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Shortened Turbo Product Codes: Encoding Design and Decoding Algorithm

机译：缩短的Turbo产品代码：编码设计和解码算法

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摘要

Shortened turbo product codes (TPCs) have already been adopted in many standards. In this paper, we study shortened TPCs from two aspects, namely encoding design and decoding algorithm. To obtain different encoding block sizes, shortened-extended Hamming codes are used as the component codes of product codes in the IEEE 802.16 standard. To design a good structure for the shortened TPC, we compute the undetected error probability of its corresponding component codes. The component codes are shortened-extended Hamming codes, and their optimal generator polynomials are selected in terms of their undetected error probability. For the decoding algorithm, we present an efficient Chase decoding algorithm for shortened TPCs in flat fading channels. In the proposed scheme, the reliability factor used in Pyndiah''s scheme is not needed; thus, the decoding complexity is greatly reduced by avoiding the normalization operation of the whole code word at each iteration. Simulation results are also presented to verify the performance of the proposed algorithm.
机译：缩短的涡轮产品代码（TPC）已在许多标准中采用。本文从编码设计和解码算法两个方面研究了缩短的TPC。为了获得不同的编码块大小，缩短扩展的汉明码被用作IEEE 802.16标准中产品代码的组件代码。为了为缩短的TPC设计一个好的结构，我们计算了其相应的组件代码的未检测到的错误概率。分量码是短扩展的汉明码，并且根据其未检测到的错误概率来选择其最佳生成多项式。对于解码算法，我们提出了一种有效的Chase解码算法，用于平坦衰落信道中缩短的TPC。在提出的方案中，不需要在Pyndiah方案中使用的可靠性因子。因此，通过避免每次迭代时整个码字的归一化操作，极大地降低了解码复杂度。仿真结果也被提出来验证所提出算法的性能。

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