CN110545156A - Combined algorithm for reducing QC-LDPC code error platform - Google Patents

Abstract

the invention relates to a joint algorithm for reducing QC-LDPC code error platforms, which comprises a joint check matrix extension and decoding algorithm. The invention has the beneficial effects that: the joint algorithm for reducing the QC-LDPC code error platform eliminates the undetectable error determined by the minimum distance by adding some check nodes at the cost of a small amount of code rate loss, and then further eliminates the trapping set of non-code words by utilizing a backtracking iterative decoding scheme, so that the decoding performance of the error plane region is better improved, the undetectable error determined by the minimum distance is eliminated by expanding a check matrix, and the minimum distance of the code is increased.

Description

combined algorithm for reducing QC-LDPC code error platform

Technical Field

The invention relates to the technical field of 5G communication, in particular to a joint algorithm for reducing a QC-LDPC code error platform.

background

The 5G communication system has determined that QC-LDPC codes are adopted as a channel coding scheme of a data channel in an embb scene, the LDPC codes are a channel coding scheme with good error correction capability and can achieve or approach Shannon limit performance in various channels, and the QC-LDPC codes are used as a branch of the LDPC codes, inherit the excellent characteristics of the proposed LDPC codes and have the characteristic of low coding complexity. Therefore, it has been adopted by many modern communication systems, especially 5G communication systems, also decide to use QC-LDPC codes as channel coding schemes for data channels in embb scenarios.

At present, with the continuous deepening of the construction, coding and decoding algorithm, performance structure analysis and the like of the LDPC codes, people find that most of the LDPC codes with medium code length have the problem of error floor, namely in a certain high signal-to-noise ratio region, the decoding performance is not obviously improved along with the increase of the signal-to-noise ratio, a performance curve presents a platform phenomenon, and the application of the LDPC codes in an actual communication system with extremely low Bit Error Rate (BER) requirement (the bit error rate requirement is lower than 10 < -12 > to 10 < -15 >) is limited.

Disclosure of Invention

The invention aims to provide a joint algorithm for reducing QC-LDPC code error platforms, which aims to solve the problem that most of LDPC codes with medium code length have error floor along with the continuous deepening of the construction, coding and decoding algorithm, performance structure analysis and the like of the LDPC codes proposed in the background technology, namely in a certain high signal-to-noise ratio region, the decoding performance is not obviously improved along with the increase of the signal-to-noise ratio, a performance curve shows a platform phenomenon, and the problem that the LDPC codes are limited to be applied to an actual communication system with extremely low Bit Error Rate (BER) (the bit error rate requirement is lower than 10 < -12 > to 10 < -15 >).

In order to achieve the purpose, the invention provides the following technical scheme: a joint algorithm for reducing QC-LDPC code error platforms is characterized by comprising a joint check matrix expansion and decoding algorithm.

Preferably, the scheme of the combined check matrix expansion and decoding algorithm is as follows:

1) Determining undetectable errors for QC-LDPC codes at high signal-to-noise ratios;

2) Expanding the check matrix in a precoding mode to eliminate the undetectable error determined by the minimum distance;

3) elimination of trapping sets (a, b) (b >0) using a backtracking iterative decoding scheme.

Preferably, the specific contents of the extended check matrix for eliminating the non-error detection errors are as follows:

errors generated by trapping sets (a, b) (b >0) can be eliminated by an improved decoding code algorithm [6] [7], but after a large number of non-code word trapping sets of QC-LDPC codes are eliminated, undetectable errors become dominant error events affecting the error floor by high signal-to-noise ratio (SNR) regions, and the structure of a special trapping set belonging to the undetectable errors is destroyed by adding some new check nodes by a method [4] and connecting the edges thereof to the trapping set to be eliminated.

Preferably, the method of said document [4] is as follows:

1) Any two trapping sets of T1, T2.. Tn involve non-intersecting variable nodes, one variable node is randomly selected from each trapping set of T1, T2.. Tn and connected to Ca, and the trapping sets of T1, T2.. Tn are eliminated;

2) Tn there are variable nodes in common, in which case one edge of Ca can eliminate multiple trapping sets containing a common variable node v. As shown in fig. 2 (b). This ensures that as many trapping sets as possible are eliminated by adding fewer edges.

preferably, the improved decoding algorithm eliminates trapping sets (a, b) (a >0, b >0) as follows: kang [6] proposes a backtracking iterative decoding algorithm to eliminate trapping sets, which does not need to know the dominant trapping sets in advance in detail and can decode codes constructed based on multiple methods. The algorithm is divided into a first backtracking decoding and a second backtracking decoding.

Preferably, the simulation result of the joint algorithm for reducing the QC-LDPC code error platform is as follows:

1) An LDPC code having a code rate of 1/2 and a code length n of 576 in the IEEE 802.16e standard;

2) The LDPC code with code rate 2/3 and code length n of 312 in the 5G standard.

preferably, the joint algorithm simulation for reducing the QC-LDPC code error platform adopts Binary Phase Shift Keying (BPSK) transmission on additive gaussian noise (AWGN) channel, and sets the maximum iteration number of the conventional sum-product decoder to 50.

compared with the prior art, the method has the following beneficial effects: by adding some check nodes, the undetected error determined by the minimum distance is eliminated at the cost of a small amount of code rate loss, then, a traceback iterative decoding scheme is utilized to further eliminate the trapping set of the non-code word, so that the decoding performance of the error flat layer area is better improved.

Drawings

FIG. 1 is a schematic diagram of (a, b) trapping sets in the present invention;

FIG. 2 is a schematic diagram of a trapping set a in the present invention;

FIG. 3 is a schematic diagram of trapping set b in the present invention;

FIG. 4 is a diagram illustrating an error pattern of a code when decoding fails according to the traceback decoding scheme of the present invention;

FIG. 5 is a schematic diagram of a parity check matrix of a WiMAX code in the invention;

FIG. 6 is a diagram of a parity check matrix of the 5G code according to the present invention.

Detailed Description

the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.

the invention provides a technical scheme that: a joint algorithm for reducing QC-LDPC code error platforms comprises a joint check matrix extension and decoding algorithm.

The method firstly eliminates the undetectable error determined by the minimum distance by adding some check nodes at the cost of a small amount of code rate loss, and then further eliminates the trapping set of non-code words by utilizing a backtracking iterative decoding scheme, thereby better improving the decoding performance of an error level region.

the general idea of the method is similar to [8], but there are many differences in details.

1) The main goal of this article is to eliminate trapping sets of QC-LDPC codes, rather than random LDPC codes.

2) The method in [8] can not be used by the original quick encoder of QC-LDPC, and the joint algorithm adopts a pre-coding mode to solve the problem.

3) The joint algorithm directly and simply modifies the existing original code, and the PEG algorithm is directly utilized to construct the code in [8 ].

Richardson [6] first proposed the concept of "trapping sets" for better analysis of the phenomenon of error floor of LDPC codes under AWGN channels. Let T be a set of error bits that eventually cause decoding failure, and if a subgraph generated in T contains a variable nodes and b odd check nodes, then T is called a (a, b) trapping set.

Taking the trapping set (5,3) as an example, the influence of the trapping set on the iterative decoding of the LDPC code is explained. The trapping set has 5 variable nodes and 3 check nodes. When these five variable nodes are in an error state, the other even degree check nodes satisfy the check relationship. Therefore, these check nodes will propagate the error information of the 5 variable nodes in the next iteration. However, there are three odd-degree check nodes that do not satisfy the check relationship, which will prevent propagation of error messages. Because the number of odd-degree check nodes in the trapping set is too small, errors caused by wrong variable nodes cannot be corrected, and therefore the decoder is prevented from converging to correct code words.

the error floor is mainly due to small trapping sets and undetectable errors, however, from a decoding point of view, this time with improved decoding algorithms [5] [6] only eliminates trapping sets (a, b) (a >0, b > 0). But fail to address special trapping sets such as undetectable codewords. If only [2] to [4] are considered to break the structure of the original trapping set by means of code construction, the code design complexity is high for the QC-LDPC code with a large number of trapping sets, and even if a dominant trapping set is found, it still takes a long time, so if the performance of the error floor region of the QC-LDPC code is to be improved better, the two factors are considered at the same time.

The new scheme of the joint check matrix expansion and decoding algorithm is described as follows:

1) undetectable errors of QC-LDPC codes at high signal-to-noise ratios are determined.

2) adopts a pre-coding mode to expand the check matrix and eliminate the undetected error determined by the minimum distance

3) Trapping sets (a, b) (b >0) are eliminated using a backtracking iterative decoding scheme.

A. Extending the check matrix to eliminate non-error detection errors

errors generated by trapping sets (a, b) (b >0) can be eliminated through an improved decoding code algorithm [6] [7], but after a large number of non-code word trapping sets of QC-LDPC codes are eliminated, undetectable errors become dominant error events affecting error floors by high signal-to-noise ratio (SNR) areas, and new check nodes can be added through a method [4] and edges of the new check nodes are connected to the trapping sets to be eliminated, so that the structure of a special trapping set belonging to the undetectable errors is damaged. The following is a summary of the method of reference [4 ]:

let n trapping sets T1, T2,. Tn, Ca to be eliminated in the Tanner graph be newly added check nodes. When but only when one edge of Ca is connected to a trapping set, the trapping set is eliminated. As shown in fig. 2. Since the variable nodes involved in T1, T2.. Tn may intersect, there are two main cases:

1) The variable nodes involved in any two trapping sets of T1, T2.. Tn do not intersect, one variable node is randomly selected from each trapping set of T1, T2.. Tn and connected to Ca, and the trapping sets T1, T2.. Tn are eliminated.

Tn there are common variable nodes in T1, T2.. in this case, one edge of Ca can eliminate multiple trapping sets that contain a common variable node v. As shown in fig. 3. This ensures that as many trapping sets as possible are eliminated by adding fewer edges. However, it is necessary to avoid the situation that two edges of a newly added check node are connected to the same trapping set at the same time, so as to avoid introducing new undetectable errors.

And (4) making some improvements on the method, namely selecting edges of newly-added check nodes to be connected with variable nodes of corresponding information bits with the largest occurrence times. Because for QC-LDPC, the fast coding can be carried out by means of the dual diagonal structure of the check matrix, and the coding complexity is low. However, when the original code changes after the parity bits are newly added in the manner of document [4], the original fast encoder is no longer applicable, and therefore, considering that the edges of the newly added check nodes are only connected to the information bits, one of the information bits is selected as a new check bit, and precoding is performed on the information bits before the information bits are sent to the encoder each time, that is, the value of the selected check bit is a modulo-2 value of the remaining other information bit values. Therefore, the original encoder can be used for encoding, and the newly-added encoding complexity is low.

B. Improved decoding algorithm eliminates trapping sets (a, b) (a >0, b >0)

Kang [6] proposes a backtracking iterative decoding algorithm to eliminate trapping sets, which does not need to know the dominant trapping sets in advance in detail and can decode codes constructed based on multiple methods. The algorithm is divided into a first backtracking decoding and a second backtracking decoding, wherein the first backtracking decoding comprises the following steps:

firstly, performing a traditional sum-product decoding algorithm, if the final decoding fails and a minimum set of unsatisfied CN in the iterative decoding process is smaller than a preset value (the parameter influences the number of reversed bits and the complexity of the algorithm), starting a first backtracking decoding process, wherein the process mainly determines some variable nodes possibly participating in a trapping set according to the unsatisfied check nodes and the error output of the original iterative decoding, setting the initial channel message of the error bits to be a maximum possible initial channel message value and the sign of the initial channel message value is opposite to the initial value of the initial channel message by reversing the error bits one by one, and then restarting the decoding process, namely the first backtracking decoding, wherein in the stage of bit guessing, if the reversed variable nodes do not belong to the trapping set, the input LLR value causing the error mode of the decoder is not influenced, the re-decoding still fails, otherwise, the re-decoding has a high probability of success, and therefore, the first traceback decoding scheme can eliminate most trapping sets.

the joint algorithm simulates two different QC-LDPC codes, namely an LDPC code with code rate of 1/2 and code length n of 576 in the IEEE 802.16e standard, and an LDPC code with code rate of 2/3 and code length n of 312 in the 5G standard. In the simulation, the transmission of Binary Phase Shift Keying (BPSK) on an additive Gaussian noise (AWGN) channel is adopted, the maximum iteration number of a traditional sum-product decoder is set to be 50, and the result shows that the QC-LDPC error floor is remarkably reduced by the combined algorithm.

The number of error patterns of the code when decoding fails is traced back to the decoding scheme.

fig. 4 lists the number of error patterns when iterative decoding fails for two examples of the traceback decoding algorithm 6 at high snr. It can be seen that the proportion of the number of undetectable errors to the total number of error frames gradually increases, and finally more than 95% of error frames are all undetectable errors. Therefore, the key to extending the check matrix by using the precoding method is to eliminate the undetectable error that the traceback decoding algorithm does not work.

example 1, let H1 be the parity check matrix of (576,288) WiMAX code, add check rows with weight of 14 to H1 according to the method proposed in section a, and the added check rows are: {109,110,111,112,240,241,242,243,244,245,246,247,248,249} this check row eliminates all 24 undetectable errors (13,0) as determined by the minimum distance, which increases from 13 to 16. A traceback iterative decoder is then used on the modified code. As can be seen from fig. 5, the frame error rate performance of the proposed joint algorithm is improved by more than an order of magnitude compared with that of the conventional SPA decoder when the signal-to-noise ratio is 3.7 dB.

Example 2, let H2 be the parity check matrix of the (312,208)5G code, add two check rows with a weight of 13 to H2 according to the method proposed in section a, the two newly added check rows are: {104,105,106,107,108,109,110,111,112,113,114,115,116} {117,118,119,120,121,122,123,124,125,126,127,128,129} they eliminate all 26 undetectable errors (8,0) determined by the minimum distance, increasing the minimum distance from 8 to 10. A traceback iterative decoder is then also used on the modified code. As can be seen from fig. 6, at a signal-to-noise ratio of 4.7dB, the frame error rate performance of the joint algorithm is improved by nearly an order of magnitude compared with that of the conventional SPA decoder.

The working principle of the embodiment is as follows: the joint algorithm of the platform for reducing the QC-LDPC code errors firstly determines the undetectable errors of the QC-LDPC code at high signal-to-noise ratio, adds some new check nodes by a method [4], and connects the edges of the check nodes to a trapping set to be eliminated to destroy the structure of a special trapping set which belongs to the undetectable errors, and the edges of the newly added check nodes are selected to be connected with variable nodes of corresponding information bits with the largest occurrence frequency. Because for QC-LDPC, the fast coding can be carried out by means of the dual diagonal structure of the check matrix, and the coding complexity is low. However, when the original code changes after the parity bits are newly added in the manner of document [4], the original fast encoder is no longer applicable, and therefore, considering that the edges of the newly added check nodes are only connected to the information bits, one of the information bits is selected as a new check bit, and before each time the new check node is sent to the encoder, pre-coding is performed on the information bits for one time, that is, the value of the selected check bit is a modulo-2 value of the remaining values of the other information bits. Therefore, the original encoder can be used for encoding, the newly-increased encoding complexity is low, then the traditional sum-product decoding algorithm is carried out, and if the final decoding fails and a group of the minimum unsatisfied CN in the iterative decoding process is smaller than a preset value (the parameter influences the number of the turning bits and the complexity of the algorithm), the first backtracking decoding process is started. The process is mainly to determine some variable nodes possibly participating in the trapping set according to the unsatisfied check nodes and the error output of the original iterative decoding. The initial channel message is set to the maximum possible initial channel message value by turning over the error bits one by one, the sign of the error bits is opposite to the initial value of the initial channel message, then the decoding process is restarted, namely, the first retrospective decoding is carried out, and the joint algorithm is utilized to simulate two different QC-LDPC codes.

although the present invention has been described in detail with reference to the foregoing embodiments, it will be apparent to those skilled in the art that various changes in the embodiments and modifications of the invention can be made, and equivalents of some features of the embodiments and modifications can be made without departing from the spirit and scope of the invention.

Claims (7)

1. A joint algorithm for reducing QC-LDPC code error platforms is characterized by comprising a joint check matrix expansion and decoding algorithm.

2. The joint algorithm for reducing the error floor of QC-LDPC codes according to claim 1, characterized by: the scheme of the combined check matrix expansion and decoding algorithm is as follows:

1) Determining undetectable errors for QC-LDPC codes at high signal-to-noise ratios;

2) Expanding the check matrix in a precoding mode to eliminate the undetectable error determined by the minimum distance;

3) Elimination of trapping sets (a, b) (b >0) using a backtracking iterative decoding scheme.

3. The extended parity check matrix of claim 2, wherein the error of non-detectable detection is eliminated as follows:

errors generated by trapping sets (a, b) (b >0) can be eliminated by an improved decoding code algorithm [6] [7], but after a large number of non-code word trapping sets of QC-LDPC codes are eliminated, undetectable errors become dominant error events affecting the error floor by high signal-to-noise ratio (SNR) regions, and the structure of a special trapping set belonging to the undetectable errors is destroyed by adding some new check nodes by a method [4] and connecting the edges thereof to the trapping set to be eliminated.

4. The document [4] method according to claim 3 is as follows:

1) Any two trapping sets of T1, T2.. Tn involve non-intersecting variable nodes, one variable node is randomly selected from each trapping set of T1, T2.. Tn and connected to Ca, and the trapping sets of T1, T2.. Tn are eliminated;

2) Tn there are variable nodes in common, in which case one edge of Ca can eliminate multiple trapping sets containing a common variable node v. As shown in fig. 2 (b). This ensures that as many trapping sets as possible are eliminated by adding fewer edges.

5. The improved decoding algorithm of claim 2 eliminating trapping sets (a, b) (a >0, b >0) is specified as follows:

Kang [6] proposes a backtracking iterative decoding algorithm to eliminate trapping sets, which does not need to know the dominant trapping sets in advance in detail and can decode codes constructed based on multiple methods. The algorithm is divided into a first backtracking decoding and a second backtracking decoding.

6. The simulation result of the joint algorithm for reducing the QC-LDPC code error platform according to claim 1 is as follows:

1) An LDPC code having a code rate of 1/2 and a code length n of 576 in the IEEE 802.16e standard;

2) the LDPC code with code rate 2/3 and code length n of 312 in the 5G standard.

7. a joint algorithm simulation for reducing the error floor of QC-LDPC codes according to claim 6, which uses Binary Phase Shift Keying (BPSK) transmission over additive Gaussian noise (AWGN) channel and sets the maximum number of iterations of the conventional sum-product decoder to 50.