基于组合交织器的高码率RA码的设计

针对一般交织器结构的重复累积(RA)码的奇偶校验矩阵中出现的短环问题,提出将一种组合技术应用于RA码的交织器结构,设计一种新型的组合交织器,使得产生的RA码具有高码率且无4环。仿真结果显示,在码长较长和高码率的情况下,组合交织的RA码译码性能优于传统交织器。     

基于Kirkman三元系的RA码交织器设计

重复累积(RA)码的随机交织器容易产生短环问题,增加了系统的误码率。通过平衡不完全区组设计中的Kirkman三元系设计,构造了KTS-RA码交织器。Kirkman三元系相遇数为1的特点使交织器中没有4环存在。RA码码率由所选平行类的个数确定,而Kirkman三元系含有较大的平行类数,因此码率可在较大范围内选择。仿真结果显示,KTS-RA码性能优于随机RA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     

Multilevel turbo coding with short interleavers

The impact of the interleaver, embedded in the encoder for a parallel concatenated code, called the turbo code, is studied. The known turbo codes consist of long random interleavers, whose purpose is to reduce the value of the error coefficients. It is shown that an increased minimum Hamming distance can be obtained by using a structured interleaver. For low bit-error rates (BERs), we show that the performance of turbo codes with a structured interleaver is better than that obtained with a random interleaver. Another important advantage of the structured interleaver is the short length required, which yields a short decoding delay and reduced decoding complexity (in terms of memory). We also consider the use of turbo codes as component codes in multilevel codes. Powerful coding structures that consist of two component codes are suggested. Computer simulations are performed in order to evaluate the reduction in coding gain due to suboptimal iterative decoding. From the results of these simulations we deduce that the degradation in the performance (due to suboptimal decoding) is very small     

Interleaver design for serially concatenated convolutional codes: theory and application

This paper addresses the problem of interleaver design for serially concatenated convolutional codes (SCCCs) tailored to the constituent codes of the SCCC configuration. We present a theoretical framework for interleaver optimization based on a cost function closely tied to the asymptotic bit-error rate (BER) of the block code C/sub s/ resulting from proper termination of the constituent codes in the SCCC code. We define a canonical form of the interleaving engine denoted as the finite state permuter (FSP) and using its structural property, develop a systematic iterative technique for construction of interleavers. The core theoretical results focus on the asymptotic behavior of a class of cost functions and their martingale property, which is then used to develop an order recursive interleaver optimization algorithm. We address the issue of the complexity of the interleaver growth algorithm presented in the paper and demonstrate that it has polynomial complexity. Subsequently, we provide details about the application of the proposed technique and present a modification of the algorithm that employs error pattern feedback for improved performance at a reduced complexity. Sample experimental results are provided for an SCCC code of rate 1/3 and information block length 320 that achieves a minimum distance of d/sub min/=44.     

Interleaver design for turbo codes

The performance of a turbo code with short block length depends critically on the interleaver design. There are two major criteria in the design of an interleaver: the distance spectrum of the code and the correlation between the information input data and the soft output of each decoder corresponding to its parity bits. This paper describes a new interleaver design for turbo codes with short block length based on these two criteria. A deterministic interleaver suitable for turbo codes is also described. Simulation results compare the new interleaver design to different existing interleavers     

Weighted nonbinary repeat-accumulate codes

Repeat-accumulate (RA) codes are random-like codes having remarkably good performance over an additive white Gaussian noise (AWGN) channel, like turbo and low-density parity-check (LDPC) codes. In this correspondence, we introduce an ensemble of random codes called "weighted nonbinary repeat-accumulate (WNRA) codes" whose encoder consists of a nonbinary repeater, a weighter, a pseudorandom symbol interleaver, and an accumulator over a finite field GF(q). They can be decoded in a simple way by applying the sum-product algorithm to their factor graphs over GF(q). Simulation results show that WNRA codes with proper weighting values over GF(4) or GF(8) are superior to binary RA codes on AWGN channels.     

Low-floor decoders for LDPC codes

One of the most significant impediments to the use of LDPC codes in many communication and storage systems is the error-rate floor phenomenon associated with their iterative decoders. The error floor has been attributed to certain subgraphs of an LDPC code?s Tanner graph induced by so-called trapping sets. We show in this paper that once we identify the trapping sets of an LDPC code of interest, a sum-product algorithm (SPA) decoder can be custom-designed to yield floors that are orders of magnitude lower than floors of the the conventional SPA decoder. We present three classes of such decoders: (1) a bi-mode decoder, (2) a bit-pinning decoder which utilizes one or more outer algebraic codes, and (3) three generalized-LDPC decoders. We demonstrate the effectiveness of these decoders for two codes, the rate-1/2 (2640,1320) Margulis code which is notorious for its floors and a rate-0.3 (640,192) quasi-cyclic code which has been devised for this study. Although the paper focuses on these two codes, the decoder design techniques presented are fully generalizable to any LDPC code.     

Combined turbo codes and interleaver design

The impact of the distance spectrum and interleaver structure on the bit error probability of turbo codes is considered. A new turbo code design method for Gaussian channels is presented. The proposed method combines a search for good component codes with interleaver design. The optimal distance spectrum is used as the design criterion to construct good turbo component codes at low signal-to-noise ratios (SNRs). In addition, an interleaver design method is proposed. This design improves the code performance at high SNR. Search for good component codes at low SNR is combined with a code matched interleaver design. This results in new turbo codes with a superior error performance relative to the best known codes at both low and high SNR. The performance is verified by both analysis and simulation     

一种非规则广义LDPC码的构造方法

广义低密度奇偶校验(Generalized Low睤ensity Parity睠heck,GLDPC)码把低密度奇偶校验(Low睤ensity Parity睠heck,LDPC)码中的单奇偶校验(Single Parity睠heck,SPC)节点替换为校验能力更强的广义约束(Generalized Constraint,GC)节点,使其在中短码和低码率的条件下具有更低的误码率。传统GLDPC码要求基矩阵的行重等于分量码的码长,这限制了GLDPC码构造的灵活性。另外,相比于传统GLDPC码中GC节点位置的随机选取,GC节点的位置选择在GLDPC码的误码率性能上有一定的优化空间。针对以上两点,提出了一种基于渐进边增长(Progressive Edge-rowth,PEG)算法的非规则GLDPC码构造方法和一种基于Tanner图边数的GC节点位置选择算法。使用PEG算法生成的非规则LDPC码作为本地码,根据本地码的校验节点度使用多种分量码,结合GC节点位置选择算法构造非规则GLDPC码。仿真结果表明,与传统方法构造的GLDPC码相比,基于Tanner图边数的GC节点位置选择算法构造的非规则PEG-LDPC码在误码率和译码复杂度上均得到明显改善。     

Coding theorems for turbo code ensembles

This paper is devoted to a Shannon-theoretic study of turbo codes. We prove that ensembles of parallel and serial turbo codes are "good" in the following sense. For a turbo code ensemble defined by a fixed set of component codes (subject only to mild necessary restrictions), there exists a positive number γ₀ such that for any binary-input memoryless channel whose Bhattacharyya noise parameter is less than γ₀, the average maximum-likelihood (ML) decoder block error probability approaches zero, at least as fast as n ^-β, where β is the "interleaver gain" exponent defined by Benedetto et al. in 1996     

Recent Advances in Turbo Code Design and Theory

The discovery of turbo codes and the subsequent rediscovery of low-density parity-check (LDPC) codes represent major milestones in the field of channel coding. Recent advances in the design and theory of turbo codes and their relationship to LDPC codes are discussed. Several new interleaver designs for turbo codes are presented which illustrate the important role that the interleaver plays in these codes. The relationship between turbo codes and LDPC codes is explored via an explicit formulation of the parity-check matrix of a turbo code, and simulation results are given for sum product decoding of a turbo code.     

Analysis, design, and iterative decoding of double seriallyconcatenated codes with interleavers

A double serially concatenated code with two interleavers consists of the cascade of an outer encoder, an interleaver permuting the outer codeword bits, a middle encoder, another interleaver permuting the middle codeword bits, and an inner encoder whose input words are the permuted middle codewords. The construction can be generalized to h cascaded encoders separated by h-1 interleavers, where h>3. We obtain upper bounds to the average maximum likelihood bit-error probability of double serially concatenated block and convolutional coding schemes. Then, we derive design guidelines for the outer, middle, and inner codes that maximize the interleaver gain and the asymptotic slope of the error probability curves. Finally, we propose a low-complexity iterative decoding algorithm. Comparisons with parallel concatenated convolutional codes, known as “turbo codes”, and with the proposed serially concatenated convolutional codes are also presented, showing that in some cases, the new schemes offer better performance     

改进交织的单层极化码高阶编码调制系统

极化码作为一种新型编码方式,被采纳为5G通信中的短码方案。本文将极化码应用到比特交织编码调制（Bit-Interleaved Coded Modulation,BICM）系统,优化交织器的设计,提出了一种新型交织算法。相比于现有的交织算法,新型交织算法的提出是基于比特信道可靠性衡量参数,将高可靠性的比特信道与低可靠性的比特信道交错设计,按照高可靠性信道对低可靠性信道辅助译码的方式,提高极化码的纠错性能。由于新型交织算法只存在于比特信道可靠度参数的简单排序,在复杂度上没有明显增加。仿真结果表明:新型交织算法具有优异的性能,当误码率为10-5,码长为256时,采用新型交织算法的极化码BICM系统与LDPC码的BICM系统相比大约有1.51 dB的增益。      

Explicit construction of families of LDPC codes with no 4-cycles

Low-density parity-check (LDPC) codes are serious contenders to turbo codes in terms of decoding performance. One of the main problems is to give an explicit construction of such codes whose Tanner graphs have known girth. For a prime power q and m/spl ges/2, Lazebnik and Ustimenko construct a q-regular bipartite graph D(m,q) on 2q/sup m/ vertices, which has girth at least 2/spl lceil/m/2/spl rceil/+4. We regard these graphs as Tanner graphs of binary codes LU(m,q). We can determine the dimension and minimum weight of LU(2,q), and show that the weight of its minimum stopping set is at least q+2 for q odd and exactly q+2 for q even. We know that D(2,q) has girth 6 and diameter 4, whereas D(3,q) has girth 8 and diameter 6. We prove that for an odd prime p, LU(3,p) is a [p/sup 3/,k] code with k/spl ges/(p/sup 3/-2p/sup 2/+3p-2)/2. We show that the minimum weight and the weight of the minimum stopping set of LU(3,q) are at least 2q and they are exactly 2q for many LU(3,q) codes. We find some interesting LDPC codes by our partial row construction. We also give simulation results for some of our codes.     

Trellis-coded differential unitary space-time modulation over flat fading channels

Coding and modulation for multiple-antenna systems have gained much attention in wireless communications. This paper investigates a noncoherent trellis-coded scheme based on differential unitary space-time modulation when neither the transmitter nor the receiver know the channel. In a time-varying flat Rayleigh fading environment, we derive differentially noncoherent decision metrics and obtain performance measures for systems with either an ideal interleaver or no interleaver. We demonstrate that with an ideal interleaver, the system performance is dominated by the minimum Hamming distance of the trellis code, while without an interleaver, the performance is dominated by the minimum free squared determinant distance (a novel generalization of the Euclidean distance) of the code. For both cases, code construction is described for Ungerboeck-type codes. Several examples that are based on diagonal cyclic group constellations and offer a good tradeoff between the coding advantage and trellis complexity are provided. Simulation results show that, by applying the soft-decision Viterbi decoder, the proposed scheme can achieve very good performance even with few receive antennas. Extensions to trellis-coded differential space-time block codes are also discussed.     

Serial concatenation of interleaved codes: performance analysis,design, and iterative decoding

A serially concatenated code with interleaver consists of the cascade of an outer encoder, an interleaver permuting the outer codewords bits, and an inner encoder whose input words are the permuted outer codewords. The construction can be generalized to h cascaded encoders separated by h-1 interleavers. We obtain upper bounds to the average maximum-likelihood bit error probability of serially concatenated block and convolutional coding schemes. Then, we derive design guidelines for the outer and inner encoders that maximize the interleaver gain and the asymptotic slope of the error probability curves. Finally, we propose a new, low-complexity iterative decoding algorithm. Throughout the paper, extensive comparisons with parallel concatenated convolutional codes known as “turbo codes” are performed, showing that the new scheme can offer superior performance     

Turbo码中交织器的设计及性能分析

在Turbo码理论中,交织器的选择具有重要的地位。分析了Turbo码的编译码方案,然后讨论了交织器在Turbo码设计方面的重要作用,给出了几种交织器的实现方法,并模拟分析了其性能。     

Zigzag codes and concatenated zigzag codes

This paper introduces a family of error-correcting codes called zigzag codes. A zigzag code is described by a highly structured zigzag graph. Due to the structural properties of the graph, very low-complexity soft-in/soft-out decoding rules can be implemented. We present a decoding rule, based on the Max-Log-APP (MLA) formulation, which requires a total of only 20 addition-equivalent operations per information bit, per iteration. Simulation of a rate-1/2 concatenated zigzag code with four constituent encoders with interleaver length 65 536, yields a bit error rate (BER) of 10^-5 at 0.9 dB and 1.3 dB away from the Shannon limit by optimal (APP) and low-cost suboptimal (MLA) decoders, respectively. A union bound analysis of the bit error probability of the zigzag code is presented. It is shown that the union bounds for these codes can be generated very efficiently. It is also illustrated that, for a fixed interleaver size, the concatenated code has increased code potential as the number of constituent encoders increases. Finally, the analysis shows that zigzag codes with four or more constituent encoders have lower error floors than comparable turbo codes with two constituent encoders     

Exploiting UEP in QAM-based BICM: interleaver and code design

In this paper we formally analyze the interleaver and code design for QAM-based BICM transmissions using the binary reflected Gray code. We develop analytical bounds on the bit error rate and we use them to predict the performance of BICM when unequal error protection (UEP) is introduced by the constellation labeling. Based on these bounds the optimum design of interleaver and code is found, and numerical results for representative configurations are presented. When the new design is used, the improvements may reach 2 dB, and they are obtained without any increase on the transceiver?s complexity. We also introduce the concept of generalized optimum distance spectrum convolutional codes, which are the optimum codes for QAM-based BICM transmissions.