Coding Theory and Applications

摘要：美国加州理工学院NCR-9505975，《编码理论与应用》，PI-McEliess：研究了现代编码理论中的三个主题：卷积码的网格复杂性、Reed Solomon码的子群子码和Turbo码。第一种涉及一种新的方式来降低一大类卷积码的维特比译码复杂度，包括目前在实践中使用的许多码(例如，穿孔卷积码和单位存储器卷积码)。这是最近关于分组码网格复杂性的大量工作中令人惊讶的副产品。第二种考虑了一类新的代数分组码，即SSRS码，它有望打破Reed-Solomon码的“瓶颈”，即码长不超过码字母表大小的限制。最后，我们将研究最近在法国引进的新型“Turbo码”。Turbo码代表了多年来在高增益、低复杂度编码方面向前迈出的最大一步。希望建立一个可信的理论来解释显著的实验结果，并使这项工作能够被推进，systematically.*****************************************************************************Aubrey M.BushProgram主任，代理副处长，网络和通信研究与基础设施部

ABSTRACT: NCR-9505975, California Institute of Technology, "Coding Theory and Applications", PI-McEliece: Three topics in modern coding theory are studied: Trellis complexity of convolutional codes, subgroup subcodes of Reed Solomon codes, and turbo-codes. The first involves a novel way of reducing the Viterbi decoding complexity of a large class of convolutional codes, including many codes currently used in practice (e.g. punctured convolutional codes and the unit memory convolutional codes). This is a surprising spinoff of the large body of recent work on the trellis complexity of block codes. The second considers a new class of algebraic block codes, the class of "SSRS" codes, which promises to break the "bottleneck" of Reed-Solomon codes, i.e. the restriction that the code length be no more that the size of the code alphabet. Finally the new class of "turbo-codes", recently introduced in France, will be studied. Turbo codes represent the biggest single step forward in many years in high gain low complexity coding. It is hoped to develop a credible theory to explain the remarkable experimental results and enable the work to be pressed forward systematically.*****************************************************************************Aubrey M. BushProgram Director, Acting Deputy Divison DirectorDivision of Networking and Communications Research and InfrastructureNational Science Foundation