算术码码谱及其应用研究

Arithmetic coding (AC) was originally proposed as a source coding technology,whose performance approaches theoretical limit.Then the classic AC was improved to get a class of so-called extended AC, e.g. joint source-channel AC (JSCAC), distributed AC (DAC), and distributed joint source-channel AC (DJSCAC). The extended AC can be widely used for source compression, error correction, joint source-channel coding (JSCC), distributed source coding (DSC), and distributed joint source-channel coding (DJSCC). However, up to now, there lacks a systematic analysis on the coding efficiency and decoding complexity of extended AC. For this reason, this project will develop a novel research tool, i.e. spectrum. This project includes in turn the following research contents: make the definition of AC spectrum, build a mathematic model for AC spectrum, give the closed-form and numeric-form of AC spectrum, prove some important properties of AC spectrum; make use of spectrum as a tool to analyze theoretical limits of coding efficiency and decoding complexity of extended AC, plot the curves of practical coding efficiency of extended AC with respect to its practical decoding complexity; lay a theoretical foundation for the applications and decoder designs of extended AC.

算术码最初是作为一种信源码提出的，其压缩性能接近理论极限。后来人们对其进行了推广，得到了联合信源信道算术码、分布式算术码、分布式联合信源信道算术码等多种扩展形式。扩展算术码可应用于信源压缩、信道纠错、信源信道联合编码、分布式信源编码、分布式信源信道联合编码等多种场合。然而迄今为止扩展算术码的编码性能和解码复杂度尚未得到全面系统的分析。为此本项目将提出一种新的研究工具- - 码谱。本项目将首先对算术码码谱进行定义和建模、给出算术码码谱的解析/数值计算方法、证明算术码码谱的重要性质；然后以码谱为工具，分析三种扩展算术码的编码性能和解码复杂度的理论极限，绘出实际编码性能与解码复杂度之间的关系曲线；从而为扩展算术码的实际应用及解码器设计提供理论指导。

联合信源信道算术码、分布式算术码、分布式联合信源信道算术码等广义算术码可广泛应用于信源压缩、信道纠错、信源信道联合编码、分布式信源编码、分布式信源信道联合编码等多种场合。然而迄今为止广义算术码的编码性能和解码复杂度尚未得到全面系统的分析。本项目针对分布式算术码开展了相关研究，提出了两种新的研究工具：码书势谱和汉明距谱；对两种码谱进行了定义和建模、给出了解析 /数值计算方法、证明了两种码谱的重要性质。然后以码谱为工具，分析了分布式算术码的编码性能和解码复杂度。经执行，本项目已在SCI期刊发表论文11篇，其中6篇发表于通信领域权威学术期刊《IEEE TCOM》；出版学术专著2部；授权国家发明专利3项；获陕西省科学技术奖三等奖1项；获生物医学领域权威国际会议AMIA-TBI’2016最佳学生论文奖1项。该项目的成果为分布式算术码的实际应用及解码器设计提供了理论指导。