIG. 21 is an illustration of a method of calculating a parity check matrix H from a parity check matrix initial value table.
  • FIG. 22 is an illustration of a structure of a parity check matrix.
  • FIG. 23 is an illustration of an example of the parity check matrix initial value table.
  • FIG. 24 is an illustration of an A matrix generated from a parity check matrix initial value table.
  • FIG. 25 is an illustration of parity interleave of a B matrix.
  • FIG. 26 is an illustration of a C matrix generated from a parity check matrix initial value table.
  • FIG. 27 is an illustration of parity interleave of a D matrix.
  • FIG. 28 is an illustration of a parity check matrix obtained by performing a column permutation serving as parity deinterleave for restoring parity interleave to an original state on a parity check matrix.
  • FIG. 29 is an illustration of a transformed parity check matrix obtained by performing a row permutation on a parity check matrix.
  • FIG. 30 is an illustration of an example of the parity check matrix initial value table.
  • FIG. 31 is an illustration of an example of the parity check matrix initial value table.
  • FIG. 32 is an illustration of an example of the parity check matrix initial value table.
  • FIG. 33 is an illustration of an example of the parity check matrix initial value table.
  • FIG. 34 is an illustration of an example of the parity check matrix initial value table.
  • FIG. 35 is an illustration of an example of the parity check matrix initial value table.
  • FIG. 36 is an illustration of an example of the parity check matrix initial value table.
  • FIG. 37 is an illustration of an example of the parity check matrix initial value table.
  • FIG. 38 is an illustration of an example of the parity check matrix initial value table.
  • FIG. 39 is an illustration of an example of the parity check matrix initial value table.
  • FIG. 40 is an illustration of an example of the parity check matrix initial value table.
  • FIG. 41 is an illustration of an example of the parity check matrix initial value table.
  • FIG. 42 is an illustration of an example of the parity check matrix initial value table.
  • FIG. 43 is an illustration of an example of the parity check matrix initial value table.
  • FIG. 44 is an illustration of an example of the parity check matrix initial value table.
  • FIG. 45 is an illustration of an example of the parity check matrix initial value table.
  • FIG. 46 is an illustration of an example of the parity check matrix initial value table.
  • FIG. 47 is an illustration of an example of the parity check matrix initial value table.
  • FIG. 48 is an illustration of an example of the parity check matrix initial value table.
  • FIG. 49 is an illustration of an example of the parity check matrix initial value table.
  • FIG. 50 is an illustration of an example of the parity check matrix initial value table.
  • FIG. 51 is an illustration of an example of the parity check matrix initial value table.
  • FIG. 52 is an illustration of an example of the parity check matrix initial value table.
  • FIG. 53 is an illustration of an example of the parity check matrix initial value table.
  • FIG. 54 is an illustration of an example of the parity check matrix initial value table.
  • FIG. 55 is an illustration of an example of the parity check matrix initial value table.
  • FIG. 56 is an illustration of an example of the parity check matrix initial value table.
  • FIG. 57 is an illustration of an example of the parity check matrix initial value table.
  • FIG. 58 is an illustration of an example of the parity check matrix initial value table.
  • FIG. 59 is an illustration of an example of the parity check matrix initial value table.
  • FIG. 60 is an illustration of an example of the parity check matrix initial value table.
  • FIG. 61 is an illustration of an example of the parity check matrix initial value table.
  • FIG. 62 is an illustration of an example of the parity check matrix initial value table.
  • FIG. 63 is an illustration of an example of the parity check matrix initial value table.
  • FIG. 64 is an illustration of an example of the parity check matrix initial value table.
  • FIG. 65 is an illustration of an example of the parity check matrix initial value table.
  • FIG. 66 is an illustration of an example of the parity check matrix initial value table.
  • FIG. 67 is an illustration of an example of the parity check matrix initial value table.
  • FIG. 68 is an illustration of an example of the parity check matrix initial value table.
  • FIG. 69 is an illustration of an example of the parity check matrix initial value table.
  • FIG. 70 is an illustration of an example of the parity check matrix initial value table.
  • FIG. 71 is an illustration of an example of the parity check matrix initial value table.
  • FIG. 72 is an illustration of an example of the parity check matrix initial value table.
  • FIG. 73 is an illustration of an example of a tanner graph of an ensemble of a degree sequence in which a column weight is 3, and a row weight is 6.
  • FIG. 74 is an illustration of an example of a tanner graph of an ensemble of a multi-edge type.
  • FIG. 75 is an illustration of a parity check matrix.
  • FIG. 76 is an illustration of a parity check matrix.
  • FIG. 77 is an illustration of a parity check matrix.
  • FIG. 78 is an illustration of a parity check matrix.
  • FIG. 79 is an illustration of a parity check matrix.
  • FIG. 80 is an illustration of a parity check matrix.
  • FIG. 81 is an illustration of a parity check matrix.
  • FIG. 82 is an illustration of a parity check matrix.
  • FIG. 83 is an illustration of an example of a constellation when a modulation scheme is 16QAM.
  • FIG. 84 is an illustration of an example of a constellation when a modulation scheme is 64QAM.
  • FIG. 85 is an illustration of an example of a constellation when a modulation scheme is 256QAM.
  • FIG. 86 is an illustration of an example of a constellation when a modulation scheme is 1024QAM.
  • FIG. 87 is an illustration of an example of a constellation when a modulation scheme is 4096QAM.
  • FIG. 88 is an illustration of an example of a constellation when a modulation scheme is 4096QAM.
  • FIG. 89 is an illustration of an example of coordinates of a signal point of a UC when a modulation scheme is QPSK.
  • FIG. 90 is an illustration of an example of coordinates of a signal point of a 2D NUC when a modulation scheme is 16QAM.
  • FIG. 91 is an illustration of an example of coordinates of a signal point of a 2D NUC when a modulation scheme is 64QAM.
  • FIG. 92 is an illustration of an example of coordinates of a signal point of a 2D NUC when a modulation scheme is 256QAM.
  • FIG. 93 is an illustration of an example of coordinates of a signal point of a 2D NUC when a modulation scheme is 256QAM.
  • FIG. 94 is an illustration of an example of coordinates of a signal point of a 1D NUC when a modulation scheme is 1024QAM.
  • FIG. 95 is an illustration of relations of a symbol y of 1024QAM with a real part Re (z q ) and an imaginary part Im (z q ) of a complex number serving as coordinates of a signal point z q of a 1D NUC corresponding to the symbol y.
  • FIG. 96 is an illustration of an example of coordinates of a signal point of a 1D NUC when a modulation scheme is 4096QAM.
  • FIG. 97 is an illustration of relations of a symbol y of 4096QAM with a real part Re (z q ) and an imaginary part Im (z q ) of a complex number serving as coordinates of a signal point z q of a 1D NUC corresponding to the symbol y.
  • FIG. 98 is an illustration of another example of a constellation when a modulation scheme is 16QAM
  • FIG. 99 is an illustration of another example of a constellation when a modulation scheme is 64QAM.
  • FIG. 100 is an illustration of another example of a constellation when a modulation scheme is 256QAM.
  • FIG. 101 is an illustration of another example of coordinates of a signal point of a 2D NUC when a modulation scheme is 16QAM.
  • FIG. 102 is an illustration of another example of coordinates of a signal point of a 2D NUC when a modulation scheme is 64QAM.
  • FIG. 103 is an illustration of another example of coordinates of a signal point of a 2D NUC when a modulation scheme is 256QAM.
  • FIG. 104 is an illustration of another example of coordinates of a signal point of a 2D NUC when a modulation scheme is 256QAM.
  • FIG. 105 is a block diagram illustrating a configuration example of a block interleaver 25 .
  • FIG. 106 is an illustration of an example of the number C of columns of parts 1 and 2 and part column lengths R 1 and R 2 for a combination of a code length N and a modulation scheme.
  • FIG. 107 is an illustration of block interleave performed by a block interleaver 25 .
  • FIG. 108 is an illustration of group-wise interleave performed by a group-wise interleaver 24 .
  • FIG. 109 is an illustration of a 1st example of a GW pattern for an LDPC code in which a code length N is 64k bits.
  • FIG. 110 is an illustration of a 2nd example of a GW pattern for an LDPC code in which a code length N is 64k bits.
  • FIG. 111 is an illustration of a 3rd example of a GW pattern for an LDPC code in which a code length N is 64k bits.
  • FIG. 112 is an illustration of a 4th example of a GW pattern for an LDPC code in which a code length N is 64k bits.
  • FIG. 113 is an illustration of a 5th example of a GW pattern for an LDPC code in which a code length N is 64k bits.
  • FIG. 114 is an illustration of a 6th example of a GW pattern for an LDPC code in which a code length N is 64k bits.
  • FIG. 115 is an illustration of a 7th example of a GW pattern for an LDPC code in which a code length N is 64k bits.
  • FIG. 116 is an illustration of an 8th example of a GW pattern for an LDPC code in which a code length N is 64k bits.
  • FIG. 117 is an illustration of a 9th example of a GW pattern for an LDPC code in which a code length N is 64k bits.
  • FIG. 118 is an illustration of a 10th example of a GW pattern for an LDPC code in which a code length N is 64k bits.
  • FIG. 119 is an illustration of an 11th example of a GW pattern for an LDPC code in which a code length N is 64k bits.
  • FIG. 120 is an illustration of a 12th example of a GW pattern for an LDPC code in which a code length N is 64k bits.
  • FIG. 121 is an illustration of a 13th example of a GW pattern for an LDPC code in which a code length N is 64k bits.
  • FIG. 122 is an illustration of a 14th example of a GW pattern for an LDPC code in which a code length N is 64k bits.
  • FIG. 123 is an illustration of a 15th example of a GW pattern for an LDPC code in which a code length N is 64k bits.
  • FIG. 124 is an illustration of a 16th example of a GW pattern for an LDPC code in which a code length N is 64k bits.
  • FIG. 125 is an illustration of a 17th example of a GW pattern for an LDPC code in which a code length N is 64k bits.
  • FIG. 126 is an illustration of an 18th example of a GW pattern for an LDPC code in which a code length N is 64k bits.
  • FIG. 127 is an illustration of a 19th example of a GW pattern for an LDPC code in which a code length N is 64k bits.
  • FIG. 128 is an illustration of a 20th example of a GW pattern for an LDPC code in which a code length N is 64k bits.
  • FIG. 129 is an illustration of a 21st example of a GW pattern for an LDPC code in which a code length N is 64k bits.
  • FIG. 130 is an illustration of a 22nd example of a GW pattern for an LDPC code in which a code length N is 64k bits.
  • FIG. 131 is an illustration of a 23rd example of a GW pattern for an LDPC code in which a code length N is 64k bits.
  • FIG. 132 is an illustration of a 24th example of a GW pattern for an LDPC code in which a code length N is 64k bits.
  • FIG. 133 is an illustration of a 25th example of a GW pattern for an LDPC code in which a code length N is 64k bits.
  • FIG. 134 is an illustration of a 26th example of a GW pattern for an LDPC code in which a code length N is 64k bits.
  • FIG. 135 is an illustration of a 27th example of a GW pattern for an LDPC code in which a code length N is 64k bits.
  • FIG. 136 is an illustration of a 28th example of a GW pattern for an LDPC code in which a code length N is 64k bits.
  • FIG. 137 is an illustration of a 29th example of a GW pattern for an LDPC code in which a code length N is 64k bits.
  • FIG. 138 is an illustration of a 30th example of a GW pattern for an LDPC code in which a code length N is 64k bits.
  • FIG. 139 is an illustration of a 31st example of a GW pattern for an LDPC code in which a code length N is 64k bits.
  • FIG. 140 is an illustration of a 32nd example of a GW pattern for an LDPC code in which a code length N is 64k bits.
  • FIG. 141 is an illustration of a 33rd example of a GW pattern for an LDPC code in which a code length N is 64k bits.
  • FIG. 142 is an illustration of a 1st example of a GW pattern for an LDPC code in which a code length N is 16k bits.
  • FIG. 143 is an illustration of a 2nd example of a GW pattern for an LDPC code in which a code length N is 16k bits.
  • FIG. 144 is an illustration of a 3rd example of a GW pattern for an LDPC code in which a code length N is 16k bits.
  • FIG. 145 is an illustration of a 4th example of a GW pattern for an LDPC code in which a code length N is 16k bits.
  • FIG. 146 is an illustration of a 5th example of a GW pattern for an LDPC code in which a code length N is 16k bits.
  • FIG. 147 is an illustration of a 6th example of a GW pattern for an LDPC code in which a code length N is 16k bits.
  • FIG. 148 is an illustration of a 7th example of a GW pattern for an LDPC code in which a code length N is 16k bits.
  • FIG. 149 is an illustration of an 8th example of a GW pattern for an LDPC code in which a code length N is 16k bits.
  • FIG. 150 is an illustration of a 9th example of a GW pattern for an LDPC code in which a code length N is 16k bits.
  • FIG. 151 is an illustration of a 10th example of a GW pattern for an LDPC code in which a code length N is 16k bits.
  • FIG. 152 is an illustration of an 11th example of a GW pattern for an LDPC code in which a code length N is 16k bits.
  • FIG. 153 is an illustration of a 12th example of a GW pattern for an LDPC code in which a code length N is 16k bits.
  • FIG. 154 is an illustration of a 13th example of a GW pattern for an LDPC code in which a code length N is 16k bits.
  • FIG. 155 is an illustration of a 14th example of a GW pattern for an LDPC code in which a code length N is 16k bits.
  • FIG. 156 is an illustration of a 15th example of a GW pattern for an LDPC code in which a code length N is 16k bits.
  • FIG. 157 is an illustration of a 16th example of a GW pattern for an LDPC code in which a code length N is 16k bits.
  • FIG. 158 is an illustration of a simulation result of a simulation of measuring an error rate.
  • FIG. 159 is an illustration of a simulation result of a simulation of measuring an error rate.
  • FIG. 160 is an illustration of a simulation result of a simulation of measuring an error rate.
  • FIG. 161 is an illustration of a simulation result of a simulation of measuring an error rate.
  • FIG. 162 is an illustration of a simulation result of a simulation of measuring an error rate.
  • FIG. 163 is an illustration of a simulation result of a simulation of measuring an error rate.
  • FIG. 164 is an illustration of a simulation result of a simulation of measuring an error rate.
  • FIG. 165 is an illustration of a simulation result of a simulation of measuring an error rate.
  • FIG. 166 is an illustration of a simulation result of a simulation of measuring an error rate.
  • FIG. 167 is an illustration of a simulation result of a simulation of measuring an error rate.
  • FIG. 168 is an illustration of a simulation result of a simulation of measuring an error rate.
  • FIG. 169 is an illustration of a simulation result of a simulation of measuring an error rate.
  • FIG. 170 is an illustration of a simulation result of a simulation of measuring an error rate.
  • FIG. 171 is an illustration of a simulation result of a simulation of measuring an error rate.
  • FIG. 172 is an illustration of a simulation result of a simulation of measuring an error rate.
  • FIG. 173 is an illustration of a simulation result of a simulation of measuring an error rate.
  • FIG. 174 is an illustration of a simulation result of a simulation of measuring an error rate.
  • FIG. 175 is an illustration of a simulation result of a simulation of measuring an error rate.
  • FIG. 176 is an illustration of a simulation result of a simulation of measuring an error rate.
  • FIG. 177 is an illustration of a simulation result of a simulation of measuring an error rate.
  • FIG. 178 is an illustration of a simulation result of a simulation of measuring an error rate.
  • FIG. 179 is an illustration of a simulation result of a simulation of measuring an error rate.
  • FIG. 180 is an illustration of a simulation result of a simulation of measuring an error rate.
  • FIG. 181 is an illustration of a simulation result of a simulation of measuring an error rate.
  • FIG. 182 is an illustration of a simulation result of a simulation of measuring an error rate.
  • FIG. 183 is an illustration of a simulation result of a simulation of measuring an error rate.
  • FIG. 184 is an illustration of a simulation result of a simulation of measuring an error rate.
  • FIG. 185 is an illustration of a simulation result of a simulation of measuring an error rate.
  • FIG. 186 is an illustration of a simulation result of a simulation of measuring an error rate.
  • FIG. 187 is an illustration of a simulation result of a simulation of measuring an error rate.
  • FIG. 188 is an illustration of a simulation result of a simulation of measuring an error rate.
  • FIG. 189 is an illustration of a simulation result of a simulation of measuring an error rate.
  • FIG. 190 is an illustration of a simulation result of a simulation of measuring an error rate.
  • FIG. 191 is an illustration of a simulation result of a simulation of measuring an error rate.
  • FIG. 192 is an illustration of a simulation result of a simulation of measuring an error rate.
  • FIG. 193 is an illustration of a simulation result of a simulation of measuring an error rate.
  • FIG. 194 is an illustration of a simulation result of a simulation of measuring an error rate.
  • FIG. 195 is an illustration of a simulation result of a simulation of measuring an error rate.
  • FIG. 196 is an illustration of a simulation result of a simulation of measuring an error rate.
  • FIG. 197 is an illustration of a simulation result of a simulation of measuring an error rate.
  • FIG. 198 is an illustration of a simulation result of a simulation of measuring an error rate.
  • FIG. 199 is an illustration of a simulation result of a simulation of measuring an error rate.
  • FIG. 200 is an illustration of a simulation result of a simulation of measuring an error rate.
  • FIG. 201 is an illustration of a simulation result of a simulation of measuring an error rate.
  • FIG. 202 is an illustration of a simulation result of a simulation of measuring an error rate.
  • FIG. 203 is an illustration of a simulation result of a simulation of measuring an error rate.
  • FIG. 204 is an illustration of a simulation result of a simulation of measuring an error rate.
  • FIG. 205 is an illustration of a simulation result of a simulation of measuring an error rate.
  • FIG. 206 is an illustration of a simulation result of a simulation of measuring an error rate.
  • FIG. 207 is a block diagram illustrating a configuration example of a receiving device 12 .
  • FIG. 208 is a block diagram illustrating a configuration example of a bit deinterleaver 165 .
  • FIG. 209 is a flowchart illustrating an example of a process performed by a demapper 164 , a bit deinterleaver 165 , and an LDPC decoder 166 .
  • FIG. 210 is an illustration of an example of a parity check matrix of an LDPC code.
  • FIG. 211 is an illustration of an example of a matrix (a transformed parity check matrix) obtained by performing a row permutation and a column permutation on a parity check matrix.
  • FIG. 212 is an illustration of an example of a transformed parity check matrix divided into 5 ⁇ 5 units.
  • FIG. 213 is a block diagram illustrating a configuration example of a decoding device that collectively performs P node operations.
  • FIG. 214 is a block diagram illustrating a configuration example of an LDPC decoder 166 .
  • FIG. 215 is a block diagram illustrating a configuration example of a block deinterleaver 54 .
  • FIG. 216 is a block diagram illustrating another configuration example of a bit deinterleaver 165 .
  • FIG. 217 is a block diagram illustrating a first configuration example of a reception system that can be applied to the receiving device 12 .
  • FIG. 218 is a block diagram illustrating a second configuration example of a reception system that can be applied to the receiving device 12 .
  • FIG. 219 is a block diagram illustrating a third configuration example of a reception system that can be applied to the receiving device 12 .
  • FIG. 220 is a block diagram illustrating a configuration example of an embodiment of a computer to which the present technology is applied.
  • the LDPC code is a linear code and it is not necessary for the LDPC code to be a binary code. However, in this case, it is assumed that the LDPC code is the binary code.
  • a maximum characteristic of the LDPC code is that a parity check matrix defining the LDPC code is sparse.
  • the sparse matrix is a matrix in which the number of “1” of elements of the matrix is very small (a matrix in which most elements are 0).
  • FIG. 1 is an illustration of an example of a parity check matrix H of the LDPC code.
  • a weight of each column (the column weight) (the number of “1”) becomes “3” and a weight of each row (the row weight) becomes “6”.
  • a generation matrix G is generated on the basis of the parity check matrix H and the generation matrix G is multiplied by binary information bits, so that a code word (LDPC code) is generated.
  • LDPC code code word
  • the code word (LDPC code) that is generated by the encoding device is received at a reception side through a predetermined communication path.
  • the LDPC code can be decoded by an algorithm called probabilistic decoding suggested by Gallager, that is, a message passing algorithm using belief propagation on a so-called Tanner graph, including a variable node (also referred to as a message node) and a check node.
  • a variable node also referred to as a message node
  • a check node the variable node and the check node are appropriately referred to as nodes simply.
  • FIG. 2 is a flowchart illustrating a decoding sequence of an LDPC code.
  • a real value (a reception LLR) that is obtained by representing the likelihood of “0” of a value of an i-th code bit of the LDPC code (one code word) received by the reception side by a log likelihood ratio is appropriately referred to as a reception value u 0i .
  • a message output from the check node is referred to as u j and a message output from the variable node is referred to as v i .
  • step S 11 the LDPC code is received, the message (check node message) u j is initialized to “0”, and a variable k taking an integer as a counter of repetition processing is initialized to “0”, and the processing proceeds to step S 12 .
  • step S 12 the message (variable node message) v i is calculated by performing an operation (variable node operation) represented by an expression (1), on the basis of the reception value u 0i obtained by receiving the LDPC code, and the message u j is calculated by performing an operation (check node operation) represented by an expression (2), on the basis of the message v i .
  • d v and d c in an expression (1) and expression (2) are respectively parameters which can be arbitrarily selected and illustrates the number of “1” in the longitudinal direction (column) and transverse direction (row) of the parity check matrix H.
  • variable node operation of the expression (1) and the check node operation of the expression (2) because a message input from an edge (line coupling the variable node and the check node) for outputting the message is not an operation target, an operation range becomes 1 to d v ⁇ 1 or 1 to d c ⁇ 1.
  • the check node operation of the expression (2) is performed actually by previously making a table of a function R (v 1 , v 2 ) represented by an expression (3) defined by one output with respect to two inputs v i and v 2 and using the table consecutively (recursively), as represented by an expression (4).
  • step S 12 the variable k is incremented by “1” and the processing proceeds to step S 13 .
  • step S 13 it is determined whether the variable k is more than the predetermined repetition decoding number of times C. When it is determined in step S 13 that the variable k is not more than C, the processing returns to step S 12 and the same processing is repeated hereinafter.
  • step S 13 When it is determined in step S 13 that the variable k is more than C, the processing proceeds to step S 14 , the message v i that corresponds to a decoding result to be finally output is calculated by performing an operation represented by an expression (5) and is output, and the decoding processing of the LDPC code ends.
  • the operation of the expression (5) is performed using messages u j from all edges connected to the variable node, different from the variable node operation of the expression (1).
  • FIG. 3 illustrates an example of the parity check matrix H of the (3, 6) LDPC code (an encoding rate of 1/2 and a code length of 12).
  • a weight of a column is set to 3 and a weight of a row is set to 6, similar to FIG. 1 .
  • FIG. 4 illustrates a Tanner graph of the parity check matrix H of FIG. 3 .
  • the check node and the variable node correspond to the row and the column of the parity check matrix H.
  • a line that couples the check node and the variable node is the edge and corresponds to “1” of elements of the parity check matrix.
  • the edge shows that a code bit corresponding to the variable node has a restriction condition corresponding to the check node.
  • variable node operation and the check node operation are repetitively performed.
  • FIG. 5 illustrates the variable node operation that is performed by the variable node.
  • the message v i that corresponds to the edge for calculation is calculated by the variable node operation of the expression (1) using messages u 1 and u 2 from the remaining edges connected to the variable node and the reception value u 0i .
  • the messages that correspond to the other edges are also calculated by the same method.
  • FIG. 6 illustrates the check node operation that is performed by the check node.
  • sign(x) is 1 in the case of x>0 and is ⁇ 1 in the case of x ⁇ 0
  • the check node operation of the expression (2) is performed according to the expression (7).
  • the message u j that corresponds to the edge for calculation is calculated by the check node operation of the expression (7) using messages v 1 , v 2 , v 3 , v 4 , and v 5 from the remaining edges connected to the check node.
  • the messages that correspond to the other edges are also calculated by the same method.
  • the functions ⁇ (x) and ⁇ ⁇ 1 (x) are mounted to hardware, the functions ⁇ (x) and ⁇ ⁇ 1 (x) may be mounted using an LUT (Look Up Table). However, both the functions ⁇ (x) and ⁇ ⁇ 1 (x) become the same LUT.
  • FIG. 7 illustrates a configuration example of an embodiment of a transmission system (a system means a logical gathering of a plurality of devices and a device of each configuration may be arranged or may not be arranged in the same casing) to which the present invention is applied.
  • the transmission system includes a transmitting device 11 and a receiving device 12 .
  • the transmitting device 11 transmits (broadcasts) (transfers) a program of television broadcasting, and so on. That is, for example, the transmitting device 11 encodes target data that is a transmission target such as image data and audio data as a program into LDPC codes, and, for example, transmits them through a communication path 13 such as a satellite circuit, a ground wave and a cable (wire circuit).
  • a communication path 13 such as a satellite circuit, a ground wave and a cable (wire circuit).
  • the receiving device 12 receives the LDPC code transmitted from the transmitting device 11 through the communication path 13 , decodes the LDPC code to obtain the target data, and outputs the target data.
  • the LDPC code used by the transmission system of FIG. 7 shows the very high capability in an AWGN (Additive White Gaussian Noise) communication path.
  • AWGN Additional White Gaussian Noise
  • burst error or erasure may be generated.
  • the communication path 13 is the ground wave
  • the burst error may be generated due to a situation of a wiring line from a receiving unit (not illustrated in the drawings) of the side of the receiving device 12 such as an antenna receiving a signal from the transmitting device 11 to the receiving device 12 or instability of a power supply of the receiving device 12 .
  • variable node operation of the expression (1) with the addition of (the reception value u0i of) the code bit of the LDPC code is performed. For this reason, if error is generated in the code bits used for the variable node operation, precision of the calculated message is deteriorated.
  • the check node operation of the expression (7) is performed using the message calculated by the variable node connected to the check node. For this reason, if the number of check nodes in which error (including erasure) is generated simultaneously in (the code bits of the LDPC codes corresponding to) the plurality of connected variable nodes increases, decoding performance is deteriorated.
  • the check node if the two or more variable nodes of the variable nodes connected to the check node become simultaneously erasure, the check node returns a message in which the probability of a value being 0 and the probability of a value being 1 are equal to each other, to all the variable nodes. In this case, the check node that returns the message of the equal probabilities does not contribute to one decoding processing (one set of the variable node operation and the check node operation).
  • tolerance against the burst error or the erasure can be improved while performance in the AWGN communication path (AWGN channel) is maintained.
  • FIG. 8 is a block diagram illustrating a configuration example of the transmitting device 11 of FIG. 7 .
  • one or more input streams corresponding to target data are supplied to a mode adaptation/multiplexer 111 .
  • the mode adaptation/multiplexer 111 performs mode selection and processes such as multiplexing of one or more input streams supplied thereto, as needed, and supplies data obtained as a result to a padder 112 .
  • the padder 112 performs necessary zero padding (insertion of Null) with respect to the data supplied from the mode adaptation/multiplexer 111 and supplies data obtained as a result to a BB scrambler 113 .
  • the BB scrambler 113 performs base-band scrambling (BB scrambling) with respect to the data supplied from the padder 112 and supplies data obtained as a result to a BCH encoder 114 .
  • the BCH encoder 114 performs BCH encoding with respect to the data supplied from the BB scrambler 113 and supplies data obtained as a result as LDPC target data to be an LDPC encoding target to an LDPC encoder 115 .
  • the LDPC encoder 115 performs LDPC encoding according to a parity check matrix or the like in which a parity matrix to be a portion corresponding to a parity bit of an LDPC code becomes a staircase (dual diagonal) structure with respect to the LDPC target data supplied from the BCH encoder 114 , for example, and outputs an LDPC code in which the LDPC target data is information bits.
  • the LDPC encoder 115 performs the LDPC encoding to encode the LDPC target data with an LDPC such as the LDPC code (corresponding to the parity check matrix) defined in the predetermined standard of the DVB-S.2, the DVB-T.2, the DVB-C.2 or the like, and the LDPC code (corresponding to the parity check matrix) or the like that is to be employed in ATSC 3.0, and outputs the LDPC code obtained as a result.
  • an LDPC such as the LDPC code (corresponding to the parity check matrix) defined in the predetermined standard of the DVB-S.2, the DVB-T.2, the DVB-C.2 or the like
  • the LDPC code corresponding to the parity check matrix
  • the LDPC code defined in the standard of the DVB-T.2 and the LDPC code that is to be employed in ATSC 3.0 are an IRA (Irregular Repeat Accumulate) code and a parity matrix of the parity check matrix of the LDPC code becomes a staircase structure.
  • the parity matrix and the staircase structure will be described later.
  • the IRA code is described in “Irregular Repeat-Accumulate Codes”, H. Jin, A. Khandekar, and R. J. McEliece, in Proceedings of 2nd International Symposium on Turbo codes and Related Topics, pp. 1-8, September 2000, for example.
  • the LDPC code that is output by the LDPC encoder 115 is supplied to the bit interleaver 116 .
  • the bit interleaver 116 performs bit interleave to be described later with respect to the LDPC code supplied from the LDPC encoder 115 and supplies the LDPC code after the bit interleave to an mapper 117 .
  • the mapper 117 maps the LDPC code supplied from the bit interleaver 116 to a signal point representing one symbol of orthogonal modulation in a unit (symbol unit) of code bits of one or more bits of the LDPC code and performs the orthogonal modulation (multilevel modulation).
  • the mapper 117 performs maps the LDPC code supplied from the bit interleaver 116 to a signal point determined by a modulation scheme performing the orthogonal modulation of the LDPC code, on an IQ plane (IQ constellation) defined by an I axis representing an I component of the same phase as a carrier and a Q axis representing a Q component orthogonal to the carrier, and performs the orthogonal modulation.
  • IQ plane IQ constellation
  • the mapper 117 maps the LDPC code supplied from the bit interleaver 116 to a signal point indicating a symbol among the 2 m signal points in units of symbols.
  • examples of the modulation scheme of the orthogonal modulation performed by the mapper 117 include a modulation scheme specified in a standard such as DVB-T.2, a modulation scheme that is scheduled to be employed in ATSC 3.0, and other modulation schemes, that is, includes Binary Phase Shift Keying (BPSK), Quadrature Phase Shift Keying (QPSK), 8 Phase-Shift Keying (8PSK), 16 Amplitude Phase-Shift Keying (APSK), 32APSK, 16 Quadrature Amplitude Modulation (QAM), 16QAM, 64QAM, 256QAM, 1024QAM, 4096QAM, and 4 Pulse Amplitude Modulation (PAM).
  • BPSK Binary Phase Shift Keying
  • QPSK Quadrature Phase Shift Keying
  • 8PSK 8 Phase-Shift Keying
  • APSK 16 Amplitude Phase-Shift Keying
  • QAM 16 Quadrature Amplitude Modulation
  • the data (a mapping result of mapping the symbol to the signal point) obtained by the process of the mapper 117 is supplied to a time interleaver 118 .
  • the time interleaver 118 performs time interleave (interleave in a time direction) in a unit of symbol with respect to the data supplied from the mapper 117 and supplies data obtained as a result to an single input single output/multiple input single output encoder (SISO/MISO encoder) 119 .
  • SISO/MISO encoder single input single output/multiple input single output encoder
  • the SISO/MISO encoder 119 performs spatiotemporal encoding with respect to the data supplied from the time interleaver 118 and supplies the data to the frequency interleaver 120 .
  • the frequency interleaver 120 performs frequency interleave (interleave in a frequency direction) in a unit of symbol with respect to the data supplied from the SISO/MISO encoder 119 and supplies the data to a frame builder/resource allocation unit 131 .
  • control data (signalling) for transfer control such as BB signaling (Base Band Signalling) (BB Header) is supplied to the BCH encoder 121 .
  • the BCH encoder 121 performs the BCH encoding with respect to the signaling supplied thereto and supplies data obtained as a result to an LDPC encoder 122 , similar to the BCH encoder 114 .
  • the LDPC encoder 122 sets the data supplied from the BCH encoder 121 as LDPC target data, performs the LDPC encoding with respect to the data, and supplies an LDPC code obtained as a result to a mapper 123 , similar to the LDPC encoder 115 .
  • the mapper 123 maps the LDPC code supplied from the LDPC encoder 122 to a signal point representing one symbol of orthogonal modulation in a unit (symbol unit) of code bits of one or more bits of the LDPC code, performs the orthogonal modulation, and supplies data obtained as a result to the frequency interleaver 124 , similar to the mapper 117 .
  • the frequency interleaver 124 performs the frequency interleave in a unit of symbol with respect to the data supplied from the mapper 123 and supplies the data to the frame builder/resource allocation unit 131 , similar to the frequency interleaver 120 .
  • the frame builder/resource allocation unit 131 inserts symbols of pilots into necessary positions of the data (symbols) supplied from the frequency interleavers 120 and 124 , configures a frame (for example, a physical layer (PL) frame, a T2 frame, a C2 frame, and so on) including symbols of a predetermined number from data (symbols) obtained as a result, and supplies the frame to an OFDM generating unit 132 .
  • a frame for example, a physical layer (PL) frame, a T2 frame, a C2 frame, and so on
  • the OFDM generating unit 132 generates an OFDM signal corresponding to the frame from the frame supplied from the frame builder/resource allocation unit 131 and transmits the OFDM signal through the communication path 13 ( FIG. 7 ).
  • the transmitting device 11 can be configured without including part of the blocks illustrated in FIG. 8 such as the time interleaver 118 , the SISO/MISO encoder 119 , the frequency interleaver 120 and the frequency interleaver 124 .
  • FIG. 9 illustrates a configuration example of the bit interleaver 116 of FIG. 8 .
  • the bit interleaver 116 has a function of interleaving data, and includes a parity interleaver 23 , a group-wise interleaver 24 , and a block interleaver 25 .
  • the parity interleaver 23 performs parity interleave for interleaving the parity bits of the LDPC code supplied from the LDPC encoder 115 into positions of other parity bits and supplies the LDPC code after the parity interleave to the group-wise interleaver 24 .
  • the group-wise interleaver 24 performs the group-wise interleave with respect to the LDPC code supplied from the parity interleaver 23 and supplies the LDPC code after the group-wise interleave to the block interleaver 25 .
  • 360 bits of one segment are used as a bit group, where the LDPC code of one code is divided into segments in units of 360 bits equal to the unit size P which will be described later, and the LDPC code supplied from the parity interleaver 23 is interleaved in units of bit groups, starting from the head.
  • the error rate can be improved to be better than when the group-wise interleave is not performed, and as a result, it is possible to secure the excellent communication quality in the data transmission.
  • the block interleaver 25 performs block interleave for demultiplexing the LDPC code supplied from the group-wise interleaver 24 , converts, for example, the LDPC code corresponding to one code into an m-bit symbol serving as a unit of mapping, and supplies the m-bit symbol to the mapper 117 ( FIG. 8 ).
  • the LDPC code corresponding to one code is converted into the m-bit symbol such that the LDPC code supplied from the group-wise interleaver 24 is written in a storage region in which columns serving as a storage region storing a predetermined number of bits in a column (vertical) direction are arranged in a row (horizontal) direction by the number m of bits of the symbol in the column direction and read from the storage region in the row direction.
  • FIG. 10 illustrates an example of the parity check matrix H that is used for LDPC encoding by the LDPC encoder 115 of FIG. 8 .
  • H Low-Density Generation Matrix
  • the information length K and the parity length M of the LDPC code having the certain code length N are determined by an encoding rate.
  • the parity check matrix H becomes a matrix in which row ⁇ column is M ⁇ N (a matrix of M ⁇ N).
  • the information matrix H A becomes a matrix of M ⁇ K and the parity matrix H T becomes a matrix of M ⁇ M.
  • FIG. 11 is an illustration of an example of the parity matrix H T of the parity check matrix H used for LDPC encoding in the LDPC encoder 115 of FIG. 8 .
  • the parity matrix H T of the parity check matrix H used for LDPC encoding in the LDPC encoder 115 is identical to, for example, the parity matrix H T of the parity check matrix H of the LDPC code specified in a standard such as DVB-T.2.
  • the parity matrix H T of the parity check matrix H of the LDPC code that is defined in the standard of the DVB-T.2 or the like becomes a staircase structure matrix (lower bidiagonal matrix) in which elements of 1 are arranged in a staircase shape, as illustrated in FIG. 11 .
  • the row weight of the parity matrix H T becomes 1 with respect to the first row and becomes 2 with respect to the remaining rows.
  • the column weight becomes 1 with respect to the final column and becomes 2 with respect to the remaining columns.
  • the LDPC code of the parity check matrix H in which the parity matrix H T becomes the staircase structure can be easily generated using the parity check matrix H.
  • the LDPC code (one code word) is represented by a row vector c and a column vector obtained by transposing the row vector is represented by C T .
  • a portion of information bits of the row vector c to be the LDPC code is represented by a row vector A and a portion of the parity bits is represented by a row vector T.
  • the row vector T that corresponds to the parity bits constituting the row vector c [A
  • FIG. 12 is an illustration of the parity check matrix H of the LDPC code that is defined in the standard of the DVB-T.2 or the like.
  • the column weight becomes X with respect KX columns from a first column of the parity check matrix H of the LDPC code defined in the standard of the DVB-T.2 or the like, becomes 3 with respect to the following K3 columns, becomes 2 with respect to the following (M ⁇ 1) columns, and becomes 1 with respect to a final column.
  • KX+K3+M ⁇ 1+1 is equal to the code length N.
  • FIG. 13 is an illustration of column numbers KX, K3, and M and a column weight X, with respect to each encoding rate r of the LDPC code defined in the standard of the DVB-T.2 or the like.
  • LDPC codes that have code lengths N of 64800 bits and 16200 bits are defined.
  • the code length N of the 64800 bits is referred to as 64 kbits and the code length N of the 16200 is referred to as 16 kbits.
  • an error rate tends to be lower in a code bit corresponding to a column of which a column weight of the parity check matrix H is large.
  • parity check matrix H that is illustrated in FIGS. 12 and 13 and is defined in the standard of the DVB-T.2 or the like, a column weight of a column of a head side (left side) tends to be large. Therefore, with respect to the LDPC code corresponding to the parity check matrix H, a code bit of a head side tends to be robust to error (there is tolerance against the error) and a code bit of an ending side tends to be weak for the error.
  • FIG. 24 illustrates an example of (a part of) a Tanner graph of the parity check matrix of the LDPC code.
  • the check node returns a message in which the probability of a value being 0 and the probability of a value being 1 are equal to each other, to all the variable nodes connected to the check node. For this reason, if the plurality of variable nodes connected to the same check node simultaneously become the erasure, decoding performance is deteriorated.
  • the LDPC code that is output by the LDPC encoder 115 of FIG. 8 is an IRA code, same as the LDPC code that is defined in the standard of the DVB-T.2 or the like, and the parity matrix H T of the parity check matrix H becomes a staircase structure, as illustrated in FIG. 11 .
  • FIG. 15 illustrates the parity matrix HT becoming the staircase structure as illustrated in FIG. 11 , and an example of a Tanner graph corresponding to the parity matrix HT.
  • a of FIG. 15 illustrates an example of the parity matrix HT becoming the staircase structure and B of FIG. 15 illustrates the Tanner graph corresponding to the parity matrix HT of A of FIG. 15 .
  • the check node connected with two variable nodes (variable nodes to find a message by the use of parity bits) corresponding to those two parity bits that became errors returns message that the probability with a value of 0 and the probability with a value of 1 are equal probability, to the variable nodes connected with the check node, and therefore the performance of decoding is deteriorated.
  • the burst length bit number of parity bits that continuously become errors
  • the number of check nodes that return the message of equal probability increases and the performance of decoding is further deteriorated.
  • the parity interleaver 23 ( FIG. 9 ) performs the parity interleave for interleaving the parity bits of the LDPC code from the LDPC encoder 115 into positions of other parity bits, to prevent the decoding performance from being deteriorated.
  • FIG. 16 is an illustration of the parity matrix H T of the parity check matrix H corresponding to the LDPC code that has undergone the parity interleave performed by the parity interleaver 23 of FIG. 9 .
  • the information matrix H A of the parity check matrix H corresponding to the LDPC code output by the LDPC encoder 115 has a cyclic structure, similarly to the information matrix of the parity check matrix H corresponding to the LDPC code specified in a standard such as DVB-T.2.
  • the cyclic structure refers to a structure in which a certain column matches one obtained by cyclically shifting another column, and includes, for example, a structure in which a position of 1 of each row of P columns becomes a position obtained by cyclically shifting a first column of the P columns in the column direction by a predetermined value such as a value that is proportional to a value q obtained by dividing a parity length M for every P columns.
  • a predetermined value such as a value that is proportional to a value q obtained by dividing a parity length M for every P columns.
  • LDPC code defined in a standard such as DVB-T2
  • code length N 64800 bits and 16200 bits
  • unit size P 360 which is one of divisors excluding 1 and M among the divisors of the parity length M.
  • the parity interleaver 23 interleaves the K+qx+y+1-th code bit among code bits of an LDPC code of N bits to the position of the K+Py+x+1-th code bit as parity interleave.
  • both of the K+qx+y+1-th code bit and the K+Py+x+1-th code bit are code bits after the K+1-th one, they are parity bits, and therefore the positions of the parity bits of the LDPC code are moved according to the parity interleave.
  • the parity interleave (the parity bits corresponding to) the variable nodes connected to the same check node are separated by the unit size P, that is, 360 bits in this case. For this reason, when the burst length is less than 360 bits, the plurality of variable nodes connected to the same check node can be prevented from simultaneously becoming the error. As a result, tolerance against the burst error can be improved.
  • the LDPC code after the interleave for interleaving the (K+qx+y+1)-th code bit into the position of the (K+Py+x+1)-th code bit is matched with an LDPC code of a parity check matrix (hereinafter, referred to as a transformed parity check matrix) obtained by performing column replacement for replacing the (K+qx+y+1)-th column of the original parity check matrix H with the (K+Py+x+1)-th column.
  • a parity check matrix hereinafter, referred to as a transformed parity check matrix
  • the pseudo cyclic structure is a structure in which the remaining portion excluding a part has the cyclic structure.
  • the transformed parity check matrix obtained by performing the column permutation corresponding to the parity interleave on the parity check matrix of the LDPC code specified in the standard such as DVB-T.2 has the pseudo cyclic structure rather than the (perfect) cyclic structure since it is one 1 element short (it is a 0 element) in a portion (a shift matrix which will be described later) of a 360 ⁇ 360 matrix of a right top corner portion of the transformed parity check matrix.
  • the transformed parity check matrix for the parity check matrix of the LDPC code output by the LDPC encoder 115 has the pseudo cyclic structure, for example, similarly to the transformed parity check matrix for the parity check matrix of the LDPC code specified in the standard such as DVB-T.2.
  • the transformed parity check matrix of FIG. 16 becomes a matrix that is obtained by performing the column replacement corresponding to the parity interleave and replacement (row replacement) of a row to configure the transformed parity check matrix with a constitutive matrix to be described later, with respect to the original parity check matrix H.
  • FIG. 17 is a flowchart illustrating processing executed by the LDPC encoder 115 , the bit interleaver 116 , and the mapper 117 of FIG. 8 .
  • the LDPC encoder 115 awaits supply of the LDPC target data from the BCH encoder 114 .
  • the LDPC encoder 115 encodes the LDPC target data with the LDPC code and supplies the LDPC code to the bit interleaver 116 .
  • the processing proceeds to step S 102 .
  • step S 102 the bit interleaver 116 performs the bit interleave on the LDPC code supplied from the LDPC encoder 115 , and supplies the symbol obtained by the bit interleave to the mapper 117 , and the process proceeds to step S 103
  • step S 102 in the bit interleaver 116 ( FIG. 9 ), the parity interleaver 23 performs parity interleave with respect to the LDPC code supplied from the LDPC encoder 115 and supplies the LDPC code after the parity interleave to the group-wise interleaver 24 .
  • the group-wise interleaver 24 performs the group-wise interleave on the LDPC code supplied from the parity interleaver 23 , and supplies the resulting LDPC code to the block interleaver 25 .
  • the block interleaver 25 performs the block interleave on the LDPC code that has undergone the group-wise interleave performed by the group-wise interleaver 24 , and supplies the m-bit symbol obtained as a result to the mapper 117 .
  • step S 103 the mapper 117 maps the symbol supplied from the block interleaver 25 to any of the 2 m signal points decided in the modulation scheme of the orthogonal modulation performed by the mapper 117 , performs the orthogonal modulation, and supplies data obtained as a result to the time interleaver 118 .
  • the parity interleaver 23 serving as the block performing the parity interleave and the group-wise interleaver 24 serving as the block performing the group-wise interleave are configured individually, but the parity interleaver 23 and the group-wise interleaver 24 may be configured integrally.
  • both the parity interleave and the group-wise interleave can be performed by writing and reading of the code bits with respect to the memory and can be represented by a matrix to convert an address (write address) to perform writing of the code bits into an address (read address) to perform reading of the code bits.
  • the block interleaver 25 can be integrally configured.
  • the block interleave executed by the block interleaver 25 can be represented by the matrix to convert the write address of the memory storing the LDPC code into the read address.
  • the parity interleave, the group-wise interleave, and the block interleave can be collectively executed by the matrixes.
  • FIG. 18 is a block diagram illustrating a configuration example of the LDPC encoder 115 of FIG. 8 .
  • the LDPC encoder 122 of FIG. 8 is also configured in the same manner.
  • the LDPC codes that have the two code lengths N of 64800 bits and 16200 bits are defined.
  • the LDPC encoder 115 can perform encoding (error correction encoding) using the LDPC code of each encoding rate having the code length N of 64800 bits or 16200 bits, according to the parity check matrix H prepared for each code length N and each encoding rate.
  • the LDPC encoder 115 includes an encoding processing unit 601 and a storage unit 602 .
  • the encoding processing unit 601 includes an encoding rate setting unit 611 , an initial value table reading unit 612 , a parity check matrix generating unit 613 , an information bit reading unit 614 , an encoding parity operation unit 615 , an a control unit 616 .
  • the encoding processing unit 601 performs the LDPC encoding of LDPC target data supplied to the LDPC encoder 115 and supplies an LDPC code obtained as a result to the bit interleaver 116 ( FIG. 8 ).
  • the encoding rate setting unit 611 sets the code length N and the encoding rate of the LDPC code, according to an operation of an operator.
  • the initial value table reading unit 612 reads a parity check matrix initial value table to be described later, which corresponds to the code length N and the encoding rate set by the encoding rate setting unit 611 , from the storage unit 602 .
  • the information bit reading unit 614 reads (extracts) information bits corresponding to the information length K, from the LDPC target data supplied to the LDPC encoder 115 .
  • the encoding parity operation unit 615 reads the parity check matrix H generated by the parity check matrix generating unit 613 from the storage unit 602 , and generates a code word (LDPC code) by calculating parity bits for the information bits read by the information bit reading unit 614 on the basis of a predetermined expression using the parity check matrix H.
  • LDPC code code word
  • the control unit 616 controls each block constituting the encoding processing unit 601 .
  • the storage unit 602 a plurality of parity check matrix initial value tables that correspond to the plurality of encoding rates illustrated in FIGS. 12 and 13 , with respect to the code lengths N such as the 64800 bits and 16200 bits, are stored.
  • the storage unit 602 temporarily stores data that is necessary for processing of the encoding processing unit 601 .
  • FIG. 19 is a flowchart illustrating an example of processing of the LDPC encoder 115 of FIG. 18 .
  • step S 201 the encoding rate setting unit 611 determines (sets) the code length N and the encoding rate r to perform the LDPC encoding.
  • step S 202 the initial value table reading unit 612 reads the previously determined parity check matrix initial value table corresponding to the code length N and the encoding rate r determined by the encoding rate setting unit 611 , from the storage unit 602 .
  • step S 203 the parity check matrix generating unit 613 calculates (generates) the parity check matrix H of the LDPC code of the code length N and the encoding rate r determined by the encoding rate setting unit 611 , using the parity check matrix initial value table read from the storage unit 602 by the initial value table reading unit 612 , supplies the parity check matrix to the storage unit 602 , and stores the parity check matrix in the storage unit.
  • step S 205 the encoding parity operation unit 615 sequentially operates parity bits of a code word c that satisfies an expression (8) using the information bits and the parity check matrix H that have been read from the information bit reading unit 614 .
  • c represents a row vector as the code word (LDPC code) and c T represents transposition of the row vector c.
  • the row vector T that corresponds to the parity bits constituting the row vector c [A
  • step S 206 the control unit 616 determines whether the LDPC encoding ends. When it is determined in step S 206 that the LDPC encoding does not end, that is, when there is LDPC target data to perform the LDPC encoding, the processing returns to step S 201 (or step S 204 ). Hereinafter, the processing of steps S 201 (or step S 204 ) to S 206 is repeated.
  • step S 206 When it is determined in step S 206 that the LDPC encoding ends, that is, there is no LDPC target data to perform the LDPC encoding, the LDPC encoder 115 ends the processing.
  • the parity check matrix initial value table corresponding to each code length N and each encoding rate r is prepared and the LDPC encoder 115 performs the LDPC encoding of the predetermined code length N and the predetermined encoding rate r, using the parity check matrix H generated from the parity check matrix initial value table corresponding to the predetermined code length N and the predetermined encoding rate r.
  • the parity check matrix initial value table is a table that represents positions of elements of 1 of the information matrix H A ( FIG. 10 ) of the parity check matrix H corresponding to the information length K according to the code length N and the encoding rate r of the LDPC code (LDPC code defined by the parity check matrix H) for every 360 columns (unit size P) and is previously made for each parity check matrix H of each code length N and each encoding rate r.
  • LDPC code defined by the parity check matrix H
  • the parity check matrix initial value table represents at least positions of elements of 1 of the information matrix H A for every 360 columns (unit size P).
  • parity check matrix H examples include a parity check matrix in which the (whole) parity matrix H T has the staircase structure, which is specified in DVB-T.2 or the like and a parity check matrix in which a part of the parity matrix H T has the staircase structure, and the remaining portion is a diagonal matrix (a unit matrix), which is proposed by CRC/ETRI.
  • an expression scheme of a parity check matrix initial value table indicating the parity check matrix in which the parity matrix H T has the staircase structure, which is specified in DVB-T.2 or the like, is referred to as a DVB scheme
  • an expression scheme of a parity check matrix initial value table indicating the parity check matrix proposed by CRC/ETRI is referred to as an ETRI scheme.
  • FIG. 20 is an illustration of an example of the parity check matrix initial value table in the DVB method.
  • FIG. 20 illustrates a parity check matrix initial value table with respect to the parity check matrix H that is defined in the standard of the DVB-T.2 and has the code length N of 16200 bits and the encoding rate (an encoding rate of notation of the DVB-T2) r of 1/4
  • the parity check matrix generating unit 613 calculates the parity check matrix H using the parity check matrix initial value table in the DVB method, as follows.
  • FIG. 21 is an illustration of a method of calculating a parity check matrix H from a parity check matrix initial value table in the DVB method.
  • FIG. 21 illustrates a parity check matrix initial value table with respect to the parity check matrix H that is defined in the standard of the DVB-T.2 and has the code length N of 16200 bits and the encoding rate r of 2/3.
  • the parity check matrix initial value table in the DVB method is the table that represents the positions of the elements of 1 of the whole information matrix H A corresponding to the information length K according to the code length N and the encoding rate r of the LDPC code for every 360 columns (unit size P).
  • row numbers (row numbers when a row number of a first row of the parity check matrix H is set to 0) of elements of 1 of a (1+360 ⁇ (i ⁇ 1)-th column of the parity check matrix H are arranged by a number of column weights of the (1+360 ⁇ (i ⁇ 1)-th column.
  • the parity matrix H T ( FIG. 10 ) corresponding to the parity length M in the parity check matrix H of the DVB scheme is fixed to the staircase structure illustrated in FIG. 15 , it is possible to obtain the parity check matrix H if it is possible to obtain the information matrix H A ( FIG. 10 ) corresponding to the information length K through the parity check matrix initial value table.
  • a row number k+1 of the parity check matrix initial value table in the DVB method is different according to the information length K.
  • a relation of an expression (9) is realized between the information length K and the row number k+1 of the parity check matrix initial value table.
  • 360 of the expression (9) is the unit size P described in FIG. 16 .
  • the column weights of the parity check matrix H that are calculated from the parity check matrix initial value table of FIG. 21 are 13 from the first column to the (1+360 ⁇ (3 ⁇ 1) ⁇ 1)-th column and are 3 from the (1+360 ⁇ (3 ⁇ 1))-th column to the K-th column.
  • the first row of the parity check matrix initial value table of FIG. 21 becomes 0, 2084, 1613, 1548, 1286, 1460, 3196, 4297, 2481, 3369, 3451, 4620, and 2622, which shows that elements of rows having row numbers of 0, 2084, 1613, 1548, 1286, 1460, 3196, 4297, 2481, 3369, 3451, 4620, and 2622 are 1 (and the other elements are 0), in the first column of the parity check matrix H.
  • the parity check matrix initial value table represents positions of elements of 1 of the information matrix H A of the parity check matrix H for every 360 columns.
  • the columns other than the (1+360 ⁇ (i ⁇ 1))-th column of the parity check matrix H, that is, the individual columns from the (2+360 ⁇ (i ⁇ 1))-th column to the (360 ⁇ i)-th column are arranged by cyclically shifting elements of 1 of the (1+360 ⁇ (i ⁇ 1))-th column determined by the parity check matrix initial value table periodically in a downward direction (downward direction of the columns) according to the parity length M.
  • a numerical value of a j-th column (j-th column from the left side) of an i-th row (i-th row from the upper side) of the parity check matrix initial value table is represented as h i,j and a row number of the j-th element of 1 of the w-th column of the parity check matrix H is represented as H w-j
  • the row number H w-j of the element of 1 of the w-th column to be a column other than the (1+360 ⁇ (i ⁇ 1))-th column of the parity check matrix H can be calculated by an expression (10).
  • H w-j mod ⁇ h i,j +mod(( w ⁇ 1), P ) ⁇ q,M ) (10)
  • mod(x, y) means a remainder that is obtained by dividing x by y.
  • P is a unit size described above.
  • P is 360.
  • the parity check matrix generating unit 613 ( FIG. 18 ) specifies the row numbers of the elements of 1 of the (1+360 ⁇ (i ⁇ 1))-th column of the parity check matrix H by the parity check matrix initial value table.
  • the parity check matrix generating unit 613 calculates the row number H w-j of the element of 1 of the w-th column to be the column other than the (1+360 ⁇ (i ⁇ 1))-th column of the parity check matrix H, according to the expression (10), and generates the parity check matrix H in which the element of the obtained row number is set to 1.
  • FIG. 22 is an illustration of a structure of the parity check matrix of the ETRI scheme.
  • the parity check matrix of the ETRI scheme is configured with an A matrix, a B matrix, a C matrix, a D matrix, and a Z matrix.
  • the B matrix is a g ⁇ g matrix having the staircase structure adjacent to the right of the A matrix.
  • the C matrix is an (N ⁇ K ⁇ g) ⁇ (K+g) matrix adjacently below the A matrix and the B matrix.
  • the D matrix is an (N ⁇ K ⁇ g) ⁇ (N ⁇ K ⁇ g) unit matrix adjacent to the right of the C matrix.
  • the Z matrix is a g ⁇ (N ⁇ K ⁇ g) zero matrix (zero matrix) adjacent to the right of the B matrix.
  • the A matrix and a portion of the C matrix configure an information matrix
  • the B matrix, the remaining portion of the C matrix, the D matrix, and the Z matrix configure a parity matrix
  • the B matrix is the matrix having the staircase structure
  • the D matrix is the unit matrix
  • a portion (a portion of the B matrix) of the parity matrix of the parity check matrix of the ETRI scheme has the staircase structure
  • the remaining portion (the portion of the D matrix) is the diagonal matrix (the unit matrix).
  • the A matrix and the C matrix have the cyclic structure for every 360 columns (the unit size P), and the parity check matrix initial value table of the ETRI scheme indicates positions of 1 elements of the A matrix and the C matrix in units of 360 columns.
  • the parity check matrix initial value table of the ETRI scheme that indicates positions of 1 elements of the A matrix and the C matrix in units of 360 columns indicates at least positions of 1 elements of the information matrix in units of 360 columns.
  • FIG. 23 is an illustration of an example of the parity check matrix initial value table of the ETRI scheme.
  • FIG. 23 illustrates an example of a parity check matrix initial value table for a parity check matrix in which the code length N is 50 bits, and the encoding rate r is 1/2.
  • the parity check matrix initial value table of the ETRI scheme is a table in which positions of 1 elements of the A matrix and the C matrix are indicated for each unit size P, and row numbers (row numbers when a row number of a first row of the parity check matrix is 0) of 1 elements of a (1+P ⁇ (i ⁇ 1))-th column of the parity check matrix that correspond in number to the column weight of the (1+P ⁇ (i ⁇ 1))-th column are arranged in an i-th row.
  • the unit size P is assumed to be, for example, 5.
  • M 2 has a value M ⁇ M 1 obtained by subtracting M 1 from the parity length M.
  • the column weight of the parity check matrix obtained from the parity check matrix initial value table of FIG. 23 is 3 in the 1st column to a (1+5 ⁇ (2 ⁇ 1) ⁇ 1)-th column and 1 in a (1+5 ⁇ (2 ⁇ 1))-th column to a 5th column.
  • 2, 6, and 18 are arranged in the 1st row of the parity check matrix initial value table of FIG. 23 , which indicates that elements of rows having the row numbers of 2, 6, and 18 are 1 (and the other elements are 0) in the 1st column of the parity check matrix.
  • the A matrix is a 15 ⁇ 25 (g ⁇ K) matrix
  • the C matrix is a 10 ⁇ 40 ((N ⁇ K ⁇ g) ⁇ (K+g)) matrix
  • rows having the row numbers of 0 to 14 in the parity check matrix are rows of the A matrix
  • rows having the row numbers of 15 to 24 in the parity check matrix are rows of the C matrix.
  • rows #2, #6, and #18 are the rows of the A matrix
  • the rows #18 is the row of the C matrix.
  • the rows #2 and #10 are the rows of the A matrix
  • the row #19 is the row of the C matrix.
  • the row #22 is the row of the C matrix.
  • the 1 elements of the (1+5 ⁇ (i ⁇ 1))-th column decided by the parity check matrix initial value table have periodically been cyclically shifted downward (downward in the column) and arranged according to the parameters Q 1 and Q 2 .
  • the (2+5 ⁇ (i ⁇ 1))-th column has been cyclically shifted downward by Q 2 ).
  • FIG. 24 is an illustration of the A matrix generated from the parity check matrix initial value table of FIG. 23 .
  • FIG. 25 is an illustration of the parity interleave of the B matrix.
  • FIG. 25 illustrates the A matrix and the B matrix after the B matrix has undergone the parity interleave.
  • FIG. 26 is an illustration of the C matrix generated from the parity check matrix initial value table of FIG. 23 .
  • the parity check matrix generating unit 613 ( FIG. 18 ) generates the C matrix using the parity check matrix initial value table, and arranges the C matrix below the A matrix and the B matrix (that has undergone the parity interleave).
  • parity check matrix generating unit 613 arranges the Z matrix at the right of the B matrix, arranges the D matrix at the right of the C matrix, and generates the parity check matrix illustrated in FIG. 26 .
  • FIG. 27 is an illustration of the parity interleave of the D matrix.
  • FIG. 27 illustrates the parity check matrix after the parity interleave of the D matrix is performed on the parity check matrix of FIG. 26 .
  • the LDPC encoder 115 performs LDPC encoding (generation of the LDPC code), for example, using the parity check matrix of FIG. 27 .
  • the LDPC code generated using the parity check matrix of FIG. 27 is the LDPC code that has undergone the parity interleave, and thus it is unnecessary to perform the parity interleave on the LDPC code generated using the parity check matrix of FIG. 27 in the parity interleaver 23 ( FIG. 9 ).
  • FIG. 28 is an illustration of the parity check matrix obtained by performing the column permutation serving as the parity deinterleave for restoring the parity interleave to an original state on the B matrix, the portion of the C matrix (the portion of the C matrix arranged below the B matrix), and the D matrix of the parity check matrix of FIG. 27 .
  • the LDPC encoder 115 can perform LDPC encoding (generation of the LDPC code) using the parity check matrix of FIG. 28 .
  • the parity interleaver 23 ( FIG. 9 ) performs the parity interleave.
  • FIG. 29 is an illustration of the transformed parity check matrix obtained by performing the row permutation on the parity check matrix of FIG. 27 .
  • the transformed parity check matrix is a matrix represented by a combination of a P ⁇ P unit matrix, a quasi unit matrix obtained by setting one or more is of the unit matrix to zero (0), a shift matrix obtained by cyclically shifting the unit matrix or the quasi unit matrix, a sum matrix serving as a sum of two or more matrices of the unit matrix, the quasi unit matrix, and the shifted matrix, and a P ⁇ P zero matrix.
  • the transformed parity check matrix is used for decoding of the LDPC code
  • an architecture of performing P check node operations and P variable node operations at the same time can be employed for decoding the LDPC code as will be described later.
  • ATSC 3.0 a terrestrial digital television broadcasting standard
  • a novel LDPC code which can be used in ATSC 3.0 and other data transmission (hereinafter referred to as a new LDPC code) will be described.
  • the LDPC code of the DVB scheme or the LDPC code of the ETRI scheme having the unit size P of 360, similarly to DVB-T.2 or the like, and corresponding to the parity check matrix having the cyclic structure can be employed as the new LDPC code.
  • the LDPC encoder 115 ( FIGS. 8 and 18 ) can perform LDPC encoding for generating a new LDPC code using the parity check matrix obtained from the parity check matrix initial value table of the new LDPC code in which the code length N is 16 kbits or 64 kbits, and the encoding rate r is any of 5/15, 6, 15, 7/15, 8/15, 9/15, 10/15, 11/15, 12/15, and 13/15.
  • the storage unit 602 of the LDPC encoder 115 ( FIG. 8 ) stores the parity check matrix initial value of the new LDPC code.
  • FIG. 30 is an illustration of an example of a parity check matrix initial value table of the DVB scheme for a parity check matrix of a new LDPC code in which the code length N is 16 kbits, and the encoding rate r is 8/15 (hereinafter, also referred to as Sony symbol (16k, 8/15)), proposed by the applicant of the present application.
  • FIG. 31 is an illustration of an example of a parity check matrix initial value table of the DVB scheme for a parity check matrix of a new LDPC code in which the code length N is 16 kbits, and the encoding rate r is 10/15 (hereinafter, also referred to as Sony symbol (16k, 10/15)), proposed by the applicant of the present application.
  • FIG. 32 is an illustration of an example of a parity check matrix initial value table of the DVB scheme for a parity check matrix of a new LDPC code in which the code length N is 16 kbits, and the encoding rate r is 12/15 (hereinafter, also referred to as Sony symbol (16k, 12/15)), proposed by the applicant of the present application.
  • FIGS. 33, 34, and 35 are illustrations of an example of a parity check matrix initial value table of the DVB scheme for a parity check matrix of a new LDPC code in which the code length N is 64 kbits, and the encoding rate r is 7/15 (hereinafter, also referred to as Sony symbol (64k, 7/15)), proposed by the applicant of the present application.
  • FIG. 34 is an illustration subsequent to FIG. 33
  • FIG. 35 is an illustration subsequent to FIG. 34 .
  • FIGS. 36, 37, and 38 are illustrations of an example of a parity check matrix initial value table of the DVB scheme for a parity check matrix of a new LDPC code in which the code length N is 64 kbits, and the encoding rate r is 9/15 (hereinafter, also referred to as Sony symbol (64k, 9/15)), proposed by the applicant of the present application.
  • FIG. 37 is an illustration subsequent to FIG. 36
  • FIG. 38 is an illustration subsequent to FIG. 37 .
  • FIGS. 39, 40, 41, and 42 are illustrations of an example of a parity check matrix initial value table of the DVB scheme for a parity check matrix of a new LDPC code in which the code length N is 64 kbits, and the encoding rate r is 11/15 (hereinafter, also referred to as Sony symbol (64k, 11/15)), proposed by the applicant of the present application.
  • FIG. 40 is an illustration subsequent to FIG. 39
  • FIG. 41 is an illustration subsequent to FIG. 40 .
  • FIGS. 43, 44, 45, and 46 are illustrations of an example of a parity check matrix initial value table of the DVB scheme for a parity check matrix of a new LDPC code in which the code length N is 64 kbits, and the encoding rate r is 13/15 (hereinafter, also referred to as Sony symbol (64k, 13/15)), proposed by the applicant of the present application.
  • FIG. 44 is an illustration subsequent to FIG. 43
  • FIG. 45 is an illustration subsequent to FIG. 44 .
  • FIGS. 47 and 48 are illustrations of an example of a parity check matrix initial value table of the DVB scheme for a parity check matrix of a new LDPC code in which the code length N is 64 kbits, and the encoding rate r is 6/15 (hereinafter, also referred to as Samsung symbol (64k, 6/15)), proposed by Samsung.
  • FIG. 48 is an illustration subsequent to FIG. 47 .
  • FIGS. 49, 50, and 51 are illustrations of an example of a parity check matrix initial value table of the DVB scheme for a parity check matrix of a new LDPC code in which the code length N is 64 kbits, and the encoding rate r is 8/15 (hereinafter, also referred to as Samsung symbol (64k, 8/15)), proposed by Samsung.
  • FIG. 50 is an illustration subsequent to FIG. 49
  • FIG. 51 is an illustration subsequent to FIG. 50 .
  • FIGS. 52, 53, and 54 are illustrations of an example of a parity check matrix initial value table of the DVB scheme for a parity check matrix of a new LDPC code in which the code length N is 64 kbits, and the encoding rate r is 12/15 (hereinafter, also referred to as Samsung symbol (64k, 12/15)), proposed by Samsung.
  • FIG. 53 is an illustration subsequent to FIG. 52
  • FIG. 54 is an illustration subsequent to FIG. 53 .
  • FIG. 55 is an illustration of an example of a parity check matrix initial value table of the DVB scheme for a parity check matrix of a new LDPC code in which the code length N is 16 kbits, and the encoding rate r is 6/15 (hereinafter, also referred to as LGE symbol (16k, 6/15)), proposed by LG Electronics Inc.
  • FIG. 56 is an illustration of an example of a parity check matrix initial value table of the DVB scheme for a parity check matrix of a new LDPC code in which the code length N is 16 kbits, and the encoding rate r is 7/15 (hereinafter, also referred to as LGE symbol (16k, 7/15)), proposed by LG Electronics Inc.
  • FIG. 57 is an illustration of an example of a parity check matrix initial value table of the DVB scheme for a parity check matrix of a new LDPC code in which the code length N is 16 kbits, and the encoding rate r is 9/15 (hereinafter, also referred to as LGE symbol (16k, 9/15)), proposed by LG Electronics Inc.
  • FIG. 58 is an illustration of an example of a parity check matrix initial value table of the DVB scheme for a parity check matrix of a new LDPC code in which the code length N is 16 kbits, and the encoding rate r is 11/15 (hereinafter, also referred to as LGE symbol (16k, 11/15)), proposed by LG Electronics Inc.
  • FIG. 59 is an illustration of an example of a parity check matrix initial value table of the DVB scheme for a parity check matrix of a new LDPC code in which the code length N is 16 kbits, and the encoding rate r is 13/15 (hereinafter, also referred to as LGE symbol (16k, 13/15)), proposed by LG Electronics Inc
  • FIGS. 60, 61, and 62 are an illustrations of an example of a parity check matrix initial value table of the DVB scheme for a parity check matrix of a new LDPC code in which the code length N is 64 kbits, and the encoding rate r is 10/15 (hereinafter, also referred to as LGE symbol (64k, 10/15)), proposed by LG Electronics Inc.
  • FIG. 61 is an illustration subsequent to FIG. 60
  • FIG. 62 is an illustration subsequent to FIG. 61 .
  • FIGS. 63, 64, and 65 are illustrations of an example of a parity check matrix initial value table of the DVB scheme for a parity check matrix of a new LDPC code in which the code length N is 64 kbits, and the encoding rate r is 9/15 (hereinafter, also referred to as NERC symbol (64k, 9/15)), proposed by NERC.
  • FIG. 64 is an illustration subsequent to FIG. 63
  • FIG. 65 is an illustration subsequent to FIG. 64 .
  • FIG. 66 is an illustration of an example of a parity check matrix initial value table of the ETRI scheme for a parity check matrix of a new LDPC code in which the code length N is 16 kbits, and the encoding rate r is 5/15 (hereinafter, also referred to as ETRI symbol (16k, 5/15)), proposed by CRC/ETRI.
  • FIGS. 67 and 68 are illustrations of an example of a parity check matrix initial value table of the ETRI scheme for a parity check matrix of a new LDPC code in which the code length N is 64 kbits, and the encoding rate r is 5/15 (hereinafter, also referred to as ETRI symbol (64k, 5/15)), proposed by CRC/ETRI.
  • FIG. 68 is an illustration subsequent to FIG. 67 .
  • FIGS. 69 and 70 are illustrations of an example of a parity check matrix initial value table of the ETRI scheme for a parity check matrix of a new LDPC code in which the code length N is 64 kbits, and the encoding rate r is 6/15 (hereinafter, also referred to as ETRI symbol (64k, 6/15)), proposed by CRC/ETRI.
  • FIG. 70 is an illustration subsequent to FIG. 69 .
  • FIGS. 71 and 72 are illustrations of an example of a parity check matrix initial value table of the ETRI scheme for a parity check matrix of a new LDPC code in which the code length N is 64 kbits, and the encoding rate r is 7/15 (hereinafter, also referred to as ETRI symbol (64k, 7/15)), proposed by CRC/ETRI.
  • FIG. 72 is an illustration subsequent to FIG. 71 .
  • the Sony symbol is an LDPC code having particularly excellent performance.
  • the LDPC code of good performance is an LDPC code obtained from an appropriate parity check matrix H.
  • the appropriate parity check matrix H is, for example, a parity check matrix that satisfies a predetermined condition to make BER (and FER) smaller when an
  • LDPC code obtained from the parity check matrix H is transmitted at low E s /N 0 or E b /N 0 (signal-to-noise power ratio per bit).
  • the appropriate parity check matrix H can be found by performing simulation to measure BER when LDPC codes obtained from various parity check matrices that satisfy a predetermined condition are transmitted at low E s /N 0 .
  • an analysis result obtained by a code performance analysis method called density evolution (Density Evolution) is excellent, and a loop of elements of 1 does not exist, which is called cycle 4, and so on.
  • the predetermined condition to be satisfied by the appropriate parity check matrix H can be arbitrarily determined from the viewpoint of the improvement in the decoding performance of LDPC code and the facilitation (simplification) of decoding processing of LDPC code, and so on.
  • FIG. 73 and FIG. 74 are diagrams to describe the density evolution that can obtain an analytical result as a predetermined condition to be satisfied by the appropriate parity check matrix H.
  • the density evolution is a code analysis method that calculates the expectation value of the error probability of the entire LDPC code (ensemble) with a code length N of ⁇ characterized by a degree sequence described later.
  • the expectation value of the error probability of a certain ensemble is 0 first, but, when the dispersion value of noise becomes equal to or greater than a certain threshold, it is not 0.
  • the threshold of the dispersion value of noise (which may also be called a performance threshold) in which the expectation value of the error probability is not 0, it is possible to decide the quality of ensemble performance (appropriateness of the parity check matrix).
  • an LDPC code of good performance can be found from LDPC codes belonging to the ensemble.
  • the above-mentioned degree sequence shows at what percentage a variable node or check node having the weight of each value exists with respect to the code length N of an LDPC code.
  • a regular (3,6) LDPC code with an encoding rate of 1/2 belongs to an ensemble characterized by a degree sequence in which the weight (column weight) of all variable nodes is 3 and the weight (row weight) of all check nodes is 6.
  • FIG. 73 illustrates a Tanner graph of such an ensemble.
  • Three branches (edge) equal to the column weight are connected with each variable node, and therefore there are totally 3N branches connected with N variable nodes.
  • branches (edge) equal to the row weight are connected with each check node, and therefore there are totally 3N branches connected with N/2 check nodes.
  • the interleaver randomly rearranges 3N branches connected with N variable nodes and connects each rearranged branch with any of 3N branches connected with N/2 check nodes.
  • an interleaver through which the branches connected with the variable nodes and the branches connected with the check nodes pass is divided into plural (multi edge), and, by this means, the ensemble is characterized more strictly.
  • FIG. 74 illustrates an example of a Tanner graph of an ensemble of the multi-edge type.
  • v1 variable nodes with one branch connected with the first interleaver and no branch connected with the second interleaver exist, v2 variable nodes with one branch connected with the first interleaver and two branches connected with the second interleaver exist, and v3 variable nodes with no branch connected with the first interleaver and two branches connected with the second interleaver exist, respectively.
  • c1 check nodes with two branches connected with the first interleaver and no branch connected with the second interleaver exist
  • c3 check nodes with no branch connected with the first interleaver and three branches connected with the second interleaver exist, respectively.
  • the parity check matrix initial value table of the Sony code is found from the above-mentioned simulation.
  • FIG. 75 is an illustration of parity check matrices H (hereinafter, also referred to as “parity check matrices H of Sony symbols (16k, 8/15), (16k, 10/15), and (16k, 12/15)”) obtained from the parity check matrix initial value table of the Sony symbols (16k, 8/15), (16k, 10/15), and (16k, 12/15).
  • the minimum cycle length (girth) is a minimum value of a length (a loop length) of a loop configured with 1 elements in the parity check matrix H.
  • a performance threshold value of the Sony symbol (16k, 8/15) is set to 0.805765
  • a performance threshold value of the Sony symbol (16k, 10/15) is set to 2.471011
  • a performance threshold value of the Sony symbol (16k, 12/15) is set to 4.269922.
  • the column weight is set to X1 for KX1 columns of the parity check matrices H of the Sony symbols (16k, 8/15), (16k, 10/15), and (16k, 12/15) starting from the 1st column, the column weight is set to X2 for KX2 columns subsequent thereto, the column weight is set to Y1 for KY1 columns subsequent thereto, the column weight is set to Y2 for KY2 columns subsequent thereto, the column weight is set to 2 for M ⁇ 1 columns subsequent thereto, and the column weight is set to 1 for the last column.
  • parity check matrices H of the Sony symbols (16k, 8/15), (16k, 10/15), and (16k, 12/15), similarly to the parity check matrix described above with reference to FIGS. 12 and 13 , columns closer to the head side (the left side) have higher column weights, and thus a code bit at the head of the Sony symbol tends to be robust to error (have error tolerance).
  • FIG. 76 is an illustration of parity check matrices H of the Sony symbols (64k, 7/15), (64k, 9/15), (64k, 11/15), and (64k, 13/15).
  • Every minimum cycle length of the parity check matrices H of the Sony symbols (64k, 7/15), (64k, 9/15), (64k, 11/15), and (64k, 13/15) has a value exceeding a cycle 4, and thus there is no cycle 4.
  • a performance threshold value of the Sony symbol (64k, 7/15) is set to ⁇ 0.093751
  • a performance threshold value of the Sony symbol (64k, 9/15) is set to 1.658523
  • a performance threshold value of the Sony symbol (64k, 11/15) is set to 3.351930
  • a performance threshold value of the Sony symbol (64k, 13/15) is set to 5.301749.
  • the column weight is set to X1 for KX1 columns of the parity check matrices H of the Sony symbols (64k, 7/15), (64k, 9/15), (64k, 11/15), and (64k, 13/15) starting from the 1st column, the column weight is set to X2 for KX2 columns subsequent thereto, the column weight is set to Y1 for KY1 columns subsequent thereto, the column weight is set to Y2 for KY2 columns subsequent thereto, the column weight is set to 2 for M ⁇ 1 columns subsequent thereto, and the column weight is set to 1 for the last column.
  • the numbers KX1, KX2, KY1, KY2, and M of columns and column weights X1, X2, Y1, and Y2 are set as illustrated in FIG. 76 .
  • the parity check matrices H of the Sony symbols (64k, 7/15), (64k, 9/15), (64k, 11/15), and (64k, 13/15) similarly to the parity check matrix described above with reference to FIGS. 12 and 13 , columns closer to the head side (the left side) have higher column weights, and thus a code bit at the head of the Sony symbol tends to be robust to error (have error tolerance).
  • an excellent BER/FER is obtained for the Sony symbols (64k, 7/15), (64k, 9/15), (64k, 11/15), and (64k, 13/15), and thus it is possible to secure the excellent communication quality in the data transmission using the Sony symbols (64k, 7/15), (64k, 9/15), (64k, 11/15), and (64k, 13/15).
  • FIG. 77 is an illustration of parity check matrices H of Samsung symbols (64k, 6/15), (64k, 8/15), and (64k, 12/15).
  • the column weight is set to X1 for KX1 columns of the parity check matrices H of the Samsung symbols (64k, 6/15), (64k, 8/15), and (64k, 12/15) starting from the 1st column, the column weight is set to X2 for KX2 columns subsequent thereto, the column weight is set to Y1 for KY1 columns subsequent thereto, the column weight is set to Y2 for KY2 columns subsequent thereto, the column weight is set to 2 for M ⁇ 1 columns subsequent thereto, and the column weight is set to 1 for the last column.
  • FIG. 78 is an illustration of parity check matrices H of the LGE symbols (16k, 6/15), (16k, 7/15), (16k, 9/15), (16k, 11/15), and (16k, 13/15).
  • the column weight is set to X1 for KX1 columns of the parity check matrices H of the LGE symbols (16k, 6/15), (16k, 7/15), (16k, 9/15), (16k, 11/15), and (16k, 13/15) starting from the 1st column, the column weight is set to X2 for KX2 columns subsequent thereto, the column weight is set to Y1 for KY1 columns subsequent thereto, the column weight is set to Y2 for KY2 columns subsequent thereto, the column weight is set to 2 for M ⁇ 1 columns subsequent thereto, and the column weight is set to 1 for the last column.
  • FIG. 79 is an illustration of parity check matrices H of the LGE symbols (64k, 10/15).
  • the column weight is set to X1 for KX1 columns of the parity check matrices H of the LGE symbols (64k, 10/15) starting from the 1st column, the column weight is set to X2 for KX2 columns subsequent thereto, the column weight is set to Y1 for KY1 columns subsequent thereto, the column weight is set to Y2 for KY2 columns subsequent thereto, the column weight is set to 2 for M ⁇ 1 columns subsequent thereto, and the column weight is set to 1 for the last column.
  • the numbers KX1, KX2, KY1, KY2, and M of columns and column weights X1, X2, Y1, and Y2 are set as illustrated in FIG. 79 .
  • FIG. 80 is an illustration of parity check matrices H of the NERC symbols (64k, 9/15).
  • the column weight is set to X1 for KX1 columns of the parity check matrices H of the NERC symbols (64k, 9/15) starting from the 1st column, the column weight is set to X2 for KX2 columns subsequent thereto, the column weight is set to Y1 for KY1 columns subsequent thereto, the column weight is set to Y2 for KY2 columns subsequent thereto, the column weight is set to 2 for M ⁇ 1 columns subsequent thereto, and the column weight is set to 1 for the last column.
  • the numbers KX1, KX2, KY1, KY2, and M of columns and column weights X1, X2, Y1, and Y2 are set as illustrated in FIG. 80 .
  • FIG. 81 is an illustration of a parity check matrix H of an ETRI symbol (16k, 5/15).
  • the code length N is 16200 and the encoding rate r is 5/15
  • FIG. 82 is an illustration of parity check matrices H of ETRI symbols of (64k, 5/15), (64k, 6/15), and (64k, 7/15).
  • FIGS. 83 to 104 are illustrations of examples of constellation types employed in the transmission system of FIG. 7 .
  • a constellation used in MODCOD can be set to MODCOD serving as a combination of a modulation scheme and an LDPC code.
  • the LDPC codes can be classified into 9 types of LDPC codes in which the encoding rate r is 5/15, 6/15, 7/15, 8/15, 9/15, 10/15, 11/15, 12, 15, and 13/15 according to the encoding rate r (regardless of the code length N), and a combination of the 9 types of LDPC codes (each of the LDPC codes in which the encoding rate r is 5/15, 6/15, 7/15, 8/15, 9/15, 10/15, 11/15, 12, 15, and 13/15) and each modulation scheme can be employed as MODCOD.
  • one or more of constellations can be set to MODCOD of 1 using the modulation scheme of MODCOD.
  • the constellations include uniform constellations (UCs) in which an arrangement of signal points is uniform, and non uniform constellations (NUCs) in which an arrangement of signal points is not uniform.
  • UCs uniform constellations
  • NUCs non uniform constellations
  • NUCs examples include a constellation called a 1-dimensional M 2 -QAM non-uniform constellation (1D NUC) and a constellation called a 2-dimensional QQAM non-uniform constellation (2D NUC).
  • 1D NUC 1-dimensional M 2 -QAM non-uniform constellation
  • 2D NUC 2-dimensional QQAM non-uniform constellation
  • the 1D NUC is better in the BER than the UC
  • the 2D NUC is better in the BER than the 1D NUC.
  • a constellation in which the modulation scheme is QPSK is the UC.
  • the 2D NUC can be employed as the constellation in which the modulation scheme is 16QAM, 64QAM, 256QAM, or the like
  • the 1D NUC can be employed as the constellation in which the modulation scheme is 1024QAM, 4096QAM, or the like.
  • NUC 2 m _r a constellation of an NUC used in MODCOD in which the modulation scheme is a modulation scheme in which an m-bit symbol is mapped to any of 2 m signal points, and an encoding rate of an LDPC is r.
  • NUC_16_6/15 indicates a constellation of an NUC used in MODCOD in which the modulation scheme is 16QAM (or the modulation scheme in which a symbol is mapped to any of 16 signal points), and the encoding rate r of the LDPC code is 6/15.
  • the modulation scheme is QPSK
  • the same constellation is used for each encoding rate r of the LDPC code.
  • the modulation scheme is 16QAM, 64QAM, or 256QAM
  • a different constellation of a 2D NUC is used according to each encoding rate r of the LDPC code.
  • the modulation scheme is 1024QAM or 4096QAM
  • a different constellation of a 1D NUC is used according to each encoding rate r of the LDPC code.
  • FIG. 87 and FIG. 88 are illustrations of examples of a constellation of a 1D
  • a horizontal axis and a vertical axis are an I axis and a Q axis
  • Re ⁇ x 1 ⁇ and Im ⁇ x 1 ⁇ indicate a real part and an imaginary part of a signal point x 1 serving as coordinates of the signal point x 1 .
  • a numerical value written after “for CR” indicates the encoding rate r of the LDPC code.
  • FIG. 89 is an illustration of an example of coordinates of a signal point of a
  • “Input cell word y” indicates a 2-bit symbol that is mapped to a UC of QPSK
  • Constellation point z q indicates coordinates a signal point z q .
  • An index q of the signal point z q indicates a discrete time (a time interval between a certain symbol and a next symbol) of a symbol.
  • NUC_2 m _r indicates coordinates of a signal point of a 2D NUC used when the modulation scheme is 2 m QAM, and the encoding rate of the LDPC code is r.
  • w#k indicates coordinates of a signal point of a first quadrant of the constellation.
  • a signal point of a second quadrant of the constellation is arranged at a position to which the signal point of the first quadrant has moved symmetrically to the Q axis
  • a signal point of a third quadrant of the constellation is arranged at a position to which the signal point of the first quadrant has moved symmetrically to an origin.
  • a signal point of a fourth quadrant of the constellation is arranged at a position to which the signal point of the first quadrant has moved symmetrically to the I axis.
  • the modulation scheme is 2 m QAM
  • m bits are used as one symbol, and one symbol is mapped to a signal point corresponding to the symbol.
  • a suffix k of w#k has an integer value within a range of 0 to b ⁇ 1, and w#k indicates coordinates of a signal point corresponding to the symbol y(k) within the range of the symbols y(0) to y(b ⁇ 1).
  • coordinates of a signal point corresponding to the symbol y(k+b) within the range of the symbols y(b) to y(2b ⁇ 1) are indicated by ⁇ conj(w#k), and coordinates of a signal point corresponding to the symbol y(k+2b) within the range of the symbols y(2b) to y(3b ⁇ 1) are indicated by conj(w#k). Further, coordinates of a signal point corresponding to the symbol y(k+3b) within the range of the symbols y(3b) to y(4b ⁇ 1) are indicated by ⁇ w#k.
  • conj(w#k) indicates a complex conjugate of w#k.
  • a column of NUC_1k_r indicates a value of u#k indicating the coordinates of the signal point of the 1D NUC used when the modulation scheme is 1024QAM, and the encoding rate of the LDPC code is r.
  • u#k indicates the real part Re(z q ) and the imaginary part Im(z q ) of the complex number serving as the coordinates of the signal point z q of the 1D NUC.
  • FIG. 95 is an illustration of a relation between the symbol y of 1024QAM and u#k serving as each of the real part Re(z q ) and the imaginary part Im(z q ) of the complex number indicating the coordinates of the signal point z q of the 1D NUC corresponding to the symbol y.
  • the 10-bit symbol y of 1024QAM is assumed to be indicated by y 0,q , y 1,q , y 2,q , y 3,q , y 4,q , y 5,q , y 6,q , y 7,q , y 8,q , and y 9,q from the first bit (the most significant bit).
  • a of FIG. 95 illustrates a correspondence relation between 5 odd-numbered bits y 0,q , y 2,q , y 4,q , y 6,q , y 8,q of the symbol y and u#k indicating the real part Re(z q ) (of the coordinates) of the signal point z q corresponding to the symbol y.
  • B of FIG. 95 is a correspondence relation between 5 even-numbered bits y 1,q , y 3,q , y 5,q , y 7,q , and y 9,q of the symbol y and u#k indicating the imaginary part Im(z q ) (of the coordinates) of the signal point z q corresponding to the symbol y.
  • each column indicates a value of u#k indicating the coordinates of the signal point of the 1D NUC used when the modulation scheme is 4096QAM and the encoding rates r of the LDPC codes are 5/15, 6/15, 7/15, 8/15, 9/15, 10/15, 11/15, 12, 15, and 13/15.
  • u#k indicates the real part Re(z q ) and the imaginary part Im(z q ) of the complex number serving as the coordinates of the signal point z q of the 1D NUC.
  • FIG. 97 is an illustration of a relation between the symbol y of 4096QAM and u#k serving as each of the real part Re(z q ) and the imaginary part Im(z q ) of the complex number indicating the coordinates of the signal point z q of the 1D NUC corresponding to the symbol y.
  • a method of obtaining the coordinates of the signal point of the 1D NUC of 4096QAM using FIGS. 96 and 97 is the same as the method of obtaining the coordinates of the signal point of the 1D NUC of 1024QAM using FIGS. 94 and 95 , and thus a description thereof is omitted.
  • FIG. 98 is an illustration of another example of the constellation of the 2D NUC for each of the 9 types of encoding rates r of the LDPC codes when the modulation scheme is 16QAM.
  • FIG. 99 is an illustration of another example of the constellation of the 2D NUC for each of the 9 types of encoding rates r of the LDPC codes when the modulation scheme is 64QAM.
  • FIG. 100 is an illustration of another example of the constellation of the 2D NUC for each of the 9 types of encoding rates r of the LDPC codes when the modulation scheme is 256QAM.
  • FIGS. 98 to 100 similarly to FIGS. 83 to 88 , a horizontal axis and a vertical axis are the 1 axis and the Q axis, and Re ⁇ x 1 ⁇ and lm ⁇ x 1 ⁇ indicate the real part and the imaginary part of the signal point x 1 serving as the coordinates of the signal point x 1 . Further, in FIGS. 98 to 100 , a numerical value written after “for CR” indicates the encoding rate r of the LDPC code.
  • FIG. 101 is an illustration of another example of the coordinates of the signal point of the 2D NUC of FIG. 98 used for each of the 9 types of encoding rates r of the LDPC codes when the modulation scheme is 16QAM.
  • FIG. 102 is an illustration of another example of the coordinates of the signal point of the 2D NUC of FIG. 99 used for each of the 9 types of encoding rates r of the LDPC codes when the modulation scheme is 64QAM.
  • FIGS. 103 and 104 are illustrations of another example of the coordinates of the signal point of the 2D NUC of FIG. 100 used for each of the 9 types of encoding rates r of the LDPC codes when the modulation scheme is 256QAM.
  • NUC_2 m _r indicates the coordinates of the signal point of the 2D NUC used when the modulation scheme is 2 m QAM, and the encoding rate of the LDPC code is r, similarly to FIGS. 90 to 93 .
  • the signal points of the 1D NUC are arranged in a grid form on a straight line parallel to the I axis or a straight line parallel to the Q axis. However, an interval between the signal points is not constant. Further, when the signal point (the mapped data) is transmitted, average power of the signal points on the constellation is normalized. The normalization is performed by multiplying each signal point z q on the constellation by a reciprocal 1/( ⁇ P ave ) of a square root ⁇ P ave of a root mean square value P ave when a root mean square value of an absolute value for (coordinates of) all signal points on the constellation is indicated by P ave .
  • FIG. 105 is a block diagram illustrating a configuration example of the block interleaver 25 of FIG. 9 .
  • the block interleaver 25 includes a storage region called a part 1 and a storage region called a part 2 .
  • Each of the parts 1 and 2 is configured such that a number C of columns equal in number to the number m of bits of the symbol and serving as storage regions that store one bit in the row (horizontal) direction and store a predetermined number of bits in the column (vertical) direction are arranged.
  • R 1 the number of bits (hereinafter, also referred to as a part column length) that are stored in the column direction by the column of the part 1 is indicated by R 1
  • R 2 the part column length of the column of the part 2 is indicated by R 2
  • N the code length of the LDPC code of the block interleave target.
  • the part column length R 1 is equal to a multiple of 360 bits serving as the unit size P
  • the part column length R 2 is equal to a remainder when a sum (hereinafter, also referred to as a column length) R 1 +R 2 of the part column length R 1 of the part 1 and the part column length R 2 of the part 2 is divided by 360 bits serving as the unit size P.
  • the column length R 1 +R 2 is equal to a value obtained by dividing the code length N of the LDPC code of the block interleave target by the number m of bits of the symbol.
  • the part column length R 2 of the part 2 is 90 bits.
  • FIG. 106 is an illustration of the number C of columns of the parts 1 and 2 and the part column lengths (the number of rows) R 1 and R 2 for a combination of the code length N and the modulation scheme.
  • FIG. 106 illustrates the number C of columns of the parts 1 and 2 and the part column lengths R 1 and R 2 for combinations of the LDPC code in which the code length N is 16200 bits and the LDPC code in which the code length N is 64800 bits and the modulation schemes of QPSK, 16QAM, 64QAM, 256QAM, 1024QAM, and 4096QAM.
  • FIG. 107 is an illustration of the block interleave performed by the block interleaver 25 of FIG. 105 .
  • the block interleaver 25 performs the block interleave by writing the LDPC code in the parts 1 and 2 and reading the LDPC code from the parts 1 and 2 .
  • writing of the code bits of the LDPC code of one code word downward (in the column direction) in the column of the part 1 is performed from the column at the left side to the column at the right side as illustrated in A of FIG. 107 .
  • the reading of the code bits from all the C columns of the part 2 is sequentially performed toward a row therebelow and the reading is performed up to an R 2 row serving as the last row.
  • the code bits read from the parts 1 and 2 in units of m bits are supplied to the mapper 117 ( FIG. 8 ) as the symbol.
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