Soft-decision Multi-stage Decoding for Linear Block Codes

本研究的目的是利用连续分量解码器之间的软值来改善多级译码方案的错误性能。为此，作者开发了一种高效的软入/软出log-MAP递归解码算法（R-logMap算法）。该算法利用了线性分组码的结构特性，与传统的BCJR算法相比，显著降低了译码复杂度。例如，计算机模拟表明，所提出算法解码长度为128的二阶Reed-Muller （RM）码所需的复杂度仅为传统BCJR算法的3%，其中复杂度是通过度量的加法等效操作的次数来衡量的。log-MAP译码在译码过程中使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。通过对R-logMAP算法稍加修改，可以更容易地实现一种高效的MAP算法。通过使用log-MAP和MAP算法，可以显著降低多阶段译码方案的总译码复杂度。在多段译码方案中，作者详细研究了最接近共集译码方案。用log-MAP或MAP解码器取代最近邻解码器的分量解码器，并引入从最后一级到第一级的反馈，可以实现一种新的多级迭代译码方案。对新方案的解码复杂度和误码性能进行了评价。仿真结果表明，对于长度为64的二阶RM码的译码，所提出的log-MAP (res.MAP) 2次（resp.5）重复译码方案在10^<-5>分组误码率下的性能比传统的最近邻集译码方案提高了0.4dB （resp.0.5sB）。最大似然解码器的误差性能下降了0.6dB (resp.0.5dB)，但所提出的方案的复杂度明显低于最大似然解码器。例如，所提出的log-MAP解码方案所需的复杂性仅为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