高速通信系统中两种Turbo迭代译码算法的比较

1993年提出的Turbo码因其优异的性能而引起编码界的关注.之后不久提出的乘积码,是Turbo码的一个分支,他是一种分组纠错码,具有良好的性能.但是多年来大多数学者将研究集中于卷积Turbo码,而很少有人关注考虑分组Turbo码（即乘积码）,事实上乘积码相比卷积Turbo码在牺牲较小性能的情况下很大程度地降低了译码复杂度.本文将基于软输入/输出的Turbo译码算法,提出并分析了传统的卷积Turbo码和分组Turbo码（乘积码）的迭代译码算法,并对比分析了两者的译码性能,最后结果表明,两类码非常适合于未来的高速移动通信系统应用,尤其对乘积码,不仅具有较高的码率,同时可以获得更好的误比特率性能,在实际应用中更具有吸引力.     

Turbo码并行译码中无冲突交织器设计方案

交织器的结构可以影响到Turbo码的最小码距,进而影响其编码增益,最终对误比特率产生较大影响。交织器的主要功能就是随机化输入信息码序列,并让两个子编码模块在任何时刻,不会同时输出码重较轻的码字。交织器的随机性直接影响着Turbo码并行译码性能,针对现有无冲突交织器中随机性较小的特点,引入行内、行间交织等处理方式,进一步增加了交织表的随机性,以此提高Turbo码并行译码的性能,并给出了行内、行间交织设计实例。     

基于Cyclic-2伪最大似然算法的Turbo乘积码在高速移动通信系统中的译码方法

采用扩展汉明码作为Turbo乘积码 (TPC)的子码时,与传统的Chase算法相比,Cyclic-2PML(循环 2伪最大似然)算法复杂度低。本文研究了基于该算法的TPC在高速移动通信系统中的译码方法,仿真比较了采用不同子码组合的TPC结合不同的调制方式在高斯信道和多径衰落信道中的性能。结果表明,以(32, 26, 4)扩展汉明码为子码的TPC,不仅具有较高的码率,同时可以获得更好的误比特率性能。     

基于校验子的Turbo乘积码仿真研究

针对Turbo乘积码译码延时的问题,提出一种基于校验子的Turbo乘积码译码算法(S-TPC),该算法根据校验子的值采取不同方式对每行(列)进行译码,节省了一部分校验子为0的码字的硬判决译码运算量。仿真结果表明,S-TPC(32,26)在迭代4次时,能在不降低译码性能的情况下,减少近50%的计算量。     

Turbo乘积码仿真研究

Turbo codes译码算法的核心是软输入/软输出迭代译码,把这种思想应用于乘积码的译码中,得到了Turbo乘积码(TPC)迭代译码算法。介绍了基于扩展汉明码的乘积码的迭代译码算法,时该算法在AWGN信道中的译码性能进行了仿真。     

Turbo乘积码在衰落信道中的应用

基于Turbo乘积码的编译码原理,利用Matlab仿真工具,对以(64,57,4)扩展汉明码为子码的Turbo乘积码进行迭代次数、量化比特数等不同参数的性能仿真,根据仿真结果选取最佳的设计参数,同时通过仿真给出了Turbo乘积码在衰落信道中的应用效果。结合Matlab仿真,在Quartus环境中完成编译码算法的硬件设计与调试,并将其应用到无线通信调制解调器中。测试结果表明,Turbo乘积码显著改善了调制解调器在衰落信道中的误码性能。     

Turbo乘积码的两种迭代译码器的比较

提出了Turbo乘积码的并行迭代译码原理,对比分析了一种新的并行迭代译码器和传统的串行译码器,给出了以扩展汉明码(32,26,4)、(64,57,4)为子码的二维Turbo乘积码(32,26,4)。、(64,57,4)。在通过两种不同的译码器时的仿真结果。仿真结果表明,采取并行迭代译码器,在保持同样的译码性能的同时降低了译码延时。     

宽带移动通信中Turbo乘积码的仿真研究

推出了一种新型的纠错码——Turbo乘积码(TPC),描述了Turbo乘积码的编译码基本思想,详细地分析了TPC的Turbo软迭代译码的核心思想,并对AWGN信道和瑞利衰落信道下的TPC的译码性能做了仿真分析,从仿真结果可以看出,在高编码效率时,TPC不仅具有更高的码率,而且可以获得很好的误码率性能,所以乘积码的软迭代译码方案有很好的应用性,在未来的宽带移动通信中具有广阔的应用前景。     

Turbo乘积码译码算法的简化

Chase算法是Turbo乘积码(TPC)软判决译码中常采用的算法之一。分析了传统Chase算法中寻找竞争码字对译码复杂度的影响,在此基础上提出了两种新的简化译码算法,省去了寻找竞争码字的过程。仿真结果表明,简化算法在基本保持传统Chase算法译码性能的基础上,降低了译码复杂度,提高了译码速度。     

基于FPGA的TPC编译码器设计与实现

介绍了Turbo乘积码(TPC)的编译码原理,并对TPC码字结构进行了分析。在高斯信道下给出了子码为扩展汉明码(64,57,4)的TPC码的误码率性能,并对编译码器的模块设计进行说明,同时采用Altera公司的EP2S180芯片完成了方案验证。结果表明,在系统时钟为100 MHz的情况下,译码时延约为44 μs,可较好地满足实时性需求。     

Refinements and asymptotic performance of bandwidth-efficient turbo product codes

In this letter, a turbo product code (TPC) is combined with multilevel modulations (8-phase-shift keying and 16-quadrature amplitude modulation). The component codes are Bose-Chaudhuri-Hocquengem (BCH) or extended BCH. We derive soft-input/soft-output modules based on the dual code, with exact Euclidean metrics, and we show that the iterative TPC decoder gains no advantage in performance from this. Next, we evaluate asymptotic approximations for maximum-likelihood (ML) decoding from a combinatorial approach that can be applied to any bit-interleaved multilevel modulated code, once the first term (or terms) of the Hamming weight spectrum are known. For the TPCs and modulations studied in this letter, random bit interleaving before modulation leads to improved ML asymptotes. Simulations confirm that this advantage is maintained also under iterative decoding.     

Estimating the fraction of erasure patterns correctable by linear codes

The conditional probability (fraction) of the successful decoding of erasure patterns of high (greater than the code distance) weights is investigated for linear codes with the partially known or unknown weight spectra of code words. The estimated conditional probabilities and the methods used to calculate them refer to arbitrary binary linear codes and binary Hamming, Panchenko, and Bose–Chaudhuri–Hocquenghem (BCH) codes, including their extended and shortened forms. Error detection probabilities are estimated under erasure-correction conditions. The product-code decoding algorithms involving the correction of high weight erasures by means of component Hamming, Panchenko, and BCH codes are proposed, and the upper estimate of decoding failure probability is presented.     

Rate Variable, Multi-Binary Turbo Codes with Controlled Error-Floor

In this letter we propose rate variable turbo codes based on the parallel concatenation of tailbiting Recursive Systematic multi-binary (m-ary) convolutional codes. Rate variability is not achieved by puncturing, which can have adverse effects on the minimum distance of the code. Using a variable number of input lines of the encoder, we obtain several different overall rates ranging from 1/2 to 7/8. The most suitable Soft-In- Soft-Out decoding algorithm for these turbo codes is based on the Dual Reciprocal Code, which is very efficient for high rate codes. A particular interleaver design, namely the ?backbone? interleaver, guarantees a high Hamming weight in codewords with information weight 2 and 3, as well as good minimum distances and fairly low multiplicities for higher information weights. Therefore, these codes have very low error floors.     

Error-erasure decoding of product codes (Corresp.)

Two error-erasure decoding algorithms for product codes that correct all the error-erasure patterns guaranteed correctable by the minimum Hamming distance of the product code are given. The first algorithm works when at least one of the component codes is majority-logic decodable. The second algorithm works for any product code. Both algorithms use the decoders of the component codes.     

On Decoding Binary Perfect and Quasi-Perfect Codes over Markov Noise Channels

We study the decoding problem when a binary linear perfect or quasi-perfect code is transmitted over a binary channel with additive Markov noise. After examining the properties of the channel block transition distribution, we derive sufficient conditions under which strict maximum-likelihood decoding is equivalent to strict minimum Hamming distance decoding when the code is perfect. Additionally, we show a near equivalence relationship between strict maximum likelihood and strict minimum distance decoding for quasi-perfect codes for a range of channel parameters and the code's minimum distance. As a result, an improved (complete) minimum distance decoder is proposed and simulations illustrating its benefits are provided.     

Asymptotic optimality of the GMD and Chase decoding algorithms

The generalized minimum distance (GMD) and Chase (1972) decoding algorithms are some of the most important suboptimum bounded distance decoding algorithms for binary linear block codes over an additive white Gaussian noise (AWGN) channel. We compute the limitation of the ratio between the probability of decoding error for the GMD or any one of the Chase decoding algorithms and that of the maximum-likelihood (ML) decoding when the signal-to-noise ratio (SNR) approaches infinity. If the minimum Hamming distance of the code is greater than 2, the limitation is shown to be equal to 1 and thus the GMD and Chase decoding algorithms are asymptotically optimum.     

关于Justesen代数几何码

本文通过建立保持Hamming距离的同构,给出了研究Justesen等(1989)所构造的代数几何码的一般方法,并取得一些新的结果。本文在进行译码研究时,首次把同类型的较小的代数几何码的码字与错误位置多项式的值相对应,从而清晰地揭示了译码过程,以及纠错能力。本文还得到一般代数几何码维数的上界和下界。最后给出了一个容易理解的译码算法。此算法类似于RS码的Peterson译码算法。     

一种低复杂度Turbo乘积码自适应Chase译码算法

针对Turbo乘积码(Turbo Product Codes, TPCs)中的译码问题,该文提出一种全新的低复杂度TPC自适应Chase迭代译码算法。与已有的报道不同,在译码过程中,新算法首先统计TPC码块内每一行(列)产生的代数译码后的备选序列与接收序列的相同最小欧氏距离的个数,然后根据统计结果,按照算法步骤调整译码所需的不可靠位数值。通过Monte Carlo仿真可验证,当TPC行列编码采用相同的扩展汉明码,且编码效率为0.879时,该算法与Pyndiah采用固定不可靠位数值迭代译码算法相比,在误码率BER为10-4处仅损失约0.08 dB的性能,但是译码平均复杂度降低可达到约40.4%。     

Simplified SCL decoding algorithm of polar codes based on critical sets

In order to reduce the high complexity of the successive cancellation list (SCL) algorithm for polar codes, a simplified SCL decoding algorithm based on critical sets (CS-SCL decoding algorithm) is proposed. The algorithm firstly constructs the critical sets according to the channel characteristics of the polar codes as well as comprehensively considering both the minimum Hamming weight (MHW) of the information bits and the channel reliability. The information bits within the critical sets and the path splitting are still performed by the SCL decoding algorithm while the information bits outside the critical sets are directly performed by the hard decision. Thus, the number of path ordering, copying, and deleting can be reduced during decoding. Furthermore, the computational complexity of the SCL decoding can also be reduced. Simulation results demonstrate that the decoding complexity of the proposed CS-SCL decoding algorithm, compared with the conventional SCL decoding algorithm, is reduced by at least 70%, while compared with the simplified SCL (PS-SS-SCL) algorithm which constructs the critical set with the first and second information bits of the Rate-1 nodes, its decoding complexity can also be reduced. Moreover, the loss of the error correction performance for the proposed CS-SCL decoding algorithm is minor. Therefore, the proposed CS-SCL algorithm is effective and can provide a reasonable tradeoff between the decoding performance and complexity for the decoding algorithm of polar codes.     

On generalized low-density parity-check codes based on Hammingcomponent codes

In this paper we investigate a generalization of Gallager's (1963) low-density (LD) parity-check codes, where as component codes single error correcting Hamming codes are used instead of single error detecting parity-check codes. It is proved that there exist such generalized low-density (GLD) codes for which the minimum distance is growing linearly with the block length, and a lower bound of the minimum distance is given. We also study iterative decoding of GLD codes for the communication over an additive white Gaussian noise channel. The performance in terms of the bit error rate, obtained by computer simulations, is presented for GLD codes of different lengths