调和分析与信道编解码研究  

Harmonic analysis and research on channel coding and decoding

作　　者：谌稳固[1] 吴国清[1] 

机构地区：[1]北京应用物理与计算数学研究所,北京100088

出　　处：《中国科学：数学》2014年第5期447-456,共10页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:10931001,11371183,11271050和61003083);中国工程物理研究院科学技术发展基金(批准号:2012B0202024和2013B0403068);北京数学与信息交叉科学2011协同创新中心资助项目

摘　　要：信道编码是通信系统的关键技术之一,其传统的理论工具是代数和有限域GF(p).本文在有噪信道的信道编码数学模型基础上,介绍基于调和分析的新型信道编码理论,分别应用调和分析的重要工具压缩感知与Walsh-Hadamard变换实现信道编解码和信道编码盲识别.本文综述基于调和分析的信道编码的一些基本结果并介绍最新进展,主要包括:Gilbert-Varshamov界、l1解码、RIP(restricted isometry property)条件和Walsh-Hadamard变换等.The channel coding is one of the key technologies in communication theory is based on algebra and the finite field GF（p）. This paper firstly establishes systems and its traditional the mathematical model of the channel coding in noisy cases, then introduces the novel channel coding theory based on harmonic analysis and applies important tools of harmonic analysis including compressed sensing and Walsh-Hadamard transform to achieve the decoding and blind recognition of channel coding. Some elementary results and newly progress of channel coding based on harmonic analysis are surveyed including Gilbert-Varshamov bound theorem, l1 decoding, RIP condition, Walsh-Hadamard transform.

关 键 词：调和分析 信道编码 压缩感知 Walsh-Hadamard 变换 

分 类 号：TN911.22[电子电信—通信与信息系统] O174.2[电子电信—信息与通信工程]