WO2004004132A1

WO2004004132A1 - Iterative decoding method and apparatus for product code based on adjoint formula

Info

Publication number: WO2004004132A1
Application number: PCT/CN2002/000457
Authority: WO
Inventors: Zongwang Li
Original assignee: Linkair Communications,Inc.
Priority date: 2002-07-01
Filing date: 2002-07-01
Publication date: 2004-01-08
Also published as: CN1555603A; AU2002320749A1

Abstract

The present invention provides an iterative decoding method and apparatus for product code. The method and apparatus are based on adjoint formula. By using a series of high speed parallel algorithm processing, i.e. two dimensional high speed sort processing, q-mode search processing based on table search, and high speed calculate processing of external information value, the hardware is make to realize high speed iterative decoding of product code and thus high speed data communications are realized.

Description

Method and device for iterative decoding of adjoint product codes

The present invention belongs to the field of communication technology, and particularly relates to decoding of a cascaded linear block code in a digital communication system, and in particular to an iterative decoding method and device based on an adjoint product code.

Background technique

Channel error correction coding is an important part of the communication system, and linear block codes are an important type of channel error correction coding. A linear block code is usually expressed as C («, /« :, which contains information bits and redundant bits, where each redundant bit is a linear combination of // <: information bits, the minimum Hamming distance is d, and the code rate is ? = yt / M. The Hamming code is a linear block code with a code length of "= ² "'-1 and information bits of "= 2"'-m-1 to correct a single error. If an even number is added to the Hamming codeword, Or odd check bits constitute the extended Hamming code. BCH codes (codes invented by Bose, Ray-Chaudhuri, and Hocquenghem respectively) are linear block codes that can correct multiple errors. If an even or odd check is added to the BCH code word The bits constitute the extended BCH code.

Concatenated codes can enhance error correction performance. Concatenated block codes are long codes formed by concatenating two or more linear block codes. A product code is a special concatenated block code. Its codeword is a matrix, which consists of row and column subcodes. [C (n, k, d) J represents that the row and column subcodes are product codes of linear block codes C (n, k, d); C {nk _x , d _x ) xC {n ₂ , k ₂ , d ₂ ) means that the row subcode is a linear block code C (n „k _x , d,) and the column subcode is a product code of the linear block code C (,, / ^ ₂ ). Iterative decoding uses soft input values and external information The value is decoded and a soft output value is generated. A new external information value is calculated based on the soft output value and fed back to the input of the decoder to decode again.

With the application of iterative decoding algorithms, product codes have once again received attention. In recent years, iterative decoding has been widely used due to its powerful error correction performance and low complexity. In the iterative decoding process, the decoder not only outputs the hard decision value of the information bits, but also the reliable value of the decoded information bits. Therefore, in order to achieve high-speed data communication, it is necessary for the hardware to implement iterative decoding of the product code at high speed. SUMMARY OF THE INVENTION The object of the present invention is to provide an iterative decoding method and device based on adjoint product codes, which are processed by a series of high-speed parallel algorithms, namely: optimized two-dimensional fast sorting processing, and q-pattern search based on table lookup Processing, and fast calculation processing of external information values, so that the hardware implements iterative decoding of the product code at high speed, thereby achieving high-speed data communication.

The object of the present invention is achieved by the following technical solutions:

An iterative decoding method for a product code based on an adjoint type is characterized in that when iteratively decoding a product code, a binary subcode of the product code needs to be decoded, and the binary subcode is decoded. It is necessary to satisfy the conditions for decoding binary linear block codes with adjointness; obtain soft output values and external information values; use the obtained soft output values and external information values to implement iterative decoding of a product code with an arbitrary number of iterations. The decoding of the binary subcodes of the product code refers to: decoding the binary row and column subcodes of the product code.

The conditions for decoding an adjoint binary linear block code include:

Soft input value SI of the input symbol vector;

Compute a hard decision binary sequence b of a symbol vector;

According to the obtained hard decision binary sequence b and the corresponding check matrix H, the adjoint vector S = Hb ^{T is obtained} ;

If s = o, the hard-decision binary sequence is the soft-decision decoded codeword e, and the decoding is completed; marking the least reliable symbol position in the soft input vector, and also the lightest-weight column vector in the check matrix H Position, where / ≤w- / _c ;

Find all-patterns of ^ d and their position set ^, satisfy the adjoint condition

(∑ei _y ^h /) ^{≡S mo} d 2 and position condition ^;. { ₀ , _Α , ··, Α— ^, xe {0, l,-, nl}, where h _; is the check matrix The ith column vector of H is one of the least reliable symbols in the soft input vector One of the positions

If the -mode is not found, the decoding failure flag is set and the decoding ends;

Calculate the weight of the pattern, that is, calculate the weight corresponding to the set of column vector labels of the check matrix H ^ | ^ /) _; |, and then store these weight values and the corresponding set of positions; find the set with the smallest weight

The binary symbols corresponding to the positions of the set in the hard decision binary sequence b are complemented to obtain the soft decision decoding codeword e, and the decoding ends.

The method for iterative decoding of a product code based on an adjoint type includes the steps of: when iteratively decoding a product code, decoding a binary row sub-code and a column sub-code of the product code, and meeting the following requirements: Conditions:

Soft input value SI of the input symbol vector;

Compute a hard decision binary sequence b of a symbol vector;

According to the obtained hard decision binary sequence b and the corresponding check matrix H, an adjoint vector S = Hb ^{T is obtained} ;

If s = o, the hard-decision binary sequence is the soft-decision decoded codeword e, and the decoding ends; find the 7 least reliable symbol positions in the soft input vector, and also the lightest-weight column vector in the check matrix H Location, where

Find all-patterns of ≤d and their set of locations, satisfying the adjoint condition

(∑; _ei ^h ') ^≡S mod 2 and position condition ^; {ρ ₀ , ··, Α— "4, ^ e {0, l, ---, nl}, where h ,. is the face correction matrix The ith column vector of H is one of the least reliable symbol positions in the soft input vector;

If the mode is not found, the decoding failure flag is set and the decoding ends;

Calculate the weight of the pattern, that is, calculate the weight of the set ^ corresponding to the column vector label of the check matrix H = ∑ ^ | ^ /) |, and then store these weight values and the corresponding set of positions; find the one with the smallest weight set; Complement the binary symbols in the hard decision binary sequence b corresponding to the positions of the set J, “, to obtain the soft decision decoding codeword e, and the decoding ends;

The steps for deriving the soft output value and external information value are:

When S is not equal to 0 and the decoding failure flag is not set, look for "bu Jing contention code word" from the output column of the above subcode decoding;

Calculate the soft output value {SO) _j = {SI) _j + {2c _J -l) when "j-competitive codeword" does not exist, or S = 0, where S / is the Jth The soft input value of 'symbols, (S /) _; =, ^ is the soft information value output by the demodulator at the first iteration; at other iterations,

(SI) j = iij + a _Wj , calculate the external information value w _; = (SO) j-(SI) j;

When there is a "j-competition codeword", select the "bu-contest codeword" with the smallest weight, calculate the soft output value (S6> = ( _-m ) (2cj -l), and calculate the external information value. = 0SO- SJ;

When a decoding failure flag has been set in the above-mentioned subcode decoding process, calculate the external information value = 0; use the obtained soft output value and external information value to decode other row or column subcodes; wait for all rows After the subcode decoding is completed, the new external information value is used to form a new soft input value to decode all column subcodes; the row subcode and column subcode are alternately decoded to implement iterative decoding of the product code of any number of iterations.

The finding the most unreliable symbol position in the soft input vector refers to: The two-dimensional fast partial sorting method suitable for hardware implementation can be used to find the most unreliable symbol position in the soft input vector. The steps include:

First, the one-dimensional array to be sorted constitutes a two-dimensional array. For example, a soft input sequence of subcodes of n = 128 can form an _{8 x 16} two-dimensional array.

Using the traditional parallel comparison sorting method, all rows of a two-dimensional array are sorted at the same time, and then all its columns are sorted at the same time.

The most / reliable symbol positions required can be obtained by comparing at most / times; for a χθ two-dimensional array, it takes up to + 0 + / clock cycles to complete the required sorting.

Finding all "patterns ≤ rf" and their set of positions satisfying the adjoint condition (∑ _;. _{Ei /} h ,.) _≡ S mod 2 and positional conditions refer to: The implementation steps using high-speed hardware based on look-up table are as follows:

Before decoding, according to the check matrix of the linear block code c, an anti-adjoint table and an adjoint table for correcting a single error are stored, where: the error position corresponding to the adjoint, if the adjoint cannot locate a single error, The corresponding position is set to the -1 flag, requiring a total of "l ₀ g ₂ n]. (2"- ^{/ £} -1) bits; the accompanying formula corresponding to the error position requires a total of "("- ^{/ c} ) bits;

Determine the single error location according to the obtained S inverse inverse table. If the position flag is not -1, a-pattern is found, where: = 1; otherwise, it means that there are multiple position errors; For unreliable symbol positions, determine other-patterns, where _{≤ £} ; when seeking-patterns, where g = 2, first check the adjoint table to determine the adjoint S _l with an error in one of the least reliable symbol position sets. ₅ then find S ^ S® ^, and finally ₂ S trans verified by the error syndrome table to determine a position, if the position flag is not -1, to find a - mode (g = 2), when taken to meet the different values of the condition, Repeat the above steps to find all the modes that meet the decoding conditions.

The step of deriving the soft output value and the external information value may further include:

If "-competitive codeword" is found, the soft output value is: ("¾ = [^ (.)-( _Min )] (2-1); , Then, the soft output value is approximately calculated as:

(SO) _j = (SI) _J + fi (2c _J -l);

If the decoding of the subcode fails, the soft output value is set to: (SO = (W;

The external information value is: = oso)-OS.;

For the above formula, the external information value is used for fast processing. When the-pattern search is completed, all the calculation of the bit external information value can be completed in parallel within 1 clock cycle, but 2 (+ ² ) · «bit storage unit is required. b is the number of quantization bits of the soft input value, and the processing steps are as follows: Initialize the two sets of depth as ", width + 2 or ^ + 3, where the extended Hamming code is qb + 2, and the extended BCH code is b + 3 Memory cells W and ^Wim '; initialized to "" and width to 1-bit flag word, and set w _min = 2 ^{? I +} 2-1, failure = 1)

W {i) = 2 " ^{b + 2-} \

W ^inv (i) = 2 ^{q 2-} \, 0 <i≤n

fl g (i) =

During the subcode decoding process, every time a pattern is found, the following formula is used to update w, W ' ^w , flag and ^w min' and set failure = 0:

fl gii) =, if i & L _q

W (i) = (L _q ), if W i)> w (L _q ) and ieL _q

W ^inv {i) = {L _q ), if W ⁱ ' ⁿ '{i)> (L _q ) and HL _q -After the pattern search is completed, calculate the external information value according to the following formula:

if failure == 1 w ,. = 0 for all Q≤i <n- \

else if flag (i) == 0 w _; = (2b _t -1)

else if W (i)> w _n , _n w _{ = (W (i) -w _mil ,) {(2b _i一 1))-Λ ()

else if W ^inv (i) ≠ 2 ^ ² -l _W;. ) (l-2b _; )-Λ ( _ζ .)

else w. = βθ, -ΐ ^) where is a binary hard decision value.

An iterative decoding device based on an adjoint product code, which includes: an input-output module, an adjoint calculation module, a selection ordering module, a -pattern search module, an external information value calculation module, and a storage module;

Input data and control signals are inputs to the input and output modules;

The input / output module stores the input data in the storage module;

The input / output module inputs data to the adjoint calculation module and the selection sorting module

The adjoint calculation module, the selection sorting module and the storage module respectively input data to the q-pattern search module;

-The pattern search module inputs data to the external information value calculation module;

The external information value calculation module feeds back signals to the input and output modules;

The input and output modules output data and status signals. The input / output module includes at least a soft input value calculation module;

The soft input value calculation module calculates the soft input value SI of each iteration of the decoder based on the soft information value U input and the external information value w generated during the decoding process, and the reliable value | si | and Binary hard decision sequence b.

The storage module may include: a data storage dual-port RAM, an accompanying table module, and an anti-adjoint table module;

The input-output module stores the input data in the data storage dual-port RAM; the adjoint table module and the anti-adjoint table module respectively input data to the q-pattern search module.

The beneficial effect of the present invention is that, by providing an iterative decoding method and device for a product code based on an adjoint type, it is possible to ensure that the product code subcode generates an optimized codeword list, and quickly calculates a code character number to output soft information, thereby having good Decoding performance and high decoding speed. This enables high-speed data communication.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is a flowchart of a binary linear block code decoding method;

FIG. 2 is a flowchart of a decoding method of a product code;

FIG. 3 is a hardware implementation block diagram of the device according to the present invention;

Figure 4 is a schematic diagram of the quick sort algorithm;

Fig. 5 is a comparison diagram of the decoding performance when the product code formed by the extended BCH code [C (64,51,6)] 2 is decoded 6 times.

detailed description

A method for iterative decoding of a product code based on an adjoint type, which is specifically implemented as follows: when iteratively decoding a product code, a binary subcode of the product code needs to be decoded, and The decoding needs to satisfy the conditions for the decoding of the binary linear block code with adjointness; obtain the soft output value and the external information value; use the obtained soft output value and the external information value to realize the iterative decoding of the product code with an arbitrary number of iterations. As shown in FIG. 1, the adjoint is used to decode binary linear block code The code steps include:

At step 1QQ, the decoding method starts.

In step 101, a symbol soft input value vector SI is input.

In step 102, a symbol vector hard decision binary sequence b is calculated.

In step 103, according to the obtained hard decision binary sequence b and the corresponding check matrix H, an adjoint vector S = Hb ^{T is} calculated.

In step 104, it is determined whether S is not equal to zero.

If the judgment result of step 104 is that S is not equal to 0, the process proceeds to step 105, otherwise proceeds to step 112.

In step 105, mark the soft input vector (usually ≤ «-the most unreliable symbol positions, and also the lightest weighted column vector position in the check matrix H).

In step 106, find all / of "patterns and their location set L, satisfying the adjoint condition

∑. _Ei h ₍ .) ≡S mod 2 and position condition ^; ο, Α, ··, ^, ^, xe {0, l, —, w— 1}, where is the first The column vector is one of the least reliable symbol positions in the soft input vector.

In step 107, it is determined whether a-pattern is found.

If the determination result of step 107 is yes, that is, a-pattern is found, the process proceeds to step 109, otherwise proceeds to 108.

In step 108, that is, if the -mode is not found, the decoding failure flag is set, and the process proceeds to step 113.

In step 109, the weight of the-pattern is calculated, that is, the weight corresponding to the set of column vector labels of the check matrix H is calculated. Then store these weight values and corresponding bits

Home collection.

At step 110, find the set J, with the smallest weight. At step 111, for the binary symbol corresponding to the position of the set ^ in the hard decision binary sequence b Complement the number, and thus obtain the soft decision decoding codeword S

In step 112, the hard decision binary sequence b is the required soft decision decoding codeword 5. In step 113, the decoding ends.

As shown in Figure 2, the steps of iterative decoding based on the adjoint product code are:

At step 200, the decoding method starts.

In step 201, the log-likelihood value of each symbol is input from the demodulator, and these received symbols are grouped into a vector of length < ₂ to form an array of X n ₂ .

In step 202, set i = 0, the number of iterations, iter = 0, w = 0, η = _ηι (the number of row _subcodes and η ₂ the number of column subcodes) and dec_stop = l

In step 203, calculate the soft input value array = ^ + where α is the weighting factor of the iter iteration, which takes into account the different variances of the sample values SI and w.

In step 204, the i-th row (or column) subcode is decoded. The specific decoding process has been described in detail in FIG.

In step 205, it is determined whether S is not equal to 0

If the judgment result of step 205 is that S is not equal to 0, the process proceeds to step 206, otherwise proceeds to step 211

At step 206, set dec_stop = 0

In step 207, it is determined whether a decoding failure flag is set.

If the judgment result of step 207 is that the decoding failure flag is set, the process proceeds to step 213, otherwise proceeds to step 208

During the iterative decoding process, two codewords are required to calculate the soft output value of a symbol. In step 204, that is, in the flowchart shown in FIG. 1, if the decoding of the subcode is successful, one of the codewords is obtained, which is recorded as e and a position set corresponding to the minimum weight, and e is applied to all code characters. Calculation of No. soft output value. If the binary numbers of positions in the hard decision binary sequence b corresponding to all elements in the set of other positions are complemented, a series of codewords can be obtained, which are useful in the calculation of soft output values. In the calculation of the soft output value of the symbol, another For the calculation of the soft output value of the J'th symbol of the codeword, the J'th symbol of this codeword is required to be different from the J'th symbol of e, and it is called "j-competition codeword". If there are multiple "competitive contention codewords" in the above decoding method, then take the codeword with the smallest set of corresponding position weights, and record it as the corresponding minimum set of position weights 4. The soft output value is calculated as follows:

(SO) _t =-(SI- (2c ^w -l) ^2- || si- (2c-l

4 'If there is no "j-competitive codeword" in the above decoding method, if s = o, it can be considered that the reliability of the decoding output is large, and the soft output value can be approximately calculated as:

(SO) _j = (SI) _J + {2c _j- \)

/? Can be a constant, or it can be dynamically modified during decoding.

If the subcode decoding fails, set the external information value _w = 0; otherwise, the external information value is calculated as follows:

w _J = (SO) _j- (SI) _j

Therefore, the soft input value of the next iterative decoding can be obtained as follows: a is a weighting factor, which is a positive factor considering the different standard deviations of the SI and w samples.

Based on the above analysis, in the iterative decoding flowchart shown in FIG. 1, after step 207, the following steps are performed.

In step 208, look for "j-contest codeword '" from the decoded output column of step 204.

In step 209, it is determined whether "j-competitive codeword" exists.

If the judgment result of step 209 is that "j-competition codeword" exists, the process proceeds to step 210, otherwise proceeds to step 212.

In step 210, the selected smallest weight ¹¹ j- competitive codeword. "

In step 211, calculate the soft output value (SO = (.-^,) (2 -1). At step 212, calculate the soft output value (SO) _; = 0S. + (2 -l), where is a constant. In step 213, the sub-decoding fails, and the external information value is set to 0.

In step 214, the external information value _w; = 0SO)-(5¾) is calculated.

In step 215, it is determined whether i <n holds.

If the judgment result of step 216 is yes, proceed to step 215, otherwise proceed to step

217.

In step 216, i is incremented by one, and then returns to step ¾ 204 to decode other rows or columns in the input array.

In step 217, it is judged whether 11 = ^ is true, that is, it is judged to be odd or even iteration.

If the determination result of step 217 is YES, proceed to step 220. Otherwise, proceed to step 218.

In step 218, it is determined whether iter <Max—iter or dec_stop = 1, that is, whether it has reached a predetermined number of iterations and whether the decoded codeword is error-free.

If the determination result of step 218 is YES, proceed to step 219. Otherwise, proceed to step 221.

In step 219, n is assigned a value of _ηm . And set i to 0, increment iter by 1, dec_stop = l, and go to step 203.

In step 220, n is assigned a value of n ₂ . And set i to 0, and go to step 203. In step 221, the hard decision output decodes the soft output value array and proceeds to step 222.

At step 222, the iterative decoding ends.

An iterative decoding method for product codes based on an adjoint type, which includes: an input-output module, an adjoint calculation module, a selection sorting module, a 2-mode search module, an external information value calculation module, and a storage module; input data and control signals Is the input of the input-output module; the input-output module stores the input data in the storage module; the input-output module inputs data to the adjoint calculation module and the selection sorting module; the adjoint calculation module, the selection sorting module and the storage module respectively enter the mode Search module input data;-pattern search module inputs data to external information value calculation module; The external information value calculation module feeds back signals to the input and output modules; the input and output modules output data and status signals. As shown in Figure 3: The black arrows in the figure indicate the data flow direction. The decoder consists of an input-output module, a companion calculation module, a selection sorting module, a pattern search module, an external information value calculation module, and a storage module. The functions of each module are described below:

The input data and control signals are input to the input / output / control module 300 of the decoder, and the decoding parameters of the decoder are initialized according to the control signals, and the anti-adjoint table of single errors is stored according to the check matrix of the linear block code. (The position of the error corresponding to the incident. If the incident cannot locate a single error, the corresponding position is set to the -1 flag, which requires a total of "1ο ^ · (2"-1) bits.) And the incident table (corresponding to the position of the error). A total of "(«-/ 0 bits) is required to store the input data; the input data is stored in the data storage dual-port RAM 302. The soft input value calculation unit in the module 300 is based on the input soft information value 11 and the decoding process. The generated external information value w (0 in initial decoding) is calculated to obtain the soft input value si of each iteration of the decoder. According to the soft input, a reliable value | si | (the absolute value of the soft input value) and binary hard Decision sequence b.

Reliable value | SI | is input to module 304 to find the location set with the smallest reliable value. A, This step is one of the key steps affecting the decoding speed, and an optimized fast sort algorithm needs to be adopted. The decoding algorithm based on the adjoint subcode does not need to sort the entire soft input sequence. It only needs to select the least reliable symbol position. Consider using a simple parallel comparison sort algorithm. Through the analysis of some sorting algorithms, a two-dimensional fast partial sorting algorithm suitable for hardware implementation is invented as shown in Figure 4. The sorting process is as follows:

First, the one-dimensional array to be sorted is formed into a two-dimensional array. For example, a soft input sequence of n = 128 _subcodes can form a two-dimensional array of _{8 x l6} .

Using a traditional parallel comparison sorting algorithm, all rows of a two-dimensional array are sorted simultaneously, and then all its columns are sorted simultaneously.

Through the comparison at most / times, the required / unreliable symbol positions can be found. for. Two-dimensional array, up to +. + Z clock cycles will complete the required sequencing. For example, suppose 128 input data X = [30 7 19 15 28 24 14 0 26 14 19 25 29 5 12 29 29 13 28 1 11 26 0 4 6 6 19 8 6 0 23 14 29 14 1 3 27 16 6

21 26 0 21 12 26 16 22 13 9 6 6 21 9 17 4 22 12 27 27 18 15 28 26 20

26 21 10 9 10 17 23 9 26 18 11 22 17 14 22 19 25 30 16 28 5 31 8 8

28 23 4 0 28 6 9 21 9 15 2 31 18 13 16 10 1 3 7 18 24 16 20 6 12 25 21 14 18 25 1 19 1 13 9 27 0 24 31 31 25], Table 1 shows the above rapid Sorting results of partial sorting algorithms. From Table 1, a simple comparison operation can be used to find the minimum value.

Table 1

The binary hard decision sequence b is input to the module 305 and its adjoint S is calculated.

The location set, _Α , and the adjoint S are input to the module 306, and the _g -pattern search algorithm designed by the application is used to look up the adjoint table 307 and the anti-adjoint table 308 to find the position set of all -patterns that satisfy the condition Location conditions. This step is one of the key steps affecting the decoding speed, and is the core of the subcode adjoint decoding. Considering the hardware structure, in order to facilitate high-speed decoding, a table-based high-speed hardware implementation algorithm is used. The process is as follows: For the obtained / reliable symbol positions, determine other modes (^ _{≤ί /} ). For example, find the pattern = 2), first check the adjoint table to determine the adjoint with a certain error in the least reliable symbol position set. S ,, then find s ^ S® ^, and finally check the anti-adjoint table by 8 ₂ to determine the error position. If the position flag is not -1, a-pattern is found (= 2). Repeat repeatedly to find all-patterns that meet the conditions of decoding step d.

-During pattern search, simultaneously initialize two sets of storage units W and W 'with depth n and width qbYl or qb + 3 (extended Hamming code b + 2, extended BCH code qb + 3) " ¹ '; Initialize flag flag with a depth of "1" and a width of 1 bit. Let w _niin = 2 " ^{b + 2} -1 and failure = 1.

W (i) = 2 ^{≠ + 2} -l

W ^inv (i) = 2 ^{≠ + 2} -l, 0≤i≤n Every time a-pattern is found, update W, W '" ^v , flag, and w _{niill as follows} . And set / a7wre = 0. flag (i ) = l, if ie L _q

W (i) = (L _q ), if W (i)> (L _q ) and ieL _q

W "' ^v (i) = {L _q ), if W ^inv (i)> {L _q ) and ig L _q if w _min > {L _q )-After the pattern search is completed, W, W'" ^v , flag , „And _ / ¾½ are input to the external information calculation module 309, and the external information values of all code character numbers are calculated in parallel according to the following formula.

if failure = 1 w _i = 0 for all 0≤i≤nl

else if flag (i) == 0 w _t = β (2 ^ -1)

le if W (i)> w ^ _n - _Wmin ) ((2b ,. -1))-Λ (.)

elseif W ^im {i) ≠ V ^M- \ w _t = (W " ^V ^ -w ^ il-lb ^ -A ^)

else = ^ (1-26;)

Where is the binary hard decision value.

After the external information value calculation is completed, it is input to the module 300 and written into the external information value storage dual-port RAM 302.

The control unit of the module 300 determines the row subcode and column subcode decoding according to the input control information and the decoding status, and starts and terminates the decoding process.

Simulation results: Here is a product code with the extended BCH code C (64,51,6) as the subcode [C (64,51,6) f. Simulation results using BPSK modulation on an additive white Gaussian channel. First, some parameters of the iterative decoding method will be determined.

Scale factor In the simulation, the external information value | _w | does not need to be normalized, and the column factor α = 0.5.

Reliability factor: It is fixed during each iterative decoding process. However, as the number of iterations increases, the following formula changes: Floating-point simulation? = 0.2 + 0.2, ^ = 6 + 6 in the hardware decoding device, ί represents the number of half iterations (one complete iteration includes one row iteration and One column iteration, half iteration refers to one row iteration or one column iteration).

Figure 5 is a diagram of the 6-item decoding of the product code formed by the extended BCH code [C (64,51,6)] 2

The method shown in Figure 2 is compared with the hardware decoding performance shown in Figure 3. In FIG. 5, the ordinate is the bit error rate (BER), and the abscissa is the bit energy signal-to-noise ratio (Eb / N0). The figure shows a comparison of the present invention preclude different coding decoding performance parameter 1, and compare them with the performance of the hardware decoder, the BER-10- ⁶ ⁷ and when 10-, and the performance of the hardware decoder The floating-point simulation results of 12, 13 are only 0.2 dB worse.

An example of the iterative decoder decoding shown in FIG. 3 is given below.

The product code [C (8, 4, 4)] ^{2 of the} extended Hamming code C (8, 4, 4) as a subcode is taken as an example to briefly explain the working process of the algorithm. The generator polynomial of the subcode is: (1 + x + x ² ). Generate the C (7, 4, 3) Hamming code plus a full check bit to form the extended Hamming code C (8, 4, 4). Table 2 is Check matrix for extended Hamming code C (8, 4, 4). Tables 3 and 4 are the adjoint tables and anti-adjoint tables obtained by extending the check matrix of the Hamming code C (8, 4, 4). Table 2

0 1 2 3 4 5 6 7

0 1 0 1 1 1 0 0 0

1 1 1 1 0 0 1 0 0

2 0 1 1 1 0 0 1 0

3 1 1 1 1 1 1 1 1 table 3

Table 4

Table 5 is the codeword matrix after the product code [C (8,4,4)] ^{2 is} coded.

table 5

As shown in Table 5, the codeword matrix encoded by the product code is an 8X8 matrix, and its 4X4 sub-matrix composed of G to 3 rows and G to 3 columns is the input information bit, and each row and each column is a C (8, 4, 4) Extended Hamming codeword. The codeword matrix in Table 2 is output to the modulator and transmitted. At the receiving end, the noise-received codeword matrix, that is, the product code [C (8,4,4)] 2, is received, as shown in Table 6.

Table 6

For example, row decoding is performed first.

The hard-decision binary sequence in the first row of Table 6 is (1 1 1 1 1 1 1 1), and its adjoint vector is calculated as (0 0 0 0), that is, s = o. There may be no errors in the received sequence. Select immediately The hard-decision binary sequence is used as the output codeword, and no other "competitive codeword" needs to be calculated. The external information value in the codeword is approximately (6 6 6 6 6 6 6 6). At this time, the value of ^ is 6 and the soft output information value vector is (21 37 37 379 35 31 37). The hard-decision binary sequence in the second row of Table 6 is (0 0 1 0 1 1 1 0), and its adjoint vector is calculated as (0 0 0 0), that is, S = 0. There may be no errors in the receiving sequence. Select immediately The hard-decision binary sequence is used as the output codeword, and no other "competitive codeword" needs to be calculated. The external information value in the codeword is approximately (-6 -6 6 -6 6 6 6 -6), and the value is 6 at this time, and the soft output information value vector is (-17 -18 21-3724 37 25 -37). The hard-decision binary sequence in the third row of Table 6 is (1 0 0 0 1 1 1 1), and its adjoint vector is calculated as (0 0 1 1), that is, S [3] = l, and the hard-decision is immediately selected for reception. There may be an odd number of errors in the sequence. Select those sets Lj that satisfy | Z ,. | = 1 or 3, so there are at most G) + (' ₂ ) sets, choose M, and first find the set of positions with the smallest weight by the ranking algorithm. {2, 6, 0, 4}, find the patterns that meet the conditions, and their corresponding error locations are: (0 0 0 0 0 0 1 0), (1 0 1 0 0 0 0 1), (0 0 1 0 1 1 0 0) and (1 1 0 0 1 0 0 0), the weights of these modes are 6, 46, 49, and 54, respectively, so the decoded output codeword is (1 0 0 0 1. 1 0 1), count The external information value of the arithmetic character number is (30 -17- 31- 6 30 12 -319), and the soft output information value vector is (40 -48 -36 -2343 43 -2540).

The other rows are calculated sequentially. See Table 7 for the external information value array after all rows are decoded. See Table 8 for the soft output information value array.

Take "= 8/16, calculate the product code [C (8, 4, 4)] ² The soft input value array of the first column decoding is shown in Table 9. Table 9

Column decoding process peer decoding. The external information value array after column decoding is shown in Table 10, and the soft output information value array is shown in Table 10. Table 10

Table 11

At this point, a complete iterative decoding is completed.

Repeat the above row decoding and column decoding process to obtain the decoded soft output value array of the second iteration, as shown in Table 12. In the second iteration, during the decoding process of the column subcode and the row subcode, all the calculated adjoint S are 0. Therefore, the decoder automatically terminates the decoding process.

Table 12

With reference to the symbol decisions in Tables 5 and 12, the decoding results of the present invention are completely correct.

The above specific implementations are only used to illustrate the present invention, but not intended to limit the present invention.

Claims

Rights request

1. An iterative decoding method for a product code based on an adjoint type, characterized in that when iteratively decoding a product code, a binary subcode of the product code needs to be decoded, and The decoding needs to satisfy the conditions for the decoding of the binary linear block code with adjointness; obtain the soft output value and the external information value; use the obtained soft output value and the external information value to realize the iterative decoding of the product code with any iteration number.

2. The method according to claim 1, wherein the decoding of the binary subcode of the product code means: decoding the binary row subcode and column subcode of the product code.

3. The method according to claim 1, wherein the conditions for the decoding of the binary linear block code by the adjoint method include:

Soft input value SI of the input symbol vector;

Compute a hard decision binary sequence b of a symbol vector;

If S = 0, the hard-decision binary sequence is the soft-decision decoded code word £, and the decoding ends; mark the 7 least reliable symbol positions in the soft input vector, and also the lightest-weight column vector in the check matrix H Position, where / ≤M-/ _C ;

Find all ^ "patterns ≤" c / and their position set, satisfy the adjoint condition

(∑ / _ei , ^h ') ^{≡S mod} and positional conditions ^; ^{^^^,,} ...,; ^^, Λ- 6 {0,1, ··, 72 -1}, where h _; is the check The / column vector of the matrix H, _A is one of the 7 least reliable symbol positions in the soft input vector;

Calculate the weight of the pattern, that is, calculate the weight corresponding to the set of column vector labels of the check matrix H, and then store these weight values and the corresponding set of positions;

Find the set A with the smallest weight;

The binary symbols corresponding to the positions of the set A ,, in the hard decision binary sequence b are complemented to obtain the soft decision decoding code word £, and the decoding is completed.

4. The method according to claim 1, comprising the steps of:

When iteratively decoding a product code, the binary row and column subcodes of the product code need to be decoded, and the following conditions must be met:

Soft input value SI of the input symbol vector;

Compute a hard decision binary sequence b of a symbol vector;

If S = 0, the hard-decision binary sequence is the soft-decision decoded code word £, and the decoding ends; find the 7 least reliable symbol positions in the soft input vector, and also the lightest weighted column vector in the check matrix H Position, where / ≤M- / C;

Find all the -patterns and their set of locations that satisfy the adjoint condition

(∑, ' _e , ^h '.) ^≡ S ^mo d and position condition; ^ ^. , ^ '…, / ^,, Xe {0, l ,, .., "_ l}, where h ,. is the ith column vector of the check matrix H, and is one of the least reliable of the soft input vectors One of the symbol positions

Calculate the weights of the pattern, that is, calculate the weights corresponding to the set of column vector labels of the check matrix H /. ^. = ∑ ^ | (<¾¾ |, and then store these weight values and corresponding position sets;

Find the set with the smallest weight

Complement the binary symbols corresponding to the positions of the set in the hard decision binary sequence b to obtain the soft decision decoding codeword e, and the decoding ends;

When S is not equal to 0 and no decoding failure flag is set, it is searched from the output column of the above subcode decoding. Look for Ί-competition code word ";

Calculate soft output value when "j-competitive codeword" does not exist, or S = 0

(SO) _i

Where /? Is a constant, / is the soft input value of the J'th symbol, and siw. Is the soft information value output by the demodulator at the first iteration; (SI) j = _Uj + awj at other iterations, calculate External information value 1 = (SO) J- (SI) J;

When "j-competition codeword" exists, select "j-competition codeword" with the smallest weight, and calculate the soft output value (SO),. = (Ψ _0- ^ „) (2c.-l), calculate External information value = 0SO) -0S /;

When a decoding failure flag is set in the above-mentioned subcode decoding process, the external information value _W = 0 is calculated; using the obtained soft output value and external information value, other row subcodes or column subcodes are decoded; After the row subcode is decoded, the new external information value is used to form a new soft input value to decode all column subcodes. The row subcode and column subcode are alternately decoded to implement iterative decoding of the product code for any number of iterations.

5. The method according to claim 4, wherein the finding one of the most unreliable symbol positions in the soft input vector refers to: finding a soft input vector using a two-dimensional fast partial sorting method suitable for hardware implementation. Among the most unreliable symbol positions, the steps include:

First, the one-dimensional array to be sorted constitutes a two-dimensional array. For example, a soft input sequence of subcodes of n = 128 can form a two-dimensional array of 8 _× i6.

The most unreliable Z symbol positions can be obtained through a maximum of / times of comparison; for a xo two-dimensional array, a maximum of; + 0 + / clock cycles can complete the required ordering.

6. The method according to claim 4, characterized in that the finding all patterns and their position set, satisfying the adjoint condition (^ h ,.) _≡ S mod 2 and the position condition means: The high-speed hardware implementation steps of the look-up table are as follows:

Before decoding, an anti-adjoint table and a companion table for correcting single errors are stored according to the check matrix of the linear block code, where: the error position corresponding to the adjoint, if the adjoint If a single error cannot be located, the corresponding position is set to the -1 flag, which requires a total of "1 ^ 4 (2" -1) bits; the companion corresponding to the error position requires a total of-bits;

According to the obtained adjoint s, check the anti-adjoint table to determine the single error position. If the position flag is not -1, a-pattern is found, where: q = l; otherwise, it means that there are multiple position errors; For the most unreliable symbol position, determine other patterns, where ^^ When the pattern is found, where = 2, first check the adjoint table to determine the adjoint S _{1 5} with an error in a certain position in the least reliable symbol position set, and then find S ^ S® ^, S ₂ trans finally verified by the syndrome table to determine a position error, if the position flag is not - 1, to find a - mode (= 2), when taken to meet the different values of the condition, the above steps will be repeated You can find all-patterns that satisfy the decoding conditions.

7. The method according to claim 4, wherein the step of deriving a soft output value and an external information value further comprises:

If a "competitive codeword" is found, the soft output value is: Ο ^) ^^)-^^)] ^ .- ¹ ); If the "competitive codeword" cannot be found when decoding the subcode, then, The soft output value is approximately calculated as:

(S0) _j = (SI) _J + fi (2c _J -l) If the subcode decoding fails, the soft output value is set to:

The external information values are:. = (SO)-(57);

For the above formula, the external information value is used for fast processing. When the pattern search is completed, all "bit external information value calculations can be completed in parallel within 1 clock cycle, but 2 (^ + 2).« Bit storage unit, Is the number of quantized bits of the soft input value, and its processing steps are as follows: Initialize the two sets of depth "", width ^ + 2 or + 3, where the extended Hamming code is qb + 2 and the extended BCH code is ^ + 3 Storage units W and W '"^v; flag word flag with an initial depth of 1 and a width of 1 bit, and set w _min = 2 ^{≠ +} 2-1, failure = 1;

W ^inv (i) = 2 ^{≠ + 2} -l, 0≤i≤n

fl g (i) = 0 In the subcode decoding process, every time a pattern is found, update w, W '" ^v , flag, and' and set failure = 0 as follows:

fl gii) = \, if ieL _q

W (i) = (L _q ), if W (i)> (L _q ) and i L _q

w _mill = (L _q ), if w _min > (L _q )

-After the pattern search is completed, calculate the external information value according to the following formula:

if failure == 1 w _; = 0 for all Q≤i≤n- \

else if flagii) == 0 w _t = β (2 ^ 一 1)

lse if W (i)> w _{min W;} = ((! ·) _-Wmin ) ((2b ,. -1))-Λ ( _ζ .)

else if W ^inv (i) ≠ 2 " ^{b +} ^2-1 w _t = (w ^inv (, :)-w ^ _n ) (1-2b,)-A (η)

else _w . = β (1-2 ^) where έ ,. is a binary hard decision value.

8. The method according to claim 4, further comprising:

First, the one-dimensional array to be sorted constitutes a two-dimensional array. For example, a soft input sequence of subcodes of η = 128 can form a two-dimensional array of _{8 x} i ₆ ;

The required / most unreliable symbol positions can be obtained through the most / times comparison; for the X ₀ two-dimensional array, it takes a maximum of ^ _{+ 0 +} / clock cycles to complete the required sorting;

The finding of all-patterns of ≤ ^ and their position set, satisfying the adjoint condition (Σ ^ h ,.) _≡ S mod 2 and the position condition means: The implementation steps using high-speed hardware based on look-up table are as follows:

Before decoding, according to the check matrix of the linear block code C (n, / ^), Anti-adjoint tables and adjoint tables, where: the error position corresponding to the adjoint, if the adjoint cannot locate a single error, the corresponding position is set to the -1 flag, a total of "1 ₀ 4 (2"- ^/ -1 ) Bits; the companion corresponding to the error position requires a total of-bits;

According to the obtained adjoint s, check the anti-adjoint table to determine the single error position. If the position flag is not -1, a-pattern is found, where: g = i; otherwise, it means that there are multiple position errors; The least reliable symbol position, determine other-patterns, where _≤ί ;

When finding the pattern, where = 2, first look at the adjoint table to determine the adjoint S _{l 5} that has an error in a certain position in the most unreliable set of symbol positions, then find s ^ s® ^, and finally check the adjoint by s ₂ The formula table determines the error position. If the position flag is not-1, a pattern is found (= 2). When taking different values that meet the conditions, repeat the above steps to find all that satisfy the decoding conditions? -Mode;

If '-competitive codeword "is found, the soft output value is:

If "_competitive codeword" cannot be found during subcode decoding, the soft output value is approximately calculated as: {SO) _J = (SI) _j + (2c _j- \); if the subcode decoding fails, soft output value is set _{to: (SO) j = (SI} ) J; external information is: ^ = (SC¾- (57) ;;

For the above formula, the external information value is used for fast processing. When the pattern search is completed, all calculations of the bit external information value can be completed in parallel within 1 clock cycle, but 2 (δ + 2). Is the number of quantized bits of the soft input value. The processing steps are as follows: Initialize the two sets of storages with a depth of π and a width of b + 2 or + 3, where the extended Hamming code is qb + 2 and the extended BCH code is + 3 Cells W and W '"^v; initial depth is π and width is

1-bit flag word flag, and set w _min = 2 ^{Φ + 2} -1, failure = 1;

W (i) = 2 ^{≠ + 2} -l

ψ ^! ην (ί) = 2 ^{≠ + 2} -1, 0≤i≤n

fl gii) = 0 In the subcode decoding process, each time a pattern is found, the following formula is used to update W, W '" ^v , flag and ^W min, and set f. U Teng = 0:

flagij) = 1, if ie L _q

W (i) = (L _q ), if W (i)> (L _q ) and ieL _q

) (J _? ), If W ^im (i)> w (L _q ) and i ^ L _q

H (J _? ), If w _{mi! 1} > {L _q ) After searching for the pattern, calculate the external information value according to the following formula:

if failure == 1 w,-= 0 for all 0≤i <n- \

else ifflag (i) = 0 w _t = -1)

else if W (i)> w _min w ,. = (:)-w _niin ) ((26 _;. -1))-Λ (.)

else w _t = (1-2δι) where b ,. is a binary hard decision value.

9. An iterative decoding device based on an adjoint product code, comprising: an input-output module, an adjoint calculation module, a selection ordering module, a pattern search module, an external information value calculation module, and a storage module;

Input data and control signals are inputs to the input and output modules;

The input / output module stores the input data in the storage module;

The adjoint calculation module, the selection sorting module and the storage module respectively input data to the pattern search module;

The pattern search module inputs data to the external information value calculation module;

The input and output modules output data and status signals.

10. The device according to claim 9, wherein the input / output module comprises at least a soft input value calculation module;

The soft input value calculation module is based on the input soft information value u and the external information generated during the decoding process. The interest value _{w is} calculated to obtain the soft input value SI of each iteration of the decoder. According to the soft input value, a reliable value | si | and a binary hard decision sequence b are obtained.

11. The device according to claim 9, wherein the storage module comprises: a dual-port data storage RAM, a companion table module, and an anti-adjoint table module;

12. The device according to claim 9, characterized in that:

The input / output module includes at least a soft input value calculation module; the soft input value calculation module calculates the soft input of each iteration of the decoder according to the input soft information value u and the external information value w generated during the decoding process. The value SI, according to the soft input is worth the reliable value | SI | and the binary hard decision sequence b;

The storage module may include: a data storage Hankou RAM, an accompanying table module, and an anti-adjoint table module; an input-output module that stores input data into a data storage dual-port RAM; an accompanying table module and an anti-adjoint table The module inputs data to the -pattern search module, respectively.