BCH-Turbo码的设计与仿真实现

本文针对Turbo码在低信噪比下迭代次数多、译码时延长问题,在分析了Turbo码的编译码原理和算法基础上,提出一种可以有效降低平均迭代次数、减少译码时延的基于BCH迭代停止准则的Turbo码迭代译码的设计方案.本方案采用BCH码作为Turbo迭代译码的停止准则,并对每一个分量译码器结果都进行判断,可提前停止迭代.通过Monte Carlo仿真表明在AWGN信道下,误码率有所降低,Turbo码译码的平均迭代次数与交叉熵准则相比有明显下降.本文还分析了BCH码编码效率和分组长度的选择对系统性能的影响.     

BCH-Turbo编码的设计与仿真实现

本文针对Turbo码在低信噪比下迭代次数多、译码时延长问题,在分析了Turbo码的编译码原理和算法基础上,提出一种可以有效降低平均迭代次数、减少译码时延的基于BCH迭代停止准则的Turbo码迭代译码的设计方案。本方案采用BCH码作为Turbo迭代译码的停止准则。并对每一个分量译码器结果都进行判断。可提前停止迭代。通过Monte Carlo仿真表明在AWGN信道下,误码率有所降低。Turbo码译码的平均迭代次数与交叉熵准则相比有明显下降。本文还分析了BCH码编码效率和分组长度的选择对系统性能的影响。     

并行级联分组码的一种新的迭代译码算法

并行级联分组码比串行级联分组码具有更高的码率,基于LLR计算的Turbo迭代译码算法使其内外分量码均做到了软判决译码。通过引入校正因子a（m）,将接收信息与子译码器的输出软信息进行线性叠加反馈能在省去繁琐的LLR计算的情况下实现并行级联分组码的Turbo迭代译码。仿真研究表明,若将译码器的输出进行简单的相关运算,可进一步改善译码器性能。     

级联RS码改善Turbo码的性能

分析了Turbo码的错误平层和迭代译码特性,研究了Turbo码与RS码的级联系统(TC-RS级联码)。分析和模拟表明:TC-RS级联系统不仅明显降低了帧错率(FER)和误比特率(BER),而且能够减少译码迭代次数,译码时间复杂度也低于标准Turbo码。     

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。     

一种简单的Turbo码的迭代停止判据

Turbo码提出之后,由于其优异的性能成为研究热点。但为了得到其优异的性能,在译码过程中需要进行多次迭代,这造成巨大的译码延时。在不影响性能的情况下,为减少译码延时,迭代停止在Turbo码迭代译码过程中十分重要。提出一种基于似然比绝对值大于某一门限的比特数目的迭代停止判据。并且给出平均迭代次数、译码性能的仿真。仿真结果证明该算法的有效性。     

Turbo码的迭代译码及在DS—CDMA和OFDM／CDMA中的应用

本文简单介绍了Turbo码基本原理、子码编码器和交织器设计等,详细地分析了Turbo码的基于MAP译码算法和基于SOVA译码算法的迭代译码方法及其性能,并与卷积码的性能进行了比较.重点论述了Turbo码在DS-CDMA移动通信系统的码率与扩频增益折衷设计、迭代译码和性能仿真结果.最后,简单论述了Turbo码在OFDM/CDMA中的应用.     

LDPC码译码算法及性能分析

为了进一步降低低密度奇偶校验(LDPC)码译码算法的复杂度,基于经典置信传播(BP)译码算法,给出了对数域迭代后验概率对数似然比(APP LLR)算法。通过概率域的和积算法(SPA)和对数域的迭代APP LLR算法的性能仿真及分析可见,迭代APP LLR算法能以较小的性能损失换取复杂度的大幅降低。进一步选用迭代APP LLR算法,结合不同地形条件下的VHF频段信道模型,仿真了LDPC码编译码系统的性能。理论分析及仿真结果均表明,基于迭代APP LLR算法的LDPC码,实现简单,性能优异,具有良好的工程应用前景。     

基于外信息收敛的Turbo码译码优化算法

目前Turbo码译码算法运算较复杂,无法满足LTE及LTE-Advanced的高速吞吐要求,因此,研究LTE环境下的Turbo码译码算法具有理论意义与工程价值。从降低译码延时考虑,评估各种迭代停止准则对性能及译码效率的影响,在分析外信息统计特性收敛的基础上,设计基于外信息收敛的双门限停止准则。仿真结果表明,改进的迭代停止准则在不影响译码性能的前提下,能较好地提高译码速率。     

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。     

Turbo Decoding on the Binary Erasure Channel: Finite-Length Analysis and Turbo Stopping Sets

This paper is devoted to the finite-length analysis of turbo decoding over the binary erasure channel (BEC). The performance of iterative belief-propagation decoding of low-density parity-check (LDPC) codes over the BEC can be characterized in terms of stopping sets. We describe turbo decoding on the BEC which is simpler than turbo decoding on other channels. We then adapt the concept of stopping sets to turbo decoding and state an exact condition for decoding failure. Apply turbo decoding until the transmitted codeword has been recovered, or the decoder fails to progress further. Then the set of erased positions that will remain when the decoder stops is equal to the unique maximum-size turbo stopping set which is also a subset of the set of erased positions. Furthermore, we present some improvements of the basic turbo decoding algorithm on the BEC. The proposed improved turbo decoding algorithm has substantially better error performance as illustrated by the given simulation results. Finally, we give an expression for the turbo stopping set size enumerating function under the uniform interleaver assumption, and an efficient enumeration algorithm of small-size turbo stopping sets for a particular interleaver. The solution is based on the algorithm proposed by Garello et al. in 2001 to compute an exhaustive list of all low-weight codewords in a turbo code.     

NEW ITERATIVE SUPER-TRELLIS DECODING WITH SOURCE A PRIORI INFORMATION FOR VLCS WITH TURBO CODES

A novel Joint Source and Channel Decoding （JSCD） scheme for Variable Length Codes （VLCs） concatenated with turbo codes utilizing a new super-trellis decoding algorithm is presented in this letter. The basic idea of our decoding algorithm is that source a priori information with the form of bit transition probabilities corresponding to the VLC tree can be derived directly from sub-state transitions in new composite-state represented super-trellis. A Maximum Likelihood （ML） decoding algorithm for VLC sequence estimations based on the proposed super-trellis is also described. Simulation results show that the new iterative decoding scheme can obtain obvious encoding gain especially for Reversible Variable Length Codes （RVLCs）, when compared with the classical separated turbo decoding and the previous joint decoding not considering source statistical characteristics.     

Turbo码概率-代数联合解码算法

Turbo码采用修正的BAHL et al.算法实现解码.这是一种基于软值的概率迭代解码算法.本文在保持Turbo码迭代软解码算法优点的基础上,充分利用Turbo码编码器结构这一确知条件,结合代数解码原理,提出了一种Turbo码概率-代数联合解码算法.该算法结合了概率解码和代数解码的优点,又有效避免了误差传播的发生,使Turbo码的纠错性能在原经典算法的基础上得到进一步的提高.该算法不仅为降低Turbo码的比特误码率和误差地板值提供了一种新的研究途径,而且因其更好的纠错性能而具有十分明显的实用价值.仿真实验结果显示,在比特误码率(BER)为10^-3~10^-4时,与经典Turbo码解码算法相比,采用该算法能获得0.1dB左右的编码增益.     

Turbo decoding as an instance of Pearl's “beliefpropagation” algorithm

We describe the close connection between the now celebrated iterative turbo decoding algorithm of Berrou et al. (1993) and an algorithm that has been well known in the artificial intelligence community for a decade, but which is relatively unknown to information theorists: Pearl's (1982) belief propagation algorithm. We see that if Pearl's algorithm is applied to the “belief network” of a parallel concatenation of two or more codes, the turbo decoding algorithm immediately results. Unfortunately, however, this belief diagram has loops, and Pearl only proved that his algorithm works when there are no loops, so an explanation of the experimental performance of turbo decoding is still lacking. However, we also show that Pearl's algorithm can be used to routinely derive previously known iterative, but suboptimal, decoding algorithms for a number of other error-control systems, including Gallager's (1962) low-density parity-check codes, serially concatenated codes, and product codes. Thus, belief propagation provides a very attractive general methodology for devising low-complexity iterative decoding algorithms for hybrid coded systems     

新的turbo迭代译码停止判据

根据turbo迭代译码算法的一动态系统的观点,本文提出了一种新的迭代译码停止判据,根据该判据进行turbo译码时,平均迭代次数减少,同时,所获得的性能没有降低。     

New stopping criteria for iterative decoding of LDPC codes in H‐ARQ systems

Under severely unreliable channel, decoding of error‐correcting codes frequently fails, which requires a lot of computational complexity, especially, in the iterative decoding algorithm. In hybrid automatic repeat request systems, most of computation power is wasted on failed decoding if a codeword is retransmitted many times. Therefore, early stopping of iterative decoding needs to be adopted. In this paper, we propose a new stopping algorithm of iterative belief propagation decoding for low‐density parity‐check codes, which is effective on both high and low signal‐to‐noise ratio ranges and scalable to variable code rate and length. The proposed stopping algorithm combines several good stopping criteria. Each criterion is extremely simple and will not be a burden to the overall system. With the proposed stopping algorithm, it is shown via numerical analysis that the decoding complexity of hybrid automatic repeat request system with adaptive modulation and coding scheme can be fairly reduced. Copyright © 2012 John Wiley & Sons, Ltd.     

Partial iterative decoding for binary turbo codes via cross-entropy based bit selection

Near-capacity performance of turbo codes is generally achieved with a large number of decoding iterations. Various iteration stopping rules introduced in the literature often induce performance loss. This paper proposes a novel partial decoding iteration scheme using a bit-level convergence test. We first establish decoding optimality of windowed partial iteration for non-converged bits given that convergence has been achieved on window boundaries. We next present two criteria for testing bit convergence based on cross-entropy, and propose a windowed partial iteration algorithm. The overall complexity and memory requirements of the new algorithm are evaluated and compared with known algorithms. Simulations reveal that the proposed scheme suffers essentially no performance loss compared to full iterations, while reducing the decoding complexity. We also briefly discuss possible extensions of the proposed scheme to general iterative receivers.     

An Efficient Stopping Criterion for Turbo Product Codes

In this letter, a stopping criterion using the error- detecting capability of linear block codes is proposed for the decoding of turbo product codes. The iterative decoding is stopped when the outputs from the Chase decoder are valid codewords for all rows and columns simultaneously. Simulation shows that the proposed method can reduce about one and half iterations compared with an existing stopping method, without noticeable BER performance loss. Some modification has also been discussed which may further reduce the decoding complexity.