WO2017080249A1 - Method of generating low-density parity-check code transmitted over channel and apparatus utilizing same - Google Patents

Abstract

The invention discloses a method of generating a low-density parity-check (LDPC) code transmitted over a channel and an apparatus utilizing the same. The method comprises: a transmitter expands a LDPC code check-based matrix to obtain a LDPC code check matrix for use in encoding; the transmitter performs, by the LDPC code check matrix for use in encoding, LDPC encoding on a code word to be encoded to obtain an encoded code word; and the transmitter shortens the encoded code word to generate a LDPC code to be transmitted in a channel. The technical scheme provided by the embodiment of the invention can provide enhanced decoding performance and enhanced flexibility, and can satisfy a need in generating a code word having different code lengths.

Description

Method and apparatus for generating low density parity check codes for transmission in a channel

This application claims priority to the CN patent application filed on November 11, 2015, the Chinese Patent Office, Application No. 201510768421.3, entitled "Method and Apparatus for Generating Low Density Parity Check Codes for Transmission in Channels" The entire content of which is incorporated herein by reference.

Technical field

The present invention relates to the field of computers, and in particular, to a method and apparatus for generating a low density parity check code for transmission in a channel.

Background technique

At present, the WLAN (Chinese: Wireless Local Area Networks) standard (IEEE 802.11n/ac/ad) optional channel coding scheme is: the transmitting end uses LDPC (Chinese: low density check; English: Low-density) Parity-check) The parity check matrix performs LDPC encoding on the codeword to be encoded, obtains the encoded codeword, and then transmits the encoded codeword through the channel.

Taking the IEEE 802.11ad standard as an example, the four LDPC code check basis matrices used in the IEEE 802.11ad standard are quasi-cyclic LDPC code (QC-LDPC) check basis matrices, and each element represents a z=42. (z is called the expansion factor) order square matrix, the code rate is

The size is m×16, where m is an integer greater than or equal to 1, therefore, the expansion factor of the four LDPC code check base matrix used in the IEEE802.11ad standard is 42, and the corresponding code length is 672 (672=16). ×42).

Please refer to FIG. 1. FIG. 1 is a code rate in the IEEE802.11ad standard.

The LDPC code check base matrix has a size of 8×16, where 0 represents an all-zero square matrix of z×z, P _i represents a cyclic permutation matrix, and i (0≤i≤z-1) represents a cyclic shift value.

The 802.11ad standard defines four channels, which respectively correspond to four different code rate LDPC code check base matrices, and the coded codewords transmitted in the four channels have a code length of 672. In the next generation In the standard 802.11ay, in order to improve the throughput rate, CB (Chinese: Channel Bonding) technology will be adopted to bind multiple channels together to provide users with higher peak bandwidth. In order to adapt to the CB technology introduced in the next-generation evolution standard 802.11ay, it is necessary to transmit a codeword having a longer code length than 672 in the bundled channel. To this end, it is necessary to generate a codeword having a longer code length than 672.

To this end, there are currently two solutions. The main idea adopted by the first solution is Second Lifting: the LDPC code check base matrix corresponding to the code length 672 in the IEEE 802.11ad standard is secondarily expanded and extended to the corresponding code length. It is an LDPC code check matrix of 1344 or 2016, and then LDPC-encodes the codeword to be coded by using the corresponding LDPC code check matrix with a code length of 1344 or 2016, and generates a codeword with a code length of 1344 or 2016.

To generate a code length of 1344 and a bit rate

The code word is an example. First, construct an 8×16 (with the IEEE 802.11ad standard code rate)

The LDPC code checks the base matrix of the same size as the quadratic expansion matrix H _s , as shown in FIG. 2 . The shift value (0 or 1) is set at the element position where the original base matrix is not -1, and the remaining position values are -1; then, the second expansion matrix H _{s is} used to perform two expansions to obtain a new 16x32 LDPC. The code check matrix H ₂ , as shown in FIG. 3, is then LDPC-encoded with the codeword to be encoded by H ₂ to generate a codeword having a code length of 1344. However, the drawback of this solution is that when the LDPC code check matrix is constructed, it needs to be expanded twice. Therefore, additional storage space is needed to store intermediate variables such as the temporarily generated quadratic expansion matrix.

The main idea adopted by the second solution is to change the spreading factor: based on the LDPC code check base matrix corresponding to the code length of 672 in the IEEE802.11ad standard, the size and elements of the check base matrix of the LDPC code are not changed. For the number, only the size of the spreading factor z is changed, and the corresponding LDPC code check matrix with the code length of 1344 or 2016 is obtained, and then the codeword to be coded with the corresponding LDPC code check matrix with the code length of 1344 or 2016 is used. Perform LDPC encoding to generate a code length of 1344 or 2016 code word. Taking the codeword with a code length of 1344 as an example, the expansion factor z=42 is changed to z=84 to obtain the corresponding LDPC code check matrix with a code length of 1344, and then the corresponding LDPC code with a code length of 1344 is used. The parity check matrix performs LDPC encoding on the codeword to be encoded, and generates a codeword having a code length of 1344. However, the drawback of this scheme is that there is a limitation on the code length of the codeword, and the code length of the codeword must be an integer multiple of 16, and the codeword of the code length of any length cannot be generated, and the flexibility is poor.

Summary of the invention

The embodiments of the present invention provide a method and a device for generating a low-density parity check code for transmission in a channel, which can obtain better decoding performance and can generate different codes by using the technical solution provided by the embodiment of the present invention. The need for long codewords.

A first aspect of the embodiments of the present invention provides a method for generating a low density parity check LDPC code for transmission in a channel, the method comprising:

The transmitting end performs an extension process on the LDPC code check base matrix to obtain an LDPC code check matrix for encoding;

The transmitting end performs LDPC encoding on the codeword to be encoded by using the LDPC code check matrix for encoding, to obtain an encoded codeword;

Transmitting, by the sending end, the encoded codeword, to generate an LDPC code for transmitting in a channel, where a code length of the encoded codeword is greater than the used for transmitting in a channel The code length of the LDPC code.

The transmitting end first performs an extension process on the LDPC code check base matrix, so that the code length corresponding to the LDPC code check matrix used for encoding is as long as possible, which is equivalent to making the code length corresponding to the LDPC code check matrix used for decoding as long as possible. Therefore, the technical solution provided by the embodiment of the present invention can obtain better decoding performance. Furthermore, since the LDPC code for transmission in the channel is a result of shortening processing of the encoded codeword, the code length of the LDPC code used for transmission in the channel can be any value. The technical solution provided by the embodiment of the present invention is more flexible and can meet the requirements of generating codewords of different code lengths.

With reference to the first aspect, in a first possible implementation manner of the first aspect, the sending end performs a shortening process on the encoded codeword to generate the LDPC code for transmitting in a channel, including:

The transmitting end determines a first order in which the confidence bits of the information bits of the encoded codeword are small to large;

The transmitting end determines the first q information bits in the first ordering as q shortening positions, where q is the code length of the encoded codeword and the code of the LDPC code used for transmitting in the channel Long difference

The transmitting end determines information bit bits corresponding to the q shortened positions in the encoded codeword as information bits that need to be shortened;

The transmitting end performs shortening processing on the information bits that need to be shortened, and generates the LDPC code used for transmission in the channel.

The smaller the confidence of the information bits, the more susceptible the information bits are to noise, and therefore the position at which the less confident information bits are located needs to be determined as the shortened position. The decoding performance is further improved.

With reference to the first aspect, in a second possible implementation manner of the first aspect, if the coded codeword is obtained by extending the same column in the LDPC code check base matrix, the obtained z pieces of information are obtained. The bits have the same confidence, z is the spreading factor used in the spreading process, and the transmitting end performs shortening processing on the encoded codeword to generate the LDPC code for transmission in the channel, including :

Determining, by the transmitting end, a second order of the confidence level of each information bit of the LDPC code check base matrix from small to large;

The transmitting end determines the first q ₀ information bits in the second sorting as q ₀ pre-shortened positions, where

The transmitting end satisfies q=z(q ₀ -1)+n according to q, and n is an integer greater than 0, or q satisfies q=zq ₀ , and is determined from each information bit of the encoded codeword. q shortened positions, q is the difference between the code length of the encoded codeword and the code length of the LDPC code used for transmission in the channel;

The transmitting end determines information bit bits corresponding to the q shortened positions in the encoded codeword as information bits that need to be shortened;

The transmitting end performs shortening processing on the information bits that need to be shortened, and generates the LDPC code used for transmission in the channel.

In the encoded codeword, the same column in the LDPC code check base matrix is expanded, and the obtained z information bits have the same confidence, and can be used according to the LDPC code used in the extended processing. The confidence level of each information bit of the base matrix is determined to determine the shortened position. Provides a more convenient way to determine the position of the shortening.

In conjunction with the second possible implementation of the first aspect, in a third possible implementation manner of the first aspect, the transmitting end satisfies q=z(q ₀ -1)+n according to q, and n is greater than An integer of 0, determining q shortened positions from respective information bits of the encoded codeword, including:

Determining, by the transmitting end, z information bits corresponding to the first q ₀ -1 pre-shortened positions in the q ₀ pre-shortened positions in the encoded codeword as z(q ₀ -1) Shortened position;

Determining, by the transmitting end, any n information bits of the z information bits corresponding to the last one of the q ₀ pre-short positions in the encoded code word as n shortened positions, or The first n information bits in the third order of the z information bit position reliability corresponding to the last shortened position are determined to be n shortened positions.

In conjunction with the second possible implementation of the first aspect, in a fourth possible implementation manner of the first aspect, the transmitting end satisfies q=zq ₀ according to q, and each information of the encoded codeword is obtained. Determine q shortened positions in the bits, including:

The transmitting end determines, as the zq ₀ shortening positions, z information bits corresponding to the q ₀ pre-shortened positions in the encoded codeword.

A second aspect of the embodiments of the present invention provides an apparatus for generating a low density parity check LDPC code for transmission in a channel, where the apparatus includes:

a processor, a memory, and a bus, the processor being coupled to the memory via the bus, the processor for:

Performing an extension process on the LDPC code check base matrix to obtain an LDPC code check matrix for encoding;

Performing LDPC encoding on the codeword to be encoded by using the LDPC code check matrix for encoding, to obtain an encoded codeword;

Performing a shortening process on the encoded codeword to generate the LDPC code for transmission in a channel, where a code length of the coded codeword is greater than a code length of the LDPC code used for transmission in a channel .

In conjunction with the second aspect, in a first possible implementation of the second aspect, the processor is configured to:

Determining a first order of confidence of each information bit of the encoded codeword from small to large;

Determining, in the first order, the first q information bits as q shortened positions, where q is the difference between the code length of the encoded codeword and the code length of the LDPC code used for transmission in the channel ;

Determining information bits corresponding to the q shortened positions in the encoded codewords as information bits that need to be shortened;

Shortening the information bits that need to be shortened to generate the LDPC code for transmission in the channel.

With reference to the second aspect, in a second possible implementation manner of the second aspect, if the coded codeword is obtained by extending the same column in the LDPC code check base matrix, the obtained z pieces of information are obtained. The bits have the same confidence, z is the spreading factor used in the spreading process, and the processor is used to:

Determining a second order of confidence that each information bit of the LDPC code check base matrix is small to large;

Determining the first q ₀ information bits in the second sort as q ₀ pre-short positions, wherein

Determining q shortened positions from each information bit of the encoded codeword according to q satisfying q=z(q ₀ -1)+n, and n is an integer greater than 0, or q satisfies q=zq ₀ And q is a difference between a code length of the encoded codeword and a code length of the LDPC code used for transmission in a channel;

Determining information bits corresponding to the q shortened positions in the encoded codewords as information bits that need to be shortened;

Shortening the information bits that need to be shortened to generate the LDPC code for transmission in the channel.

With reference to the second possible implementation of the second aspect, in a third possible implementation manner of the second aspect, the q satisfies q=z(q ₀ -1)+n, and n is an integer greater than 0 The processor is used to:

The code word in the encoded q ₀ with the pre-shortened position before pre-shortened q ₀ -1 positions respectively corresponding to information bits of z is determined as z (q ₀ -1) th shortened position;

Determining, in the encoded codeword, any n information bits of the z information bits corresponding to the last one of the q ₀ pre-shortened positions as n shortened positions, or The first n information bits in the third order of the z information bit position reliability corresponding to the last shortened position are determined to be n shortened positions.

In conjunction with the second possible implementation of the second aspect, in a fourth possible implementation of the second aspect, the q satisfies q=zq ₀ , and the processor is configured to:

The z information bits corresponding to the q ₀ pre-short positions in the encoded codeword are determined as zq ₀ shortened positions.

One or more technical solutions provided in the embodiments of the present invention have at least the following technical effects or advantages:

In order to generate an LDPC code for transmission in a channel, the transmitting end first performs an extension process on the LDPC code check base matrix to obtain an LDPC code check matrix for encoding, so that the LDPC code check matrix is used for coding. The code length corresponding to the coded LDPC code check matrix is as long as possible, which is equivalent to making the code length corresponding to the LDPC code check matrix used for decoding as long as possible (because the LDPC code check matrix used for coding and the decoding matrix for decoding) The LDPC code check matrix is the same. The longer the code length corresponding to the LDPC code check matrix used for LDPC decoding, the better the decoding performance. Therefore, the technical solution provided by the embodiment of the present invention can obtain better decoding performance. .

Then, the transmitting end performs LDPC encoding on the codeword to be encoded by using the LDPC code check matrix for encoding, to obtain the encoded codeword, and finally shortens the encoded codeword to generate a signal for transmission in the channel. LDPC code. The LDPC code used for transmission in the channel is a result of shortening the coded codeword, so that the code length of the LDPC code used for transmission in the channel may be an arbitrary value, and the technical solution provided by the embodiment of the present invention More flexibility, able to meet the needs of generating codewords of different code lengths.

DRAWINGS

In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings used in the description of the embodiments will be briefly described below. It is obvious that the drawings in the following description are only some embodiments of the present invention, Those of ordinary skill in the art do not pay creative labor Other drawings can also be obtained from these drawings.

Figure 1 shows the code rate in the IEEE802.11ad standard.

LDPC code check base matrix;

Figure 2 is an 8 × 16 quadratic expansion matrix H _s constructed in quadratic expansion;

3 is an LDPC code check matrix H ₂ for performing LDPC encoding on a codeword to be coded in a secondary extension;

4 is a schematic diagram of a communication system applicable to the technical solution provided by the embodiment of the present invention;

Figure 5 shows the code rate in the IEEE802.11ad standard.

LDPC code check base matrix;

FIG. 6 is a comparison diagram of frame error rates of the first embodiment and the second embodiment of the present invention;

FIG. 7 is a comparison diagram of frame error rates of the fourth embodiment and the fourth embodiment of the present invention;

FIG. 8 is a flowchart of a method for generating a low density parity check LDPC code for transmission in a channel according to an embodiment of the present invention;

FIG. 9 is a schematic diagram of an apparatus for generating a low density parity check LDPC code for transmission in a channel according to an embodiment of the present disclosure;

FIG. 10 is a schematic diagram of an apparatus for generating a low density parity check LDPC code for transmission in a channel according to an embodiment of the present invention.

detailed description

The technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the drawings in the embodiments of the present invention. It is a partial embodiment of the invention, and not all of the embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative efforts are within the scope of the present invention.

The embodiments of the present invention are further described in detail below with reference to the accompanying drawings.

Please refer to FIG. 4. FIG. 4 is a schematic diagram of a communication system applicable to the technical solution provided by the embodiment of the present invention. The communication system includes: a transmitting end, a channel, and a receiving end. Optionally, it also includes a noise source. The transmitting end includes a source, and the receiving end includes a sink. With the technical solution provided by the embodiment of the present invention, a codeword with a longer code length ratio of 672 can be generated, and then a codeword with a longer code length than 672 is transmitted through the bound channel, which is convenient for description, and the generated codeword is The code rate is denoted as R _f , and the code length is denoted as L _f and L _{f is} greater than 672.

Since the receiving end performs LDPC decoding on the encoded codeword by using the corresponding LDPC code check matrix with a longer code length, better decoding information can be obtained, and the LDPC code used by the receiving end for LDPC decoding is verified. The matrix is the same as the LDPC code check matrix used by the LDPC encoding at the transmitting end. Therefore, the transmitting end is required to perform LDPC encoding on the codeword to be encoded using the LDPC code check matrix with a corresponding longer code length. For convenience of description, the LDPC code check matrix used by the transmitting end for LDPC encoding or the LDPC code check matrix used by the receiving end for LDPC decoding is referred to as an LDPC code check matrix for encoding or decoding, and will be used for encoding. Or the code rate of the decoded LDPC code check matrix is denoted as R _m , and the corresponding code length is denoted as L _m .

In order to obtain a better decoding signal, in the solution provided by the embodiment of the present invention, L _{m is} greater than L _f , and in the transmitting end, LDPC encoding is performed on the codeword to be encoded using the LDPC code check matrix corresponding to the code length L _m . , the resulting codewords of length encoded L _m is, the code length for a codeword encoded L _m is shortened, and generates the code length L _f of the codeword, and then through channel transmission codes after binding A codeword of length L _f .

Correspondingly, in the receiving end, the codeword with the code length _Lf transmitted in the channel is subjected to a solution shortening process, so that the code length of the shortened codeword is restored to _Lm , and the corresponding code length is _Lm . The LDPC code check matrix performs LDPC decoding on the shortened codeword to obtain a decoded codeword. The code length corresponding to the LDPC code check matrix used by the receiving end for LDPC decoding is greater than the code length corresponding to the LDPC code check matrix used by the receiving end for LDPC decoding in the prior art, for example, receiving in the existing 802.11ad standard. The code length of the LDPC code check base matrix used for LDPC decoding is 672. The code length of the LDPC code check matrix used by the receiving end for LDPC decoding in the solution provided by the embodiment is L _m , because L _{m is} greater than 672 (L _{m is} greater than L _f and L _{f is} greater than 672), and the longer the code length corresponding to the LDPC code check matrix used for LDPC decoding, the better the decoding performance, so the technique provided by the embodiment of the present invention is adopted. The solution can get better decoding performance.

The technical solutions provided by the embodiments of the present invention are described in detail below.

It has been explained in the background art that in order to adapt to the CB technology introduced in the next generation evolution standard 802.11ay, it is necessary to generate a codeword having a longer code length than 672. To this end, the sender is required to perform the method shown in FIG. Please refer to FIG. 8. FIG. 8 is a flowchart of a method performed by a transmitting end in a solution according to an embodiment of the present invention, which is a low-density parity check LDPC code generated for transmission in a channel according to an embodiment of the present invention. Flow chart of the method. The methods performed by the sender include:

Step 81: The transmitting end performs an extension process on the LDPC code check base matrix to obtain an LDPC code check matrix used for encoding.

Step 82: The transmitting end performs LDPC encoding on the codeword to be encoded by using the LDPC code check matrix for encoding, to obtain an encoded codeword.

Step 83: The transmitting end performs shortening processing on the encoded codeword to generate the LDPC code used for transmission in a channel, where the encoded codeword has a code length greater than that used in the channel. The code length of the transmitted LDPC code.

Steps 81-83 may be referred to sequentially as an expansion step, an LDPC encoding step, and a shortening step.

In the spreading step, the transmitting end expands the LDPC code check base matrix into an LDPC code check matrix for encoding with a code length of L _m . The LDPC encoding step, the transmit end a code length encoded codeword in the parity check matrix of the LDPC code to be encoded in the LDPC encoding L _m, to obtain a codeword of length L _m is encoded. Shortening step, the transmit end proceeds to shorten the processing code length of code words encoded L _m, the generated code length codeword L _f, and then through the channel transmitting the code length after binding to L _f codeword.

Since the transmitting end sequentially performs the spreading step, the LDPC encoding step, and the shortening step, accordingly, the receiving end sequentially performs the de-shearing step and the LDPC decoding step. Shortening step in the solution, the receiving end of the codeword is transmitted in a channel code length L _f of the de-shortened code length of code words to obtain the shortened solution of L _m, L _m of code length for translation code is an LDPC code parity check matrix of the code length the shortened LDPC decoding solution for a codeword L _m to obtain the decoded codeword.

The expansion step, the LDPC encoding step, and the shortening step, which are sequentially performed by the transmitting end, in the technical solution provided by the embodiment of the present invention are described in detail below.

The transmission side LDPC code parity-yl matrix extension code length L _m of the process of the LDPC code parity check matrix for encoding is: the sending end of each sub-cyclic check matrix of the LDPC code group matrix is based on the expansion factor z The expansion process is such that the number of rows and columns of each cyclic sub-matrix of the extended LDPC code check matrix is extended by z times, and the extended LDPC code check matrix is an LDPC code for encoding with a code length of L _m . A check matrix, where L _m is the product of the number of columns of the LDPC code check base matrix and the spreading factor z. The process of performing the spreading step by the transmitting end may refer to the prior art as long as the LDPC code check matrix for encoding with a code length of L _m can be obtained.

Taking the 802.11ad standard as an example, the number of columns of the LDPC code check base matrix in the 802.11ad standard is 16, and the transmitting end performs extension processing based on the spreading factor z=112 on each cyclic sub-matrix of the LDPC code check base matrix. The number of rows and columns of each cyclic submatrix of the latter LDPC code check matrix is extended by 112 times, and an extended LDPC code check matrix of L _m =1792 (ie, 16×112) is obtained, that is, the code length L _m =1792 LDPC code check matrix for encoding.

The above is the entire process of the extension step performed by the sender. Next, the transmitting end performs an LDPC encoding step. Transmit end code length of the codeword to be encoded L _m LDPC code parity check matrix for LDPC encoding encoded to obtain a codeword of length L _m is encoded. For details on how to perform LDPC coding, refer to the prior art, and details are not described herein. Sending end to obtain a code length of code words encoded L _m, and the step of performing shortening.

In the embodiment of the present invention, before step 83, the method further includes:

Determining, by the transmitting end, q shortening positions from each information bit of the encoded codeword, where q is a code length of the encoded codeword and the LDPC code used for transmitting in the channel The difference in code length;

Accordingly, step 83 includes:

The transmitting end determines information bit bits corresponding to the q shortened positions in the encoded codeword as information bits that need to be shortened;

The transmitting end performs shortening processing on the information bits that need to be shortened, and generates the LDPC code used for transmission in the channel.

That is, to shorten the steps comprising: 1) determining the number of bits shortened, for ease of description, will be referred to as q shortened bits; 2) from the code length of each code word bits of information encoded L _m is determined in the q Shorten the position; 3) shorten the coded codeword with the code length L _m according to the q shortened positions.

The process of determining q by the transmitting end is: determining q according to the following formula:

q=L _m -L _f

For example, if L _m = 1792 and L _f = 1344, then q = 448 can be determined.

The process of determining q shortened positions from the information bits of the encoded codeword having a code length of L _m is as follows:

The transmitting end determines a first order in which the confidence bits of the information bits of the encoded codeword are small to large;

The transmitting end determines the first q information bits in the first sort as q shortened positions.

First obtaining a code length for the number of information bits of each code word encoded absolute value of L _m likelihood ratio (LLR), and for ease of description, the absolute value of logarithmic likelihood ratio (i.e., | the LLR |) It is called confidence. The smaller the confidence of the information bits, the more susceptible the information bits are to noise, and therefore the position at which the less confident information bits are located needs to be determined as the shortened position. Since the need to determine the q shortened position, it is necessary to code length of information bits of each code word encoded L _m confidence ascending sort order, and then the top bit determines information bits q Shorten the position for q.

In another embodiment of the present invention, if the coded codeword is obtained by expanding the same column in the LDPC code check base matrix, the obtained z information bits have the same confidence, and z is The spreading factor used in the expanding process, the sending end determines q shortening positions from each information bit of the encoded codeword, including:

Determining, by the transmitting end, a second order of the confidence level of each information bit of the LDPC code check base matrix from small to large;

The transmitting end determines the first q ₀ information bits in the second sorting as q ₀ pre-shortened positions, where

The transmitting end satisfies q=z(q ₀ -1)+n according to q, and n is an integer greater than 0, or q satisfies q=zq ₀ , and is determined from each information bit of the encoded codeword. q shortened positions.

If the code length of code words encoded L _m, the column obtained by the same spreading code check LDPC matrix of the z groups of information bits having the same level of confidence, e.g. 802.11ad standard LDPC code parity-yl The matrix may first determine the confidence level of each information bit of the base matrix according to the LDPC code, and determine from each information bit of the LDPC code check base matrix

Pre-shortened positions, then satisfy q=z(q ₀ -1)+n according to q, and n is an integer greater than 0, or q satisfies q=zq ₀ , from the encoded codeword with a code length of L _m q shortened positions are determined in each information bit.

For the 802.11ad standard, the 802.11 standard includes four LDPC code check base matrices, the code rates are

The confidence levels of the information bits of the four LDPC code check base matrices included in the 802.11 standard are sorted in ascending order, and the shortened priority pattern is shown in Table 1:

Table 1 Shortening Priority Patterns of Four LDPC Code Check Base Matrix Included in the 802.11 Standard

In Table 1, the shortened priority pattern contains numbers indicating the column numbers of the information bits of the LDPC code check base matrix in the 802.11 standard, and the prioritized priority is shortened, wherein each column represents Z = 42 information bits. The method of obtaining the shortened priority pattern shown in Table 1 includes the following steps:

1) Select the check matrix and the code rate to perform simulation. In the simulation condition, sigma is set to 0, but the channel is decoded, the decoding mode is log-BP, and the initial value of the decoded channel information is set to ±1 (or other). Set the number of iterations 10 times to start the simulation;

2) Output the iterative |LLR| and sort from small to large, where the smaller |LLR| indicates that it is susceptible to noise;

3) Sort the information bit positions of the corresponding positions according to the sorting in the previous step.

According to q, q = z(q ₀ -1) + n is satisfied, and n is an integer greater than 0, and the process of determining q shortened positions from each information bit of the encoded codeword having a code length of L _m is:

Determining, by the transmitting end, z information bits corresponding to the first q ₀ -1 pre-shortened positions in the q ₀ pre-shortened positions in the encoded codeword as z(q ₀ -1) Shortened position;

The transmitting end determines, as the n shortening positions, any n information bits of the z information bits corresponding to the last one of the q ₀ pre-shortened positions in the encoded code word, or The first n information bits in the third order of the z information bit position reliability corresponding to the last shortened position are determined to be n shortened positions.

If q satisfies _{q = z (q 0 -1)} + n, q ₀ is first pre-determined position of the shortened front q ₀ -1 pre-shortened position of the code length of code words encoded in the corresponding L _m, respectively The z positions are shortened positions. Then, determining that the last one pre-short position of the q ₀ pre-short positions is the shortened position in any of the z positions corresponding to the coded code words having the code length L _m , or q ₀ pre-predetermined positions shortening the last position corresponding to a pre-shortened position of confidence respective information bits of z at the position in the sorted in ascending codeword length of the encoded L _m, the first n bits of information The bit is determined to shorten the position.

For example,

And L _f =1344, taking the 802.11 standard as an example, the code rate of the LDPC code check base matrix

The expansion factor z=100, shortened the number of bits q=256. then

Figure 1 shows the code rate in the IEEE802.11ad standard.

The LDPC code check base matrix calculates the confidence of each information bit of the LDPC code check base matrix shown in FIG. 1 to determine the confidence of the second column and the fourth column to be the smallest and the second smallest, the seventh column The confidence level is the third smallest. Therefore, the position where the second column and the fourth column are located and the portion where the seventh column is located are preferentially used as the pre-shortened position, and the positions of the second column and the fourth column are at the code length L. codeword encoded _m, respectively corresponding to 100 position as a shortened position, the 100 position of the codeword in column 7 in code length L _m of the coding corresponding to any of 56 positions as a shortened position, or determining column 7 are sorted in ascending confidence code length of the codeword encoded L _m of each of information 100 corresponding to the bit position, the first 56 bits of information is determined to be shortened position .

According to q satisfying q=zq ₀ , the process of determining q shortened positions from each information bit of the encoded codeword having a code length of L _m is:

The transmitting end determines, as the zq ₀ shortening positions, z information bits corresponding to the q ₀ pre-short positions in the encoded codeword.

If q satisfies q=zq ₀ , it is determined that the z positions corresponding to the q ₀ pre-short positions in the coded codewords having the code length L _m are shortened positions.

For example,

And L _f =1344, taking the 802.11 standard as an example, the code rate of the LDPC code check base matrix

The expansion factor z=112, the number of shortening bits q=448. then

Figure 5 shows the code rate in the IEEE802.11ad standard.

The LDPC code check base matrix calculates the confidence of each information bit of the LDPC code check base matrix shown in FIG. 5, and determines that the confidence levels of the first, second, fourth, eighth, and fourth columns are the smallest, The second, third, and fourth are small, so the position of the first, second, fourth, and eighth columns is preferentially used as the pre-shortened position, and the positions of the first, second, fourth, and eighth columns are at the code length L _{m .} The corresponding 112 positions in the encoded code words are used as the shortened positions.

Next, the transmitting end performs a step of shortening the coded codeword having a code length of L _m in accordance with q shortened positions. include:

The transmitting end determines information bit bits corresponding to the q shortened positions in the encoded codeword as information bits that need to be shortened;

The transmitting end performs shortening processing on the information bits that need to be shortened, and generates the LDPC code used for transmission in the channel.

The transmitting end shortens the corresponding information bits in the coded codewords whose code length is L _m in the q-short position. For details, refer to the prior art, and details are not described herein. The transmitting end according to the q shortened position, the code length shortening a codeword encoded L _m generated code length L _f of the codeword, and then through the channel transmitting the code length after binding to L _f codeword.

The following describes the steps and results performed by the transmitting end in the technical solution provided by the embodiment of the present invention.

Embodiment 1:

The code rate of the codeword that needs to be generated

And the code length L _f =1344. Take the 802.11ad standard as an example to determine

z=100, L _m =1600, q=256, according to Table 1, determined

The position of the second column and the fourth column and the seventh column in the LDPC code check base matrix is used as the pre-short position.

a) the code rate

The LDPC code check base matrix is subjected to an extension process based on the spreading factor z=100 to obtain an LDPC code check matrix for encoding with L _m = 1600;

b) the use of L _m = code word to be encoded LDPC code parity check matrix for encoding LDPC encoding is performed 1600 to obtain the code length L _m = codeword encoded 1600;

c) taking the 100 information bits corresponding to the coded words of the second column and the fourth column in the encoded codeword of L _m = 1600 as the shortened position, and the seventh column in the coded codeword of L _m = 1600 Any 56 information bits of the corresponding 100 information bits are used as the shortened position, or the confidence of the corresponding 100 information bits in the encoded code word of the seventh column is determined from small to large, and the first 56 Information bits are determined to be shortened positions;

d) set the element at the shortened position to 0 to generate the code rate

Codeword with code length L _f =1344.

Embodiment 2

The code rate of the codeword that needs to be generated

And the code length L _f =1344. Take the 802.11ad standard as an example to determine

z=112, L _m =1792, q=448, according to Table 1, determined

The first, second, fourth, and eighth columns in the LDPC code check base matrix serve as pre-short positions.

a) the code rate

The LDPC code check base matrix is subjected to an extension process based on the spreading factor z=112 to obtain an LDPC code check matrix for encoding of L _m =1792;

b) L _m = LDPC code using a parity check matrix for encoding 1792 a codeword to be encoded LDPC encoding, to obtain the code length encoded codeword = 1792 is L _m;

c) using 112, information bits corresponding to the encoded codewords of the first, second, fourth, and eighth columns of L _m =1792 as the shortened positions;

d) set the element at the shortened position to 0 to generate the code rate

And a codeword with a code length L _f =1344.

Please refer to FIG. 6. FIG. 6 shows the simulation conditions: AWGN channel, 64QAM modulation, the decoding algorithm used is Log-SPA algorithm, and the decoding iteration is 20 times. The first embodiment and the foregoing embodiment 2 are respectively related to the existing scheme. Comparison of the frame error rate. In Fig. 6, the abscissa is SNR (dB) and the ordinate is FER.

It can be seen from FIG. 6 that the performance of the foregoing first embodiment and the foregoing second embodiment is significantly better than that of the existing solution for generating a codeword with a code length L _f =1344, wherein the first embodiment is compared with the existing solution. The performance gain is greater than or equal to 1 dB, and the performance gain of the second embodiment is about 0.8 dB with respect to the existing scheme.

Embodiment 3

The code rate of the codeword that needs to be generated

And the code length L _f =2016. Take the 802.11ad standard as an example to determine

z=140, L _m = 2240, q=224, according to Table 1, determined

The LDPC code checks the position of the second column and the fourth column in the base matrix as the pre-short position.

a) the code rate

The LDPC code check base matrix performs an extension process based on the spreading factor z=140, and obtains an LDPC code check matrix for encoding with L _m = 2240;

b) taking the corresponding 140 information bits in the LDPC code check matrix for encoding of the second column at L _m = 2240 as the shortened position, and the fourth column at L _m = 2240 for the LDPC code for encoding Any 84 information bits of the corresponding 140 information bits in the matrix are used as the shortened position, or the confidence of the corresponding 140 information bits in the LDPC code check matrix for the fourth column is determined from small to large. Sorting, determining the first 84 information bits as a shortened position;

d) set the element at the shortened position to 0 to generate the code rate

And the code length of the code length L _f =2016.

Embodiment 4

The code rate of the codeword that needs to be generated

And the code length L _f =2016. Take the 802.11ad standard as an example to determine

z=168, L _m = 2688, q=672, according to Table 1, determined

The first, second, fourth, and eighth columns in the LDPC code check base matrix serve as pre-short positions.

a) the code rate

The LDPC code check base matrix performs an extension process based on the spreading factor z=168, and obtains an LDPC code check matrix for encoding with L _m = 2688;

b) L _m = LDPC code using a parity check matrix for encoding 2688 to be encoded codeword LDPC encoding, to obtain the code length L _m = codeword encoded 2688;

c) 168 information bits corresponding to the first, second, fourth, and eighth encoded codewords of L _m = 2688 are taken as the shortened positions;

d) set the element at the shortened position to 0 to generate the code rate

And a codeword with a code length L _f = 2688.

Please refer to FIG. 7. FIG. 7 shows the simulation conditions: AWGN channel, 64QAM modulation, the decoding algorithm used is Log-SPA algorithm, and the decoding iteration is 20 times. The foregoing third embodiment and the foregoing embodiment 4 are respectively related to the existing scheme. Comparison of the frame error rate. In Fig. 7, the abscissa is SNR (dB) and the ordinate is FER.

It can be seen from FIG. 7 that for the codewords that generate the code length L _f =2016, the performance of the foregoing third embodiment and the foregoing fourth embodiment is significantly better than the performance of the existing scheme, wherein the three-phase embodiment is applicable to the existing scheme. The performance gain is equal to 0.9 dB, and the performance gain of Embodiment 4 is about 0.7 dB with respect to the existing scheme.

It can be seen from FIG. 6 and FIG. 7 that the solution provided by the embodiment of the present invention can generate a codeword with a code length of any length, and has high flexibility.

The solution shortening step and the LDPC decoding step sequentially performed by the receiving end in the technical solution provided by the embodiment of the present invention are described in detail below.

Since the shortened bit number q and the q shortening positions are known, the receiving end inserts the q shortened positions into the corresponding positions in the shortened codeword by inserting 0, and the codeword having the shortened code length _Lm is obtained. The decoded codeword is LDPC-decoded using a check matrix for decoding to obtain a decoded codeword.

The solution shortening step and the LDPC decoding step performed by the transmitting end are the shortening steps performed by the receiving end and the reverse process of the LDPC decoding step, and the implementation manners are similar, and are not described herein.

Based on the same inventive concept, an embodiment of the present invention further provides an apparatus for generating a low density parity check LDPC code for transmission in a channel. Please refer to FIG. 9, which is a schematic diagram of the device. The device can be the sender in Figure 1. The device 900 includes:

a processor 91, a memory 92, a bus 90, and the processor 91 is connected to the memory 92 via the bus 90;

The processor 91 is configured to:

Performing an extension process on the LDPC code check base matrix to obtain an LDPC code check matrix for encoding;

Performing LDPC encoding on the codeword to be encoded by using the LDPC code check matrix for encoding, to obtain an encoded codeword;

Performing shortening processing on the encoded codeword to generate the LDPC code for transmission in a channel, where the code length of the encoded codeword is greater than the code of the LDPC code used for transmission in the channel long.

Optionally, the processor 91 is configured to:

Determining a first order of confidence of each information bit of the encoded codeword from small to large;

Determining, in the first order, the first q information bits as q shortened positions, where q is the difference between the code length of the encoded codeword and the code length of the LDPC code used for transmission in the channel ;

Determining information bits corresponding to the q shortened positions in the encoded codewords as information bits that need to be shortened;

Shortening the information bits that need to be shortened to generate the LDPC code for transmission in the channel.

Optionally, if the coded codeword is obtained by extending the same column in the LDPC code check base matrix, the obtained z information bits have the same confidence, and z is in the extended process. The spreading factor used, the processor 91 is used to:

Determining a second order of confidence that each information bit of the LDPC code check base matrix is small to large;

Determining the first q ₀ information bits in the second sort as q ₀ pre-short positions, wherein

Determining q shortened positions from each information bit of the encoded codeword according to q satisfying q=z(q ₀ -1)+n, and n is an integer greater than 0, or q satisfies q=zq ₀ And q is a difference between a code length of the encoded codeword and a code length of the LDPC code used for transmission in a channel;

Determining information bits corresponding to the q shortened positions in the encoded codewords as information bits that need to be shortened;

Shortening the information bits that need to be shortened to generate the LDPC code for transmission in the channel.

Optionally, the q satisfies q=z(q ₀ -1)+n, and n is an integer greater than 0, and the processor 91 is configured to:

The code word in the encoded q ₀ with the pre-shortened position before pre-shortened q ₀ -1 positions respectively corresponding to information bits of z is determined as z (q ₀ -1) th shortened position;

Determining, in the encoded codeword, any n information bits of the z information bits corresponding to the last one of the q ₀ pre-shortened positions as n shortened positions, or The first n information bits in the third order of the z information bit position reliability corresponding to the last shortened position are determined to be n shortened positions.

Optionally, the q satisfies q=zq ₀ , and the processor 91 is configured to:

The z information bits corresponding to the q ₀ pre-short positions in the encoded codeword are determined as zq ₀ shortened positions.

Further, in FIG. 9, bus 40 can include any number of interconnected buses and bridges that connect various circuits including one or more processors represented by processor 91 and memory represented by memory 92. The bus 90 can also connect various other circuits, such as peripherals, voltage regulators, and power management circuits, as is known in the art, and therefore, will not be further described herein.

The processor 91 is responsible for managing the bus 90 and the usual processing, and the memory 92 can be used to store data used by the processor 91 when performing operations.

The various modifications and specific examples in the foregoing method shown in FIG. 8 are also applicable to the device in this embodiment. Through the foregoing detailed description of the method shown in FIG. 8, those skilled in the art can clearly understand that in this embodiment. The implementation method of the device, so for the sake of brevity of the description, it will not be described in detail here.

Based on the same inventive concept, an embodiment of the present invention further provides an apparatus for generating a low density parity check LDPC code for transmission in a channel. Please refer to FIG. 10, which is a schematic diagram of the device. The device can be the transmitting end of Figure 1. The device includes:

The expansion unit 101 is configured to perform an extension process on the LDPC code check base matrix to obtain an LDPC code check matrix for encoding;

The encoding unit 102 is configured to perform LDPC encoding on the codeword to be encoded by using the LDPC code check matrix for encoding, to obtain an encoded codeword;

a shortening unit 103, configured to perform shortening processing on the encoded codeword to generate the LDPC code for transmission in a channel, where a code length of the encoded codeword is greater than that used in the channel The code length of the transmitted LDPC code.

Optionally, the shortening unit 103 is configured to:

Determining a first order of confidence of each information bit of the encoded codeword from small to large;

Determining, in the first order, the first q information bits as q shortened positions, where q is the difference between the code length of the encoded codeword and the code length of the LDPC code used for transmission in the channel ;

Determining information bits corresponding to the q shortened positions in the encoded codewords as information bits that need to be shortened;

Shortening the information bits that need to be shortened to generate the LDPC code for transmission in the channel.

Optionally, if the coded codeword is obtained by extending the same column in the LDPC code check base matrix, the obtained z information bits have the same confidence, and z is in the extended process. The expansion factor used, the shortening unit 103 is used to:

Determining a second order of confidence that each information bit of the LDPC code check base matrix is small to large;

Determining the first q ₀ information bits in the second sort as q ₀ pre-short positions, wherein

Determining q shortened positions from each information bit of the encoded codeword according to q satisfying q=z(q ₀ -1)+n, and n is an integer greater than 0, or q satisfies q=zq ₀ And q is a difference between a code length of the encoded codeword and a code length of the LDPC code used for transmission in a channel;

Determining information bits corresponding to the q shortened positions in the encoded codewords as information bits that need to be shortened;

Shortening the information bits that need to be shortened to generate the LDPC code for transmission in the channel.

Optionally, the q satisfies q=z(q ₀ -1)+n, and n is an integer greater than 0, and the shortening unit 103 is configured to:

The code word in the encoded q ₀ with the pre-shortened position before pre-shortened q ₀ -1 positions respectively corresponding to information bits of z is determined as z (q ₀ -1) th shortened position;

Determining, in the encoded codeword, any n information bits of the z information bits corresponding to the last one of the q ₀ pre-shortened positions as n shortened positions, or The first n information bits in the third order of the z information bit position reliability corresponding to the last shortened position are determined to be n shortened positions.

Optionally, the sending end satisfies q=zq ₀ according to q, and the shortening unit 103 is configured to:

The transmitting end determines, as the zq ₀ shortening positions, z information bits corresponding to the q ₀ pre-shortened positions in the encoded codeword.

The various modifications and specific examples in the foregoing method shown in FIG. 8 are also applicable to the apparatus of the present embodiment. The foregoing detailed description of the method shown in FIG. 8 can be clearly known to those skilled in the art. The method of implementation of the device, so for the sake of brevity of the description, it will not be described in detail herein.

Those skilled in the art will appreciate that embodiments of the present application can be provided as a method, system, or computer program product. Thus, the present application can take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment in combination of software and hardware. Moreover, the application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage and optical storage, etc.) including computer usable program code.

The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (system), and computer program products according to embodiments of the present application. It will be understood that each flow and/or block of the flowchart illustrations and/or FIG. These computer program instructions can be provided to a processor of a general purpose computer, a special purpose computer, an embedded processor, or other programmable data processing device to produce a machine that enables Instructions executed by a processor of a computer or other programmable data processing device generate means for implementing the functions specified in one or more blocks of the flowchart or in a block or blocks of the flowchart.

The computer program instructions can also be stored in a computer readable memory that can direct a computer or other programmable data processing device to operate in a particular manner, such that the instructions stored in the computer readable memory produce an article of manufacture comprising the instruction device. The apparatus implements the functions specified in one or more blocks of a flow or a flow and/or block diagram of the flowchart.

These computer program instructions can also be loaded onto a computer or other programmable data processing device such that a series of operational steps are performed on a computer or other programmable device to produce computer-implemented processing for execution on a computer or other programmable device. The instructions provide steps for implementing the functions specified in one or more of the flow or in a block or blocks of a flow diagram.

It will be apparent to those skilled in the art that various modifications and changes can be made in the present application without departing from the spirit and scope of the application. Thus, it is intended that the present invention cover the modifications and variations of the present invention.

.

Claims (10)

1. A method of generating a low density parity check LDPC code for transmission in a channel, the method comprising:

   The transmitting end performs an extension process on the LDPC code check base matrix to obtain an LDPC code check matrix for encoding;

   The transmitting end performs LDPC encoding on the codeword to be encoded by using the LDPC code check matrix for encoding, to obtain an encoded codeword;

   Transmitting, by the sending end, the encoded codeword, to generate an LDPC code for transmitting in a channel, where a code length of the encoded codeword is greater than the LDPC used for transmitting in a channel The code length of the code.
2. The method according to claim 1, wherein the transmitting end performs shortening processing on the encoded codeword to generate the LDPC code for transmission in a channel, including:

   The transmitting end determines a first order in which the confidence bits of the information bits of the encoded codeword are small to large;

   The transmitting end determines the first q information bits in the first ordering as q shortening positions, where q is the code length of the encoded codeword and the code of the LDPC code used for transmitting in the channel Long difference

   The transmitting end determines information bit bits corresponding to the q shortened positions in the encoded codeword as information bits that need to be shortened;

   The transmitting end performs shortening processing on the information bits that need to be shortened, and generates the LDPC code used for transmission in the channel.
3. The method according to claim 1, wherein if the encoded codeword is obtained by spreading the same column in the LDPC code check base matrix, the obtained z information bits have The same confidence level, z is the spreading factor used in the expansion process, and the transmitting end performs the shortening process on the encoded codeword to generate the LDPC code for transmission in the channel, including:

   Determining, by the transmitting end, a second order of the confidence level of each information bit of the LDPC code check base matrix from small to large;

   The transmitting end determines the first q ₀ information bits in the second sorting as q ₀ pre-shortened positions, where

   

   The transmitting end satisfies q=z(q ₀ -1)+n according to q, and n is an integer greater than 0, or q satisfies q=zq ₀ , and is determined from each information bit of the encoded codeword. q shortened positions, q is the difference between the code length of the encoded codeword and the code length of the LDPC code used for transmission in the channel;

   The transmitting end determines information bit bits corresponding to the q shortened positions in the encoded codeword as information bits that need to be shortened;

   The transmitting end performs shortening processing on the information bits that need to be shortened, and generates the LDPC code used for transmission in the channel.
4. The method according to claim 3, wherein said transmitting end satisfies q = z(q ₀ -1) + n according to q, and n is an integer greater than 0, from each of said encoded code words The q shortened positions are determined in the information bits, including:

   Determining, by the transmitting end, z information bits corresponding to the first q ₀ -1 pre-shortened positions in the q ₀ pre-shortened positions in the encoded codeword as z(q ₀ -1) Shortened position;

   Determining, by the transmitting end, any n information bits of the z information bits corresponding to the last one of the q ₀ pre-short positions in the encoded code word as n shortened positions, or The first n information bits in the third order of the z information bit position reliability corresponding to the last shortened position are determined to be n shortened positions.
5. The method according to claim 3, wherein the transmitting end determines q shortening positions from each information bit of the encoded codeword according to q satisfying q=zq ₀ , including:

   The transmitting end determines, as the zq ₀ shortening positions, z information bits corresponding to the q ₀ pre-shortened positions in the encoded codeword.
6. An apparatus for generating a low density parity check LDPC code for transmission in a channel, the apparatus comprising:

   a processor, a memory, and a bus, the processor being coupled to the memory via the bus, the processor for:

   Performing an extension process on the LDPC code check base matrix to obtain an LDPC code check matrix for encoding;

   Performing LDPC encoding on the codeword to be encoded by using the LDPC code check matrix for encoding, to obtain an encoded codeword;

   Performing a shortening process on the encoded codeword to generate the LDPC code for transmission in a channel, where a code length of the coded codeword is greater than a code length of the LDPC code used for transmission in a channel .
7. The device of claim 6 wherein said processor is operative to:

   Determining a first order of confidence of each information bit of the encoded codeword from small to large;

   Determining, in the first order, the first q information bits as q shortened positions, where q is the difference between the code length of the encoded codeword and the code length of the LDPC code used for transmission in the channel ;

   Determining information bits corresponding to the q shortened positions in the encoded codewords as information bits that need to be shortened;

   Shortening the information bits that need to be shortened to generate the LDPC code for transmission in the channel.
8. The apparatus according to claim 6, wherein if the encoded codeword is obtained by spreading the same column in the LDPC code check base matrix, the obtained z information bits have The same confidence, z is the spreading factor used in the extension process, the processor is used to:

   Determining a second order of confidence that each information bit of the LDPC code check base matrix is small to large;

   Determining the first q ₀ information bits in the second sort as q ₀ pre-short positions, wherein

   

   Determining q shortened positions from each information bit of the encoded codeword according to q satisfying q=z(q ₀ -1)+n, and n is an integer greater than 0, or q satisfies q=zq ₀ And q is a difference between a code length of the encoded codeword and a code length of the LDPC code used for transmission in a channel;

   Determining information bits corresponding to the q shortened positions in the encoded codewords as information bits that need to be shortened;

   Shortening the information bits that need to be shortened to generate the LDPC code for transmission in the channel.
9. The apparatus of claim 8, wherein said q satisfies q = z(q ₀ -1) + n, and n is an integer greater than 0, said processor for:

   The code word in the encoded q ₀ with the pre-shortened position before pre-shortened q ₀ -1 positions respectively corresponding to information bits of z is determined as z (q ₀ -1) th shortened position;

   Determining, in the encoded codeword, any n information bits of the z information bits corresponding to the last one of the q ₀ pre-shortened positions as n shortened positions, or The first n information bits in the third order of the z information bit position reliability corresponding to the last shortened position are determined to be n shortened positions.
10. The device according to claim 8, wherein said q satisfies q = zq ₀ , said processor is for:

    The z information bits corresponding to the q ₀ pre-short positions in the encoded code words are determined as zq ₀ shortened positions.

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