CN115425989A - Marker-LDPC code transmission method based on data preprocessing - Google Patents

Marker-LDPC code transmission method based on data preprocessing Download PDF

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CN115425989A
CN115425989A CN202210923831.0A CN202210923831A CN115425989A CN 115425989 A CN115425989 A CN 115425989A CN 202210923831 A CN202210923831 A CN 202210923831A CN 115425989 A CN115425989 A CN 115425989A
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marker
executing
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柳元
李乐然
原野
韩啸宇
白羽
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Tianjin Normal University
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    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
    • H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
    • H03M13/03—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words
    • H03M13/05—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits
    • H03M13/11—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits using multiple parity bits
    • H03M13/1102—Codes on graphs and decoding on graphs, e.g. low-density parity check [LDPC] codes
    • H03M13/1105—Decoding
    • H03M13/1131—Scheduling of bit node or check node processing
    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
    • H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
    • H03M13/03—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words
    • H03M13/05—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits
    • H03M13/11—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits using multiple parity bits
    • H03M13/1102—Codes on graphs and decoding on graphs, e.g. low-density parity check [LDPC] codes
    • H03M13/1148—Structural properties of the code parity-check or generator matrix

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Abstract

The invention discloses a Marker-LDPC code transmission method based on data preprocessing, which comprises the following steps: for length K L Binary information sequence ofbPerforming LDPC code coding to obtain the length N L Of (a)d(ii) a For input code sequencedPerforming preprocessing and outputting the sequenceu(ii) a Marking MarkerwUniformly embedded into the sequenceuIn (1), the generation length is N c Is transmitted in sequencex(ii) a Will send the sequencexThe inserted/punctured-alternative channel is generated to have a length of
Figure DDA0003778788820000011
Receive sequence ofy(ii) a Marker code decoder correcting received sequenceyInserting/deleting errors in, outputting a likelihood ratio sequencel(ii) a Sequence of likelihood ratioslGenerating a sequence after replacementq(ii) a LDPC decoder according to received generated sequenceqDecoding by using a logarithm domain confidence coefficient propagation decoding algorithm and outputting the estimation of the information sequence
Figure DDA0003778788820000012
The invention can effectively improve the performance of correcting insertion, deletion and substitution errors of the system.

Description

Marker-LDPC code transmission method based on data preprocessing
Technical Field
The invention relates to the field of digital communication error control coding, in particular to a Marker-low density parity check code (Marker-LDPC) code transmission method based on data preprocessing.
Background
The synchronization errors include insertion and puncturing of bits/symbols. This type of error is widely present in various types of systems, such as: high speed communication systems, differential pulse position modulation systems, data storage systems, and the like. A large number of insertions/deletions will seriously deteriorate the communication quality, resulting in a system out of synchronization and failure to achieve highly reliable data transmission. Davey and Mackay designed a concatenated coding scheme that can correct synchronization errors, called the DM (Davey-Mackay) construction. The structure adopts nonlinear watermark codes as inner codes and non-binary LDPC codes as outer codes, wherein the watermark decoding algorithm is used for correcting insertion/deletion nodes, and the outer decoding algorithm is used for correcting all residual errors, thereby obtaining excellent error correction performance. However, the watermark decoding method in the DM structure is only suitable for the exclusive or cascade method of the watermark code, and the flexibility of the algorithm is limited.
Then, based on DM construction, a cascade code transmission scheme based on weighted edit distance is provided, the scheme uniformly embeds Marker codes into information sequences, and adopts a symbol-level synchronous decoding algorithm based on weighted edit distance to correct insertion/deletion errors in received sequences, the scheme is not limited in a cascade mode of inner and outer codes any more, can be flexibly applied to an embedded and exclusive-or cascade code system, and enhances the flexibility of the algorithm.
In the above algorithm, the outer decoder corrects residual errors according to the soft information sequence output by the inner decoder, and the error correction capability of the outer decoder is related to the accuracy of the soft information. Since the inner decoding algorithm is a recursive forward-backward algorithm, the reliability of the forward probability decreases with the increase of the recursion times, as does the backward metric; this phenomenon will result in burst errors in the output soft information sequence. In view of the above problems, it is necessary to design a data preprocessing method capable of correcting burst errors in the output sequence of the inner decoder, so as to improve the reliability of likelihood information and further improve the error correction capability of the system.
Disclosure of Invention
The invention provides a Marker-LDPC code transmission method based on data preprocessing, which is characterized in that on the basis of a synchronization algorithm based on a weighted edit distance, an LDPC code is stored into a two-dimensional matrix and transferred to a next module after transposition; the preprocessing module is used for disorganizing the regularity of the transmitted code words, weakening the correlation of data sequences before and after sequencing, reducing the probability of sudden errors occurring in the soft information sequence and improving the reliability of information transmission; compared with the traditional symbol-level synchronization scheme based on the weighted edit distance, the symbol-level synchronization method based on the weighted edit distance can effectively improve the performance of correcting insertion, deletion and substitution errors of a system under the condition of hardly increasing the calculation complexity, and is described in detail in the following:
a Marker-LDPC code transmission method based on data preprocessing comprises the following steps:
for length K L Binary information sequence ofbPerforming LDPC code coding to obtain length N L Of (a) a coding sequenced(ii) a For input code sequencedPerforming preprocessing and outputting the sequenceu；
The Marker codewUniformly embedded into the sequenceuIn, the generation length is N c Is transmitted in a sequence ofx(ii) a Will send the sequencexThe inserted/punctured-alternative channel is generated to have a length of
Figure BDA0003778788800000021
Receive sequence ofy；
Marker code decoder correcting received sequenceyInserting/deleting errors in, outputting a sequence of likelihood ratiosl；
Sequence of likelihood ratioslGenerating sequences after replacementq(ii) a LDPC decoder according to received generated sequenceqDecoding by using a logarithm domain confidence coefficient propagation decoding algorithm and outputting the estimation of the information sequence
Figure BDA0003778788800000022
Wherein the encoding of the inputCode sequencedPerforming pre-processing and outputting the sequenceuComprises the following steps:
encoding the sequencedDivided into a groups of f bits each, where f = N L A; arranging the subsequences according to rows to form a matrix g with dimension a multiplied by f; solving the transpose g' of the matrix g, and outputting the sequenceu。
Further, the sequence of likelihood ratioslGenerating a sequence after replacementqComprises the following steps:
sequence of likelihood ratioslDivided into f groups of a, where f = N L A; arranging the subsequences in rows to form an f multiplied by a matrix h; the matrix h is transposed h' and the generated sequence is outputq。
Wherein, the coding sequencedDivided into a groups of f bits each, where f = N L A; arranging the subsequences in rows to form a matrix g with dimension a x f; transpose g' of matrix g, output sequenceuComprises the following steps:
(2.1) defining a two-dimensional array g of a rows and f columns, where f = N L A, a is a preset interweaving depth;
(2.2) let line variable i =0;
(2.3) let the column variable j =0;
(2.4)g[i][j]＝d[i*f+j]，j＝j+1；
(2.5) judging whether j is smaller than f, if so, executing the step (2.4); if not, i = i +1, performing step (2.6);
(2.6) judging whether i is smaller than a, if so, executing the step (2.3); if not, outputting a two-dimensional array g;
(2.7) definition of k as the sequenceuLet k =0, j =0;
(2.8) let i =0;
(2.9)u[k]＝g[i][j]，i＝i+1，k＝k+1；
(2.10) judging whether i is smaller than a, if so, executing the step (2.9); if not, j = j +1, executing step (2.11);
(2.11) judging whether j is smaller than f, if so, executing the step (2.8); if not, the process ends.
Further, the likelihood ratio is determinedSequence oflDivided into f groups of a, where f = N L A; arranging the subsequences according to rows to form an f multiplied by a matrix h; the matrix h is transposed h' and the generated sequence is outputqComprises the following steps:
(6.1) defining a two-dimensional array v of a rows and f columns, where f = N L A, a is a preset interweaving depth;
(6.2) let the column subscript j =0;
(6.3) let row subscript i =0;
(6.4)l[j*a+i]＝v[i][j]，i＝i+1；
(6.5) judging whether i is smaller than a, if so, executing the step (6.4); if not, j = j +1, executing step (6.6);
(6.6) judging whether j is smaller than f, if so, executing the step (6.3); if not, outputting the sequencev；
(6.7) definition of k as the sequenceqLet k =0, i =0;
(6.8) let j =0;
(6.9)q[k]＝v[i][j]，k＝k+1，j＝j+1；
(6.10) judging whether j is smaller than f, if so, executing the step (6.9); if not, i = i +1, performing step (6.11);
(6.11) judging whether i is smaller than a, if so, executing the step (6.8); if not, the process ends.
Wherein the Marker code iswUniformly embedded into the sequenceuIn (1), the generation length is N c Is transmitted in sequencexComprises the following steps:
preprocessing the binary LDPC codeuDividing into N sub-blocks, each sub-block having m bits, where N = N L /m；
Random generation of Marker code of length N by internal encoderwCoding the MarkerwDividing into N subsequences with length of lambda, inserting each subsequence into preprocessed binary LDPC codeuBefore each symbol of (2), generating a length of N c Is transmitted as a codewordxWherein, N is c ＝N L +N。
The technical scheme provided by the invention has the beneficial effects that:
1. on the basis of a synchronization algorithm based on a weighted editing distance, the invention proposes to adopt a preprocessing method to disorder the regularity of the LDPC codes of a transmission sequence, so that the correlation of data sequences before and after processing is weakened, and the probability of sudden errors in a soft information sequence is reduced;
2. the invention reduces the error rate of the system, improves the error correction capability of the system and obtains the performance gain under the condition of hardly increasing the calculation complexity.
Drawings
FIG. 1 is a block diagram of a Marker-LDPC code transmission method based on data preprocessing;
FIG. 2 is a flow chart of data pre-processing;
FIG. 3 is a flow chart of data post-processing;
FIG. 4 is a graph of a performance simulation of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, embodiments of the present invention are described in further detail below.
The embodiment of the invention designs a Marker-LDPC code transmission method based on data preprocessing under the framework of a synchronization algorithm based on weighted edit distance, and compared with the traditional scheme, the embodiment of the invention is modified as follows:
before the code word is cascaded with a Marker code, a transmission sequence is disturbed by adopting data preprocessing, the correlation of the data sequence before and after processing is weakened, the probability of burst errors of the soft information sequence is reduced, the error rate is reduced under the condition of hardly increasing the computational complexity, and the performance gain is obtained.
The following describes a Marker-LDPC code transmission method based on data preprocessing according to an embodiment of the present invention in detail with reference to the accompanying drawings, and the following description refers to the following:
as shown in fig. 1, the method comprises the following seven steps:
(1) For length K L Binary information sequence ofbPerforming LDPC code coding to obtain length N L Of (a)d；
(2) For input code sequencedPerforming preprocessing and outputting the sequenceu；
(2.1) encoding sequencedDivided into a groups of f bits each, where f = N L /a；
(2.2) arranging the subsequences in rows to form a matrix g with dimension a x f;
(2.3) transpose g' of matrix g, output sequenceu。
(3) Marking MarkerwUniformly embedded into the sequenceuIn, the generation length is N c Is transmitted in a sequence ofx；
Wherein, marker codewAs is well known to those skilled in the art, the embodiments of the present invention will not be described in detail herein.
(4) Will send the sequencexGenerating a length of the inserted/punctured-alternate channel as
Figure BDA0003778788800000041
Receive sequence ofy；
(5) Marker code decoder correcting received sequenceyInserting/deleting errors in, outputting a sequence of likelihood ratiosl；
(6) Sequence of likelihood ratioslGenerating sequences after replacementq；
(6.1) sequencing likelihood ratioslDivided into f groups of a, where f = N L /a；
(6.2) arranging the subsequences in rows to form an f x a matrix h;
(6.3) solving the transpose h' of the matrix h and outputting the generated sequenceq。
(7) LDPC decoder according to received generated sequenceqDecoding by using a logarithm domain confidence coefficient propagation decoding algorithm and outputting the estimation of the information sequence
Figure BDA0003778788800000051
The specific implementation process of the above seven steps is described as follows:
as shown in FIG. 2, the input code sequence in step (2)dPerforming preprocessing and outputting the sequenceuComprises the following steps:
(2.1) defining a two-dimensional array g of a rows and f columns, where f = N L A, a is a preset interweaving depth;
(2.2) let line variable i =0;
(2.3) let the column variable j =0;
(2.4)g[i][j]＝d[i*f+j]，j＝j+1；
(2.5) judging whether j is smaller than f, if so, executing the step (2.4); if not, i = i +1, performing step (2.6);
(2.6) judging whether i is smaller than a, if so, executing the step (2.3); if not, outputting a two-dimensional array g;
(2.7) definition of k as the sequenceuLet k =0, j =0;
(2.8) let i =0;
(2.9)u[k]＝g[i][j]，i＝i+1，k＝k+1；
(2.10) judging whether i is smaller than a, if so, executing the step (2.9); if not, j = j +1, executing step (2.11);
(2.11) judging whether j is smaller than f, if so, executing the step (2.8); if not, the process ends.
Namely, the above steps (2.1) to (2.6) constitute one sub-cycle, and the steps (2.7) to (2.11) constitute another sub-cycle.
Marking Marker codes in step (3)wUniformly embedded into the sequenceuIn, the generation length is N c Is transmitted in sequencexComprises the following steps:
(3.1) preprocessing the binary LDPC codeuDividing into N sub-blocks, each sub-block having m bits, where N = N L /m；
(3.2) the inner encoder randomly generates a Marker code of length NwCoding the MarkerwDividing into N subsequences with length of lambda, inserting each subsequence into preprocessed binary LDPC codeuBefore each symbol of (2), generating a length of N c Is transmitted as a codewordxWherein, N is c ＝N L +N。
Transmitting code word in step (4)xGenerates a length of
Figure BDA0003778788800000052
Receive sequence ofyComprises the following steps:
transmitting codeword x i Parameter P by inserting/deleting alternative channels i ，P d And P s Respectively representing insertion, puncturing and replacement probabilities of the channel. Probability of transmission P t ＝1-P i -P d 。
The steps of calculating the symbol-level forward probability, calculating the symbol-level backward probability and calculating the log-likelihood ratio in step (5) are well known to those skilled in the art, and are not described in detail in the embodiment of the present invention.
Step (6) likelihood ratio sequencelGenerating sequences after replacementqComprises the following steps:
(6.1) defining a two-dimensional array v of a rows and f columns, where f = N L A, a is a preset interweaving depth;
(6.2) let the column subscript j =0;
(6.3) let row subscript i =0;
(6.4)l[j*a+i]＝v[i][j]，i＝i+1；
(6.5) judging whether i is smaller than a, if so, executing the step (6.4); if not, j = j +1, executing step (6.6);
(6.6) judging whether j is smaller than f, if so, executing the step (6.3); if not, outputting the sequencev；
(6.7) definition of k as the sequenceqLet k =0, i =0;
(6.8) let j =0;
(6.9)q[k]＝v[i][j]，k＝k+1，j＝j+1；
(6.10) judging whether j is smaller than f, if so, executing the step (6.9); if not, i = i +1, executing step (6.11);
(6.11) judging whether i is smaller than a, if so, executing the step (6.8); if not, the process ends.
Namely, the above steps (6.1) to (6.6) constitute one sub-cycle, and the steps (6.7) to (6.11) constitute another sub-cycle.
Step (7) binary LDPC decoder utilization sequenceqComplete the processThe step of iteratively decoding, outputting an estimate of the information sequence, comprises comparing the sequence of likelihood ratioslSend to a post-processor to generate a sequenceq(ii) a Will be sequencedqSending the data into a binary LDPC decoder; decoding by adopting a logarithm domain BP decoding algorithm of a binary LDPC code; repeating the decoding steps until reaching the preset maximum iteration number delta max 。
DETAILED DESCRIPTION OF EMBODIMENT (S) OF INVENTION
The embodiment of the invention selects the code length N c The concatenated code with the code rate of 0.33 is a special case, and a Marker-LDPC code transmission method based on data preprocessing is introduced. In simulation, a pseudo-random sequence is used as an internal mark code, a binary LDPC code is used as an external code, wherein lambda =1,m =2,N L ＝576，R L ＝1/2，a＝24，
Figure BDA0003778788800000061
The maximum number of insertion errors per bit I in the channel is 5 i ＝P d The decoder of the LDPC code adopts a logarithm domain confidence propagation decoding algorithm, and the maximum iteration time is 20 times.
Fig. 4 shows a plot of the frame error rate of the system as a function of the insertion/deletion probability when the substitution probabilities are the same, where the frame error rate is equal to the number of error frames divided by the number of transmitted frames. As can be seen in FIG. 4, with P i Or P d The frame error rate is reduced, and the system performance is enhanced.
Further, the performance of the transmission scheme provided by the embodiment of the invention is superior to that of the transmission scheme based on the weighted edit distance. At a frame error rate of 10 -2 For example, when P s =0.001, the proposed scheme can correct about 49 synchronization errors per frame, while the weighted edit distance based transmission scheme with the same code length and code rate can correct about 45.5 insertion-erasure errors.
It can be known that the scheme proposed by the embodiment of the present invention corrects 3.5 more insertions and deletions per frame on average. Meanwhile, the complexity of the algorithm required by the scheme provided by the embodiment of the invention is O (N) L ) The decoding complexity required by the system is O (N) c log N c ) To understand the original informationThe algorithm complexity increment of the scheme provided by the embodiment is negligible compared with that of the whole system. In conclusion, the scheme provided by the embodiment of the invention obtains performance gain under the condition of hardly increasing the complexity of the algorithm.
In the embodiment of the present invention, except for the specific description of the model of each device, the model of other devices is not limited, as long as the device can perform the above functions.
Those skilled in the art will appreciate that the drawings are only schematic illustrations of preferred embodiments, and the above-described embodiments of the present invention are merely provided for description and do not represent the merits of the embodiments.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.

Claims (6)

1. A Marker-LDPC code transmission method based on data preprocessing is characterized by comprising the following steps:
for length K L Binary information sequence ofbPerforming LDPC code coding to obtain length N L Of (a) a coding sequenced(ii) a For input code sequencedPerforming preprocessing and outputting the sequenceu；
Marking MarkerwUniformly embedded into a sequenceuIn, the generation length is N c Is transmitted in a sequence ofx(ii) a Will send the sequencexGenerating a length of the inserted/punctured-alternate channel as
Figure FDA0003778788790000011
Receive sequence ofy；
Marker code decoder correcting received sequenceyInserting/deleting errors in, outputting a likelihood ratio sequencel；
Sequence of likelihood ratioslGenerating sequences after replacementq(ii) a LDPC decoder according to received generated sequenceqDecoding by using a logarithm domain confidence coefficient propagation decoding algorithm and outputting the estimation of the information sequence
Figure FDA0003778788790000012
2. The method for transmitting Marker-LDPC code based on data preprocessing of claim 1, wherein the input code sequence is encodeddPerforming pre-processing and outputting the sequenceuComprises the following steps:
encoding the sequencedDivided into a groups of f bits each, where f = N L A; arranging the subsequences according to rows to form a matrix g with dimension a multiplied by f; solving the transpose g' of the matrix g, and outputting the sequenceu。
3. The method for transmitting Marker-LDPC code based on data preprocessing as claimed in claim 1, wherein the sequence of likelihood ratios islGenerating a sequence after replacementqComprises the following steps:
sequence of likelihood ratioslDivided into f groups of a, where f = N L A; arranging the subsequences in rows to form an f multiplied by a matrix h; transpose h' is solved for matrix h, and the generated sequence is outputq。
4. The method for transmitting Marker-LDPC code based on data preprocessing of claim 2, wherein the coded sequence is encodeddDivided into a groups of f bits each, where f = N L A; arranging the subsequences according to rows to form a matrix g with dimension a multiplied by f; transpose g' of matrix g, output sequenceuComprises the following steps:
(2.1) defining a two-dimensional array g of a rows and f columns, where f = N L A, a is a preset interweaving depth;
(2.2) let row variable i =0;
(2.3) let column variable j =0;
(2.4)g[i][j]＝d[i*f+j]，j＝j+1；
(2.5) judging whether j is smaller than f, if so, executing the step (2.4); if not, i = i +1, performing step (2.6);
(2.6) judging whether i is smaller than a, if so, executing the step (2.3); if not, outputting a two-dimensional array g;
(2.7) definition of k as a sequenceuLet k =0, j =0;
(2.8) let i =0;
(2.9)u[k]＝g[i][j]，i＝i+1，k＝k+1；
(2.10) judging whether i is smaller than a, if so, executing the step (2.9); if not, j = j +1, executing step (2.11);
(2.11) judging whether j is smaller than f, if so, executing the step (2.8); if not, the process ends.
5. The method for transmitting Marker-LDPC code based on data preprocessing as claimed in claim 3, wherein the likelihood ratio sequence islDivided into f groups of a, where f = N L A; arranging the subsequences according to rows to form an f multiplied by a matrix h; the matrix h is transposed h' and the generated sequence is outputqComprises the following steps:
(6.1) defining a two-dimensional array v of a rows and f columns, where f = N L A, a is a preset interweaving depth;
(6.2) let the column subscript j =0;
(6.3) let row subscript i =0;
(6.4)l[j*a+i]＝v[i][j]，i＝i+1；
(6.5) judging whether i is smaller than a, if so, executing the step (6.4); if not, j = j +1, executing step (6.6);
(6.6) judging whether j is smaller than f, if so, executing the step (6.3); if not, outputting the sequencev；
(6.7) definition of k as the sequenceqLet k =0,i =0;
(6.8) let j =0;
(6.9)q[k]＝v[i][j]，k＝k+1，j＝j+1；
(6.10) judging whether j is smaller than f, if so, executing the step (6.9); if not, i = i +1, performing step (6.11);
(6.11) judging whether i is smaller than a, if so, executing the step (6.8); if not, the process ends.
6. The method for transmitting the Marker-LDPC code based on data preprocessing of claim 1, wherein the Marker code is transmitted according to the mode of transmissionwUniformly embedded into the sequenceuIn (1), the generation length is N c Is transmitted in a sequence ofxComprises the following steps:
preprocessing the binary LDPC codeuDividing into N sub-blocks, each sub-block having m bits, where N = N L /m；
The inner encoder randomly generates a Marker code of length NwCoding the MarkerwDividing into N subsequences with length of lambda, inserting each subsequence into preprocessed binary LDPC codeuBefore each symbol of (2), generating a length of N c Is transmitted as a codewordxWherein N is c ＝N L +N。
CN202210923831.0A 2022-08-02 2022-08-02 Marker-LDPC code transmission method based on data preprocessing Pending CN115425989A (en)

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