非二元线性随机喷泉码与最大距离可分码的并行级联
Parallel Concatenation of Non-Binary Linear Random Fountain Codes with Maximum Distance Separable Codes
摘要：
研究了一种基于最大距离可分码（MDS）和线性随机喷泉码级联的新型编码方案的性能和译码复杂度。与Raptor码（其基于高速率外部块码和内部Luby变换码的串行级联）不同，所提出的编码方案可以被视为MDS码和线性随机喷泉码的并行级联，两者都在同一有限域上操作。最大似然（ML）解码下的解码失败概率的上限和下限。例如，示出了在$16$阶的有限域$\mathbb {F}_{16}$上的$(15,10)$ Reed-Solomon（RS）码和线性随机喷泉码的级联如何在具有$ε=5\cdot10^{-2}$的擦除概率的信道中对于相同的接收机开销带来比线性随机喷泉码的解码失败概率低几个数量级的解码失败概率$4$。它示出了新方案的性能如何接近理想化的喷泉码的高阶字段和中等的擦除概率。本文提出了一种适用于广义RS码的有效译码算法。
英文摘要：
The performance and the decoding complexity of a novel coding scheme based on the concatenation of maximum distance separable (MDS) codes and linear random fountain codes are investigated. Differently from Raptor codes (which are based on a serial concatenation of a high-rate outer block code and an inner Luby-transform code), the proposed coding scheme can be seen as a parallel concatenation of a MDS code and a linear random fountain code, both operating on the same finite field. Upper and lower bounds on the decoding failure probability under maximum-likelihood (ML) decoding are developed. It is shown how, for example, the concatenation of a $(15,10)$ Reed-Solomon (RS) code and a linear random fountain code over a finite field of order $16$, $\mathbb {F}_{16}$, brings to a decoding failure probability $4$ orders of magnitude lower than the one of a linear random fountain code for the same receiver overhead in a channel with a erasure probability of $ε=5\cdot10^{-2}$. It is illustrated how the performance of the novel scheme approaches that of an idealized fountain code for higher-order fields and moderate erasure probabilities. An efficient decoding algorithm is developed for the case of a (generalized) RS code.
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