The design of efficiently-encodable rate-compatible LDPC codes - [transactions papers]

We present a new class of irregular low-density parity-check (LDPC) codes for moderate block lengths (up to a few thousand bits) that are well-suited for rate-compatible puncturing. The proposed codes show good performance under puncturing over a wide range of rates and are suitable for usage in incremental redundancy hybrid-automatic repeat request (ARQ) systems. In addition, these codes are linear-time encodable with simple shift-register circuits. For a block length of 1200 bits the codes outperform optimized irregular LDPC codes and extended irregular repeat-accumulate (eIRA) codes for all puncturing rates 0.6~0.9 (base code performance is almost the same) and are particularly good at high puncturing rates where good puncturing performance has been previously difficult to achieve.     

On construction of rate-compatible low-density Parity-check codes

In this letter, we present a framework for constructing rate-compatible low-density parity-check (LDPC) codes. The codes are linear-time encodable and are constructed from a mother code using puncturing and extending. Application of the proposed construction to a type-II hybrid automatic repeat request (ARQ) scheme with information block length k=1024 and code rates 8/19 to 8/10, using an optimized irregular mother code of rate 8/13, results in a throughput which is only about 0.7 dB away from Shannon limit. This outperforms existing similar schemes based on turbo codes and LDPC codes by up to 0.5 dB.     

一种新的码率兼容LDPC码打孔方案

该文研究码率兼容LDPC码的打孔问题。Ha等人研究LDPC码打孔时提出的Grouping和Sorting方案使低k-SR节点的数目最大化,它相对于随机打孔有了很大增益,但此方案只保证有一个存活校验节点。该文研究多个存活校验节点的作用,提出MSCN打孔方案最大化打孔节点的存活校验节点数。AWGN信道上的仿真结果显示,低码率时MSCN方案具有比Grouping和Sorting方案更为优越的性能。理论推导及实验结果均表明,码率兼容LDPC码打孔时,多个存活校验节点有益于译码性能的提升。     

Rate-compatible puncturing of low-density parity-check codes

In this correspondence, we consider puncturing of low-density parity-check (LDPC) codes for additive white Gaussian noise (AWGN) channels. We show that good puncturing patterns exist and that the puncturing can be performed in a rate-compatible fashion. Furthermore, rate-compatible puncturing results in a small loss of performance with respect to threshold, namely, the punctured code is good (in terms of threshold) across a range of rates when compared with the optimal codes for each rate. This allows one to implement a single "mother" encoder and decoder that is good across a wide range of rates.     

Rate-compatible low-density generator matrix codes

We propose a family of rate-compatible codes based on the concatenation of two linear codes with low-density generator matrix, which are a special class of LDPC codes with low encoding complexity. The proposed scheme is characterized by its simplicity of construction, and does not require optimization of the puncturing pattern.     

Design of rate-compatible structured LDPC codes for hybrid ARQ applications

In this paper, families of rate-compatible protograph-based LDPC codes that are suitable for incrementalredundancy hybrid ARQ applications are constructed. A systematic technique to construct low-rate base codes from a higher rate code is presented. The base codes are designed to be robust against erasures while having a good performance on error channels. A progressive node puncturing algorithm is devised to construct a family of higher rate codes from the base code. The performance of this puncturing algorithm is compared to other puncturing schemes. Using the techniques in this paper, one can construct a rate-compatible family of codes with rates ranging from 0.1 to 0.9 that are within 1 dB from the channel capacity and have good error floors.     

Capacity Achieving LDPC Codes Through Puncturing

The performance of punctured low-definition parity-check (LDPC) codes under maximum-likelihood (ML) decoding is studied in this correspondence via deriving and analyzing their average weight distributions (AWDs) and the corresponding asymptotic growth rate of the AWDs. In particular, it is proved that capacity-achieving codes of any rate and for any memoryless binary-input output-symmetric (MBIOS) channel under ML decoding can be constructed by puncturing some original LDPC code with small enough rate. Moreover, it is shown that the gap to capacity of all the punctured codes can be the same as the original code with a small enough rate. Conditions under which puncturing results in no rate loss with asymptotically high probability are also given in the process. These results show high potential for puncturing to be used in designing capacity-achieving codes, and in rate-compatible coding under any MBIOS channel.      

Design and analysis of E2RC codes

We consider the design and analysis of the efficiently-encodable rate-compatible (E²RC) irregular LDPC codes proposed in previous work. In this work we introduce semi-structured E²RC-like codes and protograph E²RC codes. EXIT chart based methods are developed for the design of semi-structured E²RC-like codes that allow us to determine near-optimal degree distributions for the systematic part of the code while taking into account the structure of the deterministic parity part, thus resolving one of the open issues in the original construction. We develop a fast EXIT function computation method that does not rely on Monte-Carlo simulations and can be used in other scenarios as well. Our approach allows us to jointly optimize code performance across the range of rates under puncturing.We then consider protograph E²RC codes (that have a protograph representation) and propose rules for designing a family of rate-compatible punctured protographs with low thresholds. For both the semi-structured and protograph E²RC families we obtain codes whose gap to capacity is at most 0.3 dB across the range of rates when the maximum variable node degree is twenty.     

比特级码率兼容多元LDPC码打孔算法

多元低密度奇偶校验(Non-binary Low-density Parity-check,NB-LDPC)码在中短码情况下性能优于传统二元LDPC码,更接近香农限.针对多元LDPC码码率兼容(Rate-compatible)的问题,提出了一种基于比特级的新型多元打孔算法.首先采用二进制镜像矩阵概念对多元校验矩阵进行映...     

可变速率多元LDPC码高阶调制系统

由于无线信道的时变性及无线频谱资源的短缺,码率自适应技术及高频谱效率的高阶调制技术均为未来高速率无线通信发展的必然方向,本文提出了一种基于多元速率兼容LDPC（RC-LDPC）码的可变速率高阶编码调制方案。该方案基于符号级的多元LDPC码缩短和打孔算法,并与高阶映射联合优化设计,获得了比二元RC-LDPC码方案优异的性能,实现了多元LDPC码率从1/3到5/6灵活变化,并且所有子码都可以共享母码的编译码器,因此相对于多元母码,基本不增加系统复杂度。仿真结果证明采用64-QAM调制时,本方案的误码率性能比二元码对应方案在各个码率分别有0.5到1.3dB的增益。      

New Table-Switching and Data-Multiplexing Schemes of Rate-Compatible Punctured Convolutional Codes for Unequal Error Protection

In this letter, rate-compatible punctured convolutional (RCPC) codes are further investigated for the application to unequal error protection (UEP). Besides the rate-compatible restriction, we show that puncturing tables should be switched in a special way called soft-switching to guarantee the designed UEP performance. A new data-multiplexing scheme is also proposed for RCPC codes which can achieve similar UEP performance as the conventional scheme but requires no extra zero-padding for frame termination to improve the system throughput.     

Design of Rate-Compatible Irregular Repeat Accumulate Codes

We consider the design of efficient rate-compatible (RC) irregular repeat accumulate (IRA) codes over a wide code rate range. The goal is to provide a family of RC codes to achieve high throughput in hybrid automatic repeat request (ARQ) scheme for high-speed data packet wireless systems. As a subclass of low-density parity-check codes, IRA codes have an extremely simple encoder and a low-complexity decoder while providing capacity approaching performance. We focus on a hybrid design method which employs both puncturing and extending. We propose a simple puncturing method based on minimizing the maximal recoverable step of the punctured nodes. We also propose a new extending scheme for IRA codes by introducing the degree-1 parity bits for the lower rate codes and obtaining the optimal proportions of extended nodes through density evolution analysis. The throughput performance of the designed RC-IRA codes in hybrid ARQ is evaluated for both AWGN and block fading channels. Simulation results demonstrate that our designed RC codes offer good error correction performance over a wide rate range and provide high throughput, especially in the high and low signal-to-noise ratio regions.     

中短码长的率匹配多进制LDPC码研究设计

该课题研究构造了纠错能力强、编译码复杂度低的中短码长的率匹配多进制LDPC码。提出了一种校验位高效编码删余算法,以得到高性能的多进制RC-LDPC码。该删余算法以设计的高性能中短码长、中等码率(1/2码率)的多进制LDPC母码为基础,采用高效的结构化编码删余算法,实现比较宽的速率范围(例如1/10到9/10)内设计高性能的纠错码。仿真结果表明,此算法性能优于传统的随机删余和节点分组与排序删余算法。     

结构半随机LDPC码的递增冗余HARQ方案

提出了结构半随机LDPC码,分析了其在不同码率时,编、译码具有兼容性的特性。介绍了基于结构半随机LDPC码的递增冗余HARQ方案,给出了这种方案的吞吐量性能封闭解。在AWGN信道和Rayleigh衰落信道下,通过仿真将新方案的性能和随机LDPC码的性能进行了比较,结果显示,结构半随机LDPC码的递增冗余HARQ方案性能接近随机LDPC码,但编、译码更简单,参数选择范围更广。     

Accumulate-Repeat-Accumulate Codes

In this paper, we propose an innovative channel coding scheme called accumulate-repeat-accumulate (ARA) codes. This class of codes can be viewed as serial turbo-like codes or as a subclass of low-density parity check (LDPC) codes, and they have a projected graph or protograph representation; this allows for high-speed iterative decoding implementation using belief propagation. An ARA code can be viewed as precoded repeat accumulate (RA) code with puncturing or as precoded irregular repeat accumulate (IRA) code, where simply an accumulator is chosen as the precoder. The amount of performance improvement due to the precoder will be called precoding gain. Using density evolution on their associated protographs, we find some rate-1/2 ARA codes, with a maximum variable node degree of 5 for which a minimum bit SNR as low as 0.08 dB from channel capacity threshold is achieved as the block size goes to infinity. Such a low threshold cannot be achieved by RA, IRA, or unstructured irregular LDPC codes with the same constraint on the maximum variable node degree. Furthermore, by puncturing the inner accumulator, we can construct families of higher rate ARA codes with thresholds that stay close to their respective channel capacity thresholds uniformly. Iterative decoding simulation results are provided and compared with turbo codes. In addition to iterative decoding analysis, we analyzed the performance of ARA codes with maximum-likelihood (ML) decoding. By obtaining the weight distribution of these codes and through existing tightest bounds we have shown that the ML SNR threshold of ARA codes also approaches very closely to that of random codes. These codes have better interleaving gain than turbo codes     

多元速率兼容LDPC码的自适应编码调制系统研究

本文设计了一种基于有限域GF(q)上的多元速率兼容LDPC (RC-LDPC) 码结合高阶调制的自适应编码调制(Adaptive Coded Modulation, ACM) 系统。并提出了多元RC-LDPC码在独立和相关衰落信道下的增量冗余型自适应编码调制方案。本方案中多元LDPC码码率从1/3到5/6灵活变化,以较低的系统复杂度,有效提高了系统的频带利用率。仿真结果表明:随着系统吞吐率提高,多元ACM系统相对于二元ACM系统具有越来越明显的编码增益,最高可达约9 dB。      

Speech transmission using rate-compatible trellis codes andembedded source coding

This paper presents bandwidth-efficient speech transmission systems using rate-compatible channel coders and variable bitrate embedded source coders. Rate-compatible punctured convolutional codes (RCPC) are often used to provide unequal error protection (UEP) via progressive bit puncturing. RCPC codes are well suited for constellations for which Euclidean and Hamming distances are equivalent (BPSK and 4-PSK). This paper introduces rate-compatible punctured trellis codes (RCPT) where rate compatibility and UEP are provided via progressive puncturing of symbols in a trellis. RCPT codes constitute a special class of codes designed to maximize residual Euclidean distances (RED) after symbol puncturing. They can be designed for any constellation, allowing for higher throughput than when restricted to using 4-PSK. We apply RCPC and RCPT to two embedded source coders: a perceptual subband coder and the ITU embedded ADPCM G.727 standard. Different operating modes with distinct source/channel bit allocation and UEP are defined. Each mode is optimal for a certain range of AWGN channel SNRs. Performance results using an 8-PSK constellation clearly illustrate the wide range of channel conditions at which the adaptive scheme using RCPT can operate. For an 8-PSK constellation, RCPT codes are compared to RCPC with bit interleaved coded modulation codes (RCPC-BICM). We also compare performance to RCPC codes used with a 4-PSK constellation     

Rate-compatible convolutional codes for multirate DS-CDMA systems

New rate-compatible convolutional (RCC) codes with high constraint lengths and a wide range of code rates are presented. These new codes originate from rate 1/4 optimum distance spectrum (ODS) convolutional parent encoders with constraint lengths 7-10. Low rate encoders (rates 115 down to 1/10) are found by a nested search, and high rate encoders (rates above 1/4) are found by rate-compatible puncturing. The new codes form rate-compatible code families more powerful and flexible than those previously presented. It is shown that these codes are almost as good as the existing optimum convolutional codes of the same fates. The effects of varying the design parameters of the rate-compatible punctured convolutional (RCPC) codes, i.e., the parent encoder rate, the puncturing period, and the constraint length, are also examined. The new codes are then applied to a multicode direct-sequence code-division multiple-access (DS-CDMA) system and are shown to provide good performance and rate-matching capabilities. The results, which are evaluated in terms of the efficiency for Gaussian and Rayleigh fading channels, show that the system efficiency increases with decreasing code rate     

High-performance simple-encoding generator-based systematic irregular LDPC codes and resulted product codes

Low-Density Parity-Check (LDPC) code is one of the most exciting topics among the coding theory community.It is of great importance in both theory and practical communications over noisy channels.The most advantage of LDPC codes is their relatively lower decoding complexity compared with turbo codes,while the disadvantage is its higher encoding complexity.In this paper,a new ap- proach is first proposed to construct high performance irregular systematic LDPC codes based on sparse generator matrix,which can significantly reduce the encoding complexity under the same de- coding complexity as that of regular or irregular LDPC codes defined by traditional sparse parity-check matrix.Then,the proposed generator-based systematic irregular LDPC codes are adopted as con- stituent block codes in rows and columns to design a new kind of product codes family,which also can be interpreted as irregular LDPC codes characterized by graph and thus decoded iteratively.Finally, the performance of the generator-based LDPC codes and the resultant product codes is investigated over an Additive White Gaussian Noise (AWGN) and also compared with the conventional LDPC codes under the same conditions of decoding complexity and channel noise.     

Combined puncturing and path pruning for convolutional codes and the application to unequal error protection

In this paper, puncturing and path pruning are combined for convolutional codes to construct a new coding scheme for unequal error protection (UEP), called the hybrid punctured and path-pruned convolutional codes. From an algebraic viewpoint, we show that the hybrid codes not only inherit all the advantages of the conventional rate-compatible punctured convolutional codes and path-compatible pruned convolutional codes but also can provide more flexible choices of protection capability for UEP. In addition, a data-multiplexing scheme originally proposed for path-pruned codes which can guarantee smooth transition between rates without additional zero-padding for frame termination is proven applicable to the hybrid codes to improve the system throughput.