基于消息传播的LDPC码环统计算法

基于节点间的外部消息传播机制,提出一种新的LDPC码环统计算法,使用和积算法处理消息传播的过程,可有效地统计Tanner图中长度为g,g＋2,…,2g-2的环的数量,其中g为围长。与现有方法相比,本算法复杂度较低,特别适合于围长较长的LDPC码。     

一种低密度奇偶校验码的环数统计方法

对于Tanner图中给定码长的序列,LDPC码的短环对码的性能有重要影响.本文在分析LDPc码在Tanner图中的环在校验矩阵中的形状的基础上,提出了一种统计LDPC码中不同环长的环数的方法.首先对校验矩阵中一定数目的行组合中的环数进行统计,然后将所有行组合中的环数相加即得到校验矩阵中的环数.该方法可根据LDPC码的短环分布情况对其性能进行评估.应用提出的方法分别对MacKay的随机码和Fossorier的准循环码进行了环数统计.BER性能显示,尽管随机码环数特性比准循环码要差,但它的误码率性能比准循环码要好.     

多元LDPC码与二元LDPC码的性能分析

为了比较多元LDPC码与二元LDPC码的性能,文章从校验矩阵、Tanner图、BP译码算法等方面将两者进行有效的分析,并结合具体的Monte Carlo仿真实验,得出多元LDPC码的性能确实优于等长度码长的二元LDPC码.     

TS-LDPC Codes: Turbo-Structured Codes With Large Girth

We consider turbo-structured low-density parity-check (TS-LDPC) codes-structured regular codes whose Tanner graph is composed of two trees connected by an interleaver. TS-LDPC codes with good girth properties are easy to construct: careful design of the interleaver component prevents short cycles of any desired length in its Tanner graph. We present algorithms to construct TS-LDPC codes with arbitrary column weight jges2 and row weight k and arbitrary girth g. We develop a linear complexity encoding algorithm for a type of TS-LDPC codes-encoding friendly TS-LDPC (EFTS-LDPC) codes. Simulation results demonstrate that the bit-error rate (BER) performance at low signal-to-noise ratio (SNR) is competitive with the error performance of random LDPC codes of the same size, with better error floor properties at high SNR     

Error-Correction Capability of Column-Weight-Three LDPC Codes

In this paper, the error-correction capability of column-weight-three low-density parity-check (LDPC) codes when decoded using the Gallager A algorithm is investigated. It is proved that a necessary condition for a code to correct all error patterns with up to k ges 5 errors is to avoid cycles of length up to 2k in its Tanner graph. As a consequence of this result, it is shown that given any alpha > 0, exist N such that forall n > N, no code in the ensemble of column-weight-three codes can correct all alphan or fewer errors. The results are extended to the bit flipping algorithms.     

A CLASS OF LDPC CODE''''S CONSTRUCTION BASED ON AN ITERATIVE RANDOM METHOD

This letter gives a random construction for Low Density Parity Check (LDPC) codes, which uses an iterative algorithm to avoid short cycles in the Tanner graph. The construction method has great flexible choice in LDPC code's parameters including codelength, code rate, the least girth of the graph, the weight of column and row in the parity check matrix. The method can be applied to the irregular LDPC codes and strict regular LDPC codes. Systemic codes have many applications in digital communication, so this letter proposes a construction of the generator matrix of systemic LDPC codes from the parity check matrix. Simulations show that the method performs well with iterative decoding.     

QC LDPC码低复杂度消环算法

QC LDPC (Quasi-才yclic Low-density Parity-check)是一类半结构化的低密度奇偶校验码,其分块的矩阵结构具有超大规模集成电路实现上的便利,同时保持了优异的纠错性能. 本文针对QC LDPC码的基矩阵,提出一种移位因子的搜索方法及其改进版本。通过对基矩阵的扩展矩阵的Tanner图进行树形展开来进行环的检验,避免了传统算法中的复杂算术操作,降低了复杂度。在采用和IEEE 802.16e中码率为0.5的LDPC码方案相同的基矩阵条件下,本文的算法构造出的QC LDPC码具有更优的环长分布,同时纠错性能也有提升。      

基于PEG算法的准循环LDPC码构造方法研究

PEG算法,即逐步边增长算法,是一种基于Tanner图构造LDPC码的方法,研究表明该方法构造的LDPC码具有优 异的纠错性能.在PEG算法的基础上,本文提出了一种准循环LDPC码的构造方法.仿真结果表明,所提出的方法构造的LDPC码与用原始PEG算法构造的随机LDPC码具有几乎相同的优异性能,而且由于准循环特性,用本文提出的方法编译码更简单,可以通过反馈移位寄存器来实现.此外,码率更易于调整.     

A CLASS OF LDPC CODE’S CONSTRUCTION BASED ON AN ITERATIVE RANDOM METHOD

This letter gives a random construction for Low Density Parity Check （LDPC） codes, which uses an iterative algorithm to avoid short cycles in the Tanner graph. The construction method has great flexible choice in LDPC code＇s parameters including codelength, code rate, the least girth of the graph, the weight of column and row in the parity check matrix. The method can be applied to the irregular LDPC codes and strict regular LDPC codes. Systemic codes have many applications in digital communication, so this letter proposes a construction of the generator matrix of systemic LDPC codes from the parity check matrix. Simulations show that the method performs well with iterative decoding.     

Effective identification of dominant fully absorbing sets for Raptor-like LDPC codes

The error-rate floor of low-density parity-check (LDPC) codes is attributed to the trapping sets of their Tanner graphs. Among them, fully absorbing sets dominantly affect the error-rate performance, especially for short blocklengths. Efficient methods to identify the dominant trapping sets of LDPC codes were thoroughly researched as exhaustively searching them is NP-hard. However, the existing methods are ineffective for Raptor-like LDPC codes, which have many types of trapping sets. An effective method to identify dominant fully absorbing sets of Raptor-like LDPC codes is proposed. The search space of the proposed algorithm is optimized into the Tanner subgraphs of the codes to afford time-efficiency and search-effectiveness. For 5G New Radio (NR) base graph (BG) 2 LDPC codes for short blocklengths, the proposed algorithm finds more dominant fully absorbing sets within one seventh of the computation time of the existing search algorithm, and its search-effectiveness is verified using importance sampling. The proposed method is also applied to 5G NR BG1 LDPC code and Advanced Television Systems Committee 3.0 type A LDPC code for large blocklengths.     

Error rate estimation of low-density parity-check codes on binary symmetric channels using cycle enumeration

The performance of low-density parity-check (LDPC) codes decoded by hard-decision iterative decoding algorithms can be accurately estimated if the weight J and the number |E_J| of the smallest error patterns that cannot be corrected by the decoder are known. To obtain J and |E_J|, one would need to perform the direct enumeration of error patterns with weight ι ⩽ J. The complexity of enumeration increases exponentially with J, essentially as η^J, where η is the code block length. This limits the application of direct enumeration to codes with small η and J. In this letter, we approximate J and |E_J | by enumerating and testing the error patterns that are subsets of short cycles in the code's Tanner graph. This reduces the computational complexity by several orders of magnitude compared to direct enumeration, making it possible to estimate the error rates for almost any practical LDPC code. To obtain the error rate estimates, we propose an algorithm that progressively improves the estimates as larger cycles are enumerated. Through a number of examples, we demonstrate that the proposed method can accurately estimate both the bit error rate (BER) and the frame error rate (FER) of regular and irregular LDPC codes decoded by a variety of hard-decision iterative decoding algorithms.     

Regular Low-Density Parity-Check codes based on shifted identity matrices

This paper extends the class of Low-Density Parity-Check （LDPC） codes that can be constructed from shifted identity matrices. To construct regular LDPC codes, a new method is proposed. Two simple inequations are adopted to avoid the short cycles in Tanner graph, which makes the girth of Tanner graphs at least 8. Because their parity-check matrices are made up of circulant matrices, the new codes are quasi-cyclic codes. They perform well with iterative decoding.     

Pseudorandom construction of low-density parity-check codes using linear congruential sequences

We consider maximal-length linear congruential sequences generated using a simple recursion to generate the bipartite graph of a low-density parity-check (LDPC) code. The main advantage is that the graph structure of the codes (edge connections) can be generated using a recursion, rather than having to store the graph connections in memory, which facilitates hardware implementation of the decoder. For this class of codes, sufficient conditions on the recursion parameters are derived, such that regular LDPC codes can be constructed with no cycles of length four or less. Simulation results show that these codes provide almost the same performance of a constrained pseudorandom construction that explicitly avoids cycles of length less than or equal to four.     

LDPC码的一种循环差集构造方法

提出了一种由组合数学中的循环差集构造LDPC码的新方法,它能产生大量的列重和行重均为恒定值的规则码,并且可以排除圈长为4的圈和减少圈长等于6的圈。利用和积译码算法通过计算机仿真验证了这种码字具有优良的特性。     

有限平面LDPC码的停止集

有限平面LDPC码是一类重要的有结构的LDPC码,在利用和积算法(SPA)等迭代译码方法进行译码时表现出卓越的纠错性能。众所周知,次优的迭代译码不是最大似然译码,因而如何对迭代译码的性能进行理论分析一直是LDPC码的核心问题之一。近几年来,Tanner图上的停止集(stopping set)和停止距离(stopping distance)由于其在迭代译码性能分析中的重要作用而引起人们的重视。该文通过分析有限平面LDPC码的停止集和停止距离,从理论上证明了有限平面LDPC码的最小停止集一定是最小重量码字的支撑,从而对有限平面LDPC码在迭代译码下的良好性能给出了理论解释。     

基于FFT-BP算法的多元域LDPC码译码器设计与FPGA实现

GF(q)域上的LDPC码是二进制LDPC码的扩展,它具有比二进制LDPC码更好的纠错性能。FFT-BP算法是高效的LDPC码译码算法,本文在GF(4)域上探讨该算法的设计与实现。本文的创新之处在于,根据FFT-BP算法的特点设计了一种利用Tanner图进行信息索引的方式,简化了地址查询模块的设计。实验表明,在归一化信噪比为2.6dB时,译码器的误码率可达到10-6。     

基于稀疏二进制序列的低密度奇偶校验码

通过对低密度奇偶校验(LDPC)码构造的研究,提出了一种利用稀疏二进制序列构造规则LDPC码的新颖而简单的方法。在构造中,还提出了奇偶校验矩阵里元素‘1’的分布矩阵的概念。为了确保码Tanner图的最小圈长为8,利用了序列的周期自相关函数和周期互相关函数。通过仿真表明构造的新码在和积算法下进行迭代解码性能优异。由于产生的LDPC码本身固有的准循环结构,还能得到较低的编码复杂度。     

Design of Quasi‐Cyclic Low‐Density Parity Check Codes with Large Girth

In this paper we propose a graph‐theoretic method based on linear congruence for constructing low‐density parity check (LDPC) codes. In this method, we design a connection graph with three kinds of special paths to ensure that the Tanner graph of the parity check matrix mapped from the connection graph is without short cycles. The new construction method results in a class of (3, ρ)‐regular quasi‐cyclic LDPC codes with a girth of 12. Based on the structure of the parity check matrix, the lower bound on the minimum distance of the codes is found. The simulation studies of several proposed LDPC codes demonstrate powerful bit‐error‐rate performance with iterative decoding in additive white Gaussian noise channels.     

基于非正规LDPC码的中继协作通信及其联合迭代译码的性能研究

 本文构造了一种适用于中继协作通信的非正规LDPC系统码,并将双非正规LDPC系统码应用于中继协作系统中. 提出了目的点接收机基于双LDPC码联合Tanner图的对多路接收信号进行联合迭代译码的新算法. 理论分析和数值模拟表明本文所提出的新方法将高效信道编码和协作技术有机地结合起来以充分实现编码协作所具有的潜在分集和编码增益,与非协作系统相比可显著地提高系统性能.     

A class of low-density parity-check codes constructed based on Reed-Solomon codes with two information symbols

This letter presents an algebraic method for constructing regular low-density parity-check (LDPC) codes based on Reed-Solomon codes with two information symbols. The construction method results in a class of LDPC codes in Gallager's original form. Codes in this class are free of cycles of length 4 in their Tanner graphs and have good minimum distances. They perform well with iterative decoding.