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Low-Complexity Chase Decoding of Reed-Solomon Codes Using Module
IEEE Transactions on Communications ( IF 8.3 ) Pub Date : 2020-10-01 , DOI: 10.1109/tcomm.2020.3011991
Jiongyue Xing , Li Chen , Martin Bossert

The interpolation based algebraic soft decoding yields a high decoding performance for Reed-Solomon (RS) codes with a polynomial-time complexity. Its computationally expensive interpolation can be facilitated using the module structure. The desired Gröbner basis can be achieved by reducing the basis of a module. This paper proposes the low-complexity Chase (LCC) decoding algorithm using this module basis reduction (BR) interpolation technique, namely the LCC-BR algorithm. By identifying $\eta $ unreliable symbols, $2^\eta $ decoding test-vectors will be formulated. The LCC-BR algorithm first constructs a common basis which will be shared by the decoding of all test-vectors. This eliminates the redundant computation in decoding each test-vector, resulting in a lower decoding complexity and latency. This paper further proposes the progressive LCC-BR algorithm that decodes the test-vectors sequentially and terminates once the maximum-likelihood decision decoding outcome is reached. Exploiting the difference between the adjacent test-vectors, this progressive decoding is realized without any additional memory cost. Complexity analysis shows that the LCC-BR algorithm yields a lower complexity and latency, especially for high rate codes, which will be validated by the numerical results.

中文翻译:

使用模块对 Reed-Solomon 码进行低复杂度 Chase 解码

基于内插的代数软解码为具有多项式时间复杂度的里德-所罗门 (RS) 码产生高解码性能。使用模块结构可以促进其计算成本高的插值。可以通过减少模块的基来实现所需的 Gröbner 基。本文提出了使用这种模块基约简(BR)插值技术的低复杂度Chase(LCC)解码算法,即LCC-BR算法。通过识别 $\eta $ 不可靠符号,将制定 $2^\eta $ 解码测试向量。LCC-BR 算法首先构建一个公共基础,该基础将由所有测试向量的解码共享。这消除了解码每个测试向量时的冗余计算,从而降低了解码复杂度和延迟。本文进一步提出了渐进式 LCC-BR 算法,该算法按顺序对测试向量进行解码,并在达到最大似然决策解码结果时终止。利用相邻测试向量之间的差异,无需任何额外的内存成本即可实现这种渐进式解码。复杂度分析表明,LCC-BR 算法具有较低的复杂度和延迟,特别是对于高速率代码,这将通过数值结果进行验证。
更新日期:2020-10-01
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