Soft-decision Multi-stage Decoding for Linear Block Codes

本研究的目的是利用连续分量译码器之间的软值来改善多级译码方案的误码性能。为此，作者提出了n种有效的软输入软输出Log-MAP递归译码算法（R-logMap算法）。该算法充分利用了线性分组码的结构特性，与传统的BCJR算法相比，大大降低了译码复杂度。例如，计算机模拟表明，所提出的算法所需的解码长度为128的二阶Reed-Muller（RM）码的复杂度只有3%的传统的BCJR算法，其中的复杂度是由度量的加法等价运算的数量来衡量的。log-MAP译码在译码过程中采用了一些近似来降低计算复杂度，因此其性能不如最优MAP译码。通过稍微修改R-logMAP算法， 关于我们 可以容易地实现有效的MAP算法。通过使用所提出的log-MAP和MAP算法，所提出的多级解码方案的总解码复杂度可以显着降低。在多级译码方案中，作者详细研究了最近陪集译码方案。通过用对数MAP或MAP译码器代替最近陪集译码器的分量译码器，并在末级到第一级之间引入一个反馈，可以实现一种新的多级迭代译码方案。分析了新方案的译码复杂度和误码性能。仿真结果表明，对于长度为64的二阶RM码的译码，与传统的最接近陪集译码方案相比，在10^误块率下，采用两次（分别为五次）重复的log-MAP（res.MAP）译码方案的性能提高了0.4dB（分别为0.5sB）<-5>。与最大似然（ML）译码器相比，译码器的误码性能下降为0.6dB（相对于0.5dB），但算法复杂度明显低于ML译码器。例如，所提出的方案与log-MAP解码所需的复杂度只有ML解码器的五分之一。少

The purpose of this research project is to improve the error performances of multistage decoding schemes by using soft-values between consecutive component decoders. For this sake, the authors have developed n efficient soft-in/soft-out log-MAP recursive decoding algorithm (R-logMap algorithm). The algorithm makes use of the structural properties of linear block codes, and reduces the decoding complexity significantly compared to the conventional BCJR algorithm. For example, computer simulation showed that the complexity of the proposed algorithm necessary for decoding of the second-order Reed-Muller (RM) code of length 128 is only 3% of that of the conventional BCJR algorithm, where the complexity is measured by the number of addition-equivalent operations of metrics. The log-MAP decoding uses some approximations in decoding process to reduce computational complexity and therefore its performance is not as good as the optimal MAP decoding. By modifying the R-logMAP algorithm slightly, … More an efficient MAP algorithm can be realized easily. By using the proposed log-MAP and MAP algorithms, the total decoding complexity of the proposed multistage decoding scheme can be reduced significantly. Among multistage decoding schemes, the authors have investigated closest-coset decoding schemes in details. A new multistage iterative decoding scheme can be realized by replacing component decoders of the closest-coset decoder with log-MAP or MAP decpder and introducing a feedback from the last stage to the first stage. The decoding complexity and the error performance of the new scheme are evaluated. Simulation results show that, for the decoding of the second-order RM code of length 64, the proposed scheme with log-MAP (res.MAP) decoding with two (resp.five) repetition improves the performance by 0.4dB (resp.0.5sB) at 10^<-5> block error rate, compared to the conventional closest-coset decoding scheme. The error performance degraduation from the maximum likelihood (ML) decoder is 0.6dB (resp.0.5dB), but the proposed schemes have significantly smaller complexity than the ML decoder. For example, the complexity necessary for the proposed scheme with log-MAP decoding is only one fifth of that of the ML decoder. Less