Studies on Controlling the Message-Passing Decoding Algorithms and Constructing Error Correcting Codes Suitable for Such Algorithms

在高速、无处不在的网络环境下，纠错和纠错控制策略是通信和存储的重要组成部分。Turbo编码和LDPC编码是近年来发展中最受关注的实用化编码。目前已有移动电话系统、下一代无线局域网系统标准草案等实例。这些编码的不足之处在于：(1)解码算法不是最优的，为了获得更好的结果，需要进行重复。(2)代码是渐近好的，但很少有办法在有限的代码长度下找到好的代码。在本研究中，我们提出了几种通过排序控制消息传递译码反馈的方法，如和积译码和Turbo译码(1)控制突发错误信道的和积译码，(2)硬入软出译码，(3)ML和MAP译码的求值查找表算法。我们还构造了新的LDPC和Turbo码基码，这是(4)不等LDPC码的新构造方法。(5)从代数LDPC码构造具有随机校验矩阵的LDPC码；(6)不对称Turbo-Hadamard码（ATHC）； (7) ATHC码与LDPC码的串联编码方案。最后研究了所提出的编解码方案在数字水印系统中的应用。

Today's high-speed and ubiquitous network environments, error correcting and error controlling strategies are the important element of communications and storages. Turbo coding and LDPC coding are the most interested coding for practical use in recent development. Already there are practical examples such as mobile phone system, draft for wireless LAN system standards for next generation and so on. Those code have inferiority in following points, (1) The decoding algorithms are sub optimal, and repetitions are required to get better results. (2) Code is asymptotically good, but there are few idea for finding good code for limited code length.In this study, we propose several ways of controlling the feedback by ordering for message passing decoding such as sum-product decoding and Turbo decoding (1) sum-product decoding with control for burst-error channel, (2)Hard-in Soft-out decoding, and (3) evaluation look up table algorithm for ML and MAP decodingWe also construct new LDPC and Turbo code base codes, which are (4) new construction method of unequal LDPC code, (5) constructing LDPC code having random like check matrix from algebraic LDPC code, (6)asymmetric Turbo-Hadamard code(ATHC), and (7) concatenate coding scheme using ATHC and LDPC codes. Finally we study application of our proposed coding and decoding scheme to digital watermarking system.