Development of Universal Decoding Algorithms for BCH codes and LDPC codes

BCH码和LDPC码通用解码算法的开发

• 批准号: 15560319
• 负责人: UYEMATSU Tomohiko
• 金额: $ 1.28万
• 依托单位: Tokyo Institute of Technology
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2003
• 资助国家: 日本
• 起止时间: 2003 至 2004
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-15560319/
• 关键词: additive channel; channel coding; linear code; minimum entropy decoder; multistage coding; decoding; trellis; universal decoder; additive channel; channel coding; linear code; minimum entropy decoder; multistage coding; decoding; trellis; universal decoder

For a given class of linear codes such that BCH codes or LDPC(Low Density Parity Check) codes, we develop universal decoders which do not depend on the statistical characteristics of the discrete memoryless channel, and obtained following results.1.We investigate the performance of the well-known universal decoder called the minimum entropy decoder. For a class of M-ary additive channels, we have derived an upper bound on the probability of decoding error when the minimum entropy decoder is employed. The obtained bound depends on the weight spectrum of the given code as well as the transition probability of the channel. Further, we have clarified a condition such that the obtained error exponent coincides with the random coding exponent as the block length of the code tends to infinity.2.In order to reduce the complexity of the universal decoder, we have proposed a new scheme called universal multistage decoder. By combining this decoder with the conventional multilevel coding scheme, the capacity of the channel can be achieved. Further, we also derive an upper bound on the probability of decoding error for a class of M-ary additive channels, when the proposed multistage decoder is employed.3.We have shown that both the minimum entropy decoder and the universal multistage decoder can be efficiently implemented by using the trellis of the code. We have also clarified the performance of the proposed universal decoder by using computer simulation.

对于给定的线性代码，例如BCH代码或LDPC（低密度平等检查）代码，我们开发了通用解码器，这些解码器不取决于离散无内存通道的统计特征，并获得了以下结果。1。我们研究了众所周知的通用解码器的性能，称为最小熵解码器。对于一类M-Ary添加剂通道，我们在使用最小熵解码器时，已经在解码误差的概率上得出了上限。获得的结合取决于给定代码的重量谱以及通道的过渡概率。此外，我们已经阐明了一种条件，使得获得的误差指数与随机编码指数重合，因为代码的块长度倾向于无穷大。2.为了降低通用解码器的复杂性，我们提出了一种称为通用多阶段解码器的新方案。通过将该解码器与常规的多层编码方案相结合，可以实现通道的能力。此外，当采用提出的多阶段解码器时，我们还可以在解码误差的概率上得出上限。3。我们已经证明，最小熵解码器和通用多阶段解码器都可以通过使用代码的Trellis来有效地实现。我们还通过使用计算机模拟阐明了所提出的通用解码器的性能。