Improved construction of irregular progressive edge-growth Tanner graphs

Progressive Differences Convolutional Low-Density Parity-Check Codes

We present a new family of low-density parity-check (LDPC) convolutional codes that can be designed using ordered sets of progressive differences. We study their properties and define a subset of codes in this class that have some desirable features, such as fixed minimum distance and Tanner graphs without short cycles. The design approach we propose ensures that these properties are guaranteed independently of the code rate. This makes these codes of interest in many practical applications, particularly when high rate codes are needed for saving bandwidth. We provide some examples of coded tr…

Optimized puncturing distributions for irregular non-binary LDPC codes

In this paper we design non-uniform bit-wise puncturing distributions for irregular non-binary LDPC (NB-LDPC) codes. The puncturing distributions are optimized by minimizing the decoding threshold of the punctured LDPC code, the threshold being computed with a Monte-Carlo implementation of Density Evolution. First, we show that Density Evolution computed with Monte-Carlo simulations provides accurate (very close) and precise (small variance) estimates of NB-LDPC code ensemble thresholds. Based on the proposed method, we analyze several puncturing distributions for regular and semi-regular code…

On the Tanner Graph Cycle Distribution of Random LDPC, Random Protograph-Based LDPC, and Random Quasi-Cyclic LDPC Code Ensembles

In this paper, we study the cycle distribution of random low-density parity-check (LDPC) codes, randomly constructed protograph-based LDPC codes, and random quasi-cyclic (QC) LDPC codes. We prove that for a random bipartite graph, with a given (irregular) degree distribution, the distributions of cycles of different length tend to independent Poisson distributions, as the size of the graph tends to infinity. We derive asymptotic upper and lower bounds on the expected values of the Poisson distributions that are independent of the size of the graph, and only depend on the degree distribution an…

Design of Non-Binary Quasi-Cyclic LDPC Codes by ACE Optimization

An algorithm for constructing Tanner graphs of non-binary irregular quasi-cyclic LDPC codes is introduced. It employs a new method for selection of edge labels allowing control over the code's non-binary ACE spectrum and resulting in low error-floor. The efficiency of the algorithm is demonstrated by generating good codes of short to moderate length over small fields, outperforming codes generated by the known methods.

Asymptotic Average Multiplicity of Structures within Different Categories of Trapping Sets, Absorbing Sets and Stopping Sets in Random Regular and Irregular LDPC Code Ensembles

The performance of low-density parity-check (LDPC) codes in the error floor region is closely related to some combinatorial structures of the code's Tanner graph, collectively referred to as {\it trapping sets (TSs)}. In this paper, we study the asymptotic average number of different types of trapping sets such as {\em elementary TSs (ETS)}, {\em leafless ETSs (LETS)}, {\em absorbing sets (ABS)}, {\em elementary ABSs (EABS)}, and {\em stopping sets (SS)}, in random variable-regular and irregular LDPC code ensembles. We demonstrate that, regardless of the type of the TS, as the code's length te…

具有接近于容量的端接LDPC卷积码

Terminated LDPC Convolutional Codes with Thresholds Close to Capacity

考虑了由置换矩阵组成的校验矩阵的LDPC卷积码系综。利用密度演化技术，分析了二进制输入输出对称无记忆信道下基于迭代置信传播的卷积码译码器的收敛性.我们观察到，结构化的不规则性在坦纳图的代码导致显着更好的阈值相比，相应的LDPC块码。

Characterization and Efficient Exhaustive Search Algorithm for Elementary Trapping Sets of Irregular LDPC Codes

In this paper, we propose a characterization of elementary trapping sets (ETSs) for irregular low-density parity-check (LDPC) codes. These sets are known to be the main culprits in the error floor region of such codes. The characterization of ETSs for irregular codes has been known to be a challenging problem due to the large variety of non-isomorphic ETS structures that can exist within the Tanner graph of these codes. This is a direct consequence of the variety of the degrees of the variable nodes that can participate in such structures. The proposed characterization is based on a hierarchic…

图上删余码译码复杂度的界

Bounds on the decoding complexity of punctured codes on graphs

我们提出了两个序列的合奏的非系统的不规则重复累积码渐近（因为它们的块长度趋于无穷大）实现容量的二进制擦除信道（BEC）的有限的复杂性，每个信息位。这是在对比所有以前的建设能力，实现序列的合奏，其复杂性增长至少像对数的倒数差距（率）的能力。新的有界复杂度的结果是通过打孔比特，并以这种方式允许足够数量的状态节点在坦纳图表示的代码。我们还推导出一个信息理论上的图上的随机打孔码的解码复杂度的下界。该界对每个无记忆二进制输入输出对称信道都成立，并对BEC进行了改进。

MAP译码下LDPC和LDGM码的紧界

Tight bounds for LDPC and LDGM codes under MAP decoding

提出了一种分析低密度奇偶检验（LDPC）码和低密度生成矩阵（LDGM）码比特最大后验概率（MAP）译码性能的新方法。该方法基于Francesco Guerra开发的严格的自旋玻璃方法。它允许构造下限上的熵的条件，收到的消息。基于启发式统计力学计算，我们推测这样的界限是紧的。当用于二进制输入输出对称通道时，该结果适用于标准的不规则合奏。该方法首先发展为具有Poisson左度分布的Tanner图系综。然后，它被推广到“多泊松”图，并通过一个完成程序，任意程度的分布。

Design of LDPC Codes using Multipath EMD Strategies and Progressive Edge Growth

Low-density parity-check (LDPC) codes are capable of achieving excellent performance and provide a useful alternative for high performance applications. However, at medium to high signal-to-noise ratios (SNR), an observable error floor arises from the loss of independence of messages passed under iterative graph-based decoding. In this paper, the error floor performance of short block length codes is improved by use of a novel candidate selection metric in code graph construction. The proposed Multipath EMD approach avoids harmful structures in the graph by evaluating certain properties of the…

Repeat Accumulate Based Designs for LDPC Codes on Fading Channels

Irregular repeat-accumulate Root-Check LDPC codes based on Progressive Edge Growth (PEG) techniques for block-fading channels are proposed. The proposed Root-Check LDPC codes are {both suitable for channels under $F = 2, 3$ independent fadings per codeword and} for fast fading channels. An IRA(A) Root-Check structure is devised for $F = 2, 3$ independent fadings. The performance of the new codes is investigated in terms of the Frame Error Rate (FER). Numerical results show that the IRAA LDPC codes constructed by the proposed algorithm {outperform by about 1dB the existing} IRA Root-Check LDPC …