CIF: Small: An Algebraic Approach to Distributed Source Coding

CIF：小：分布式源编码的代数方法

• 批准号: 1018148
• 负责人: Aditya Ramamoorthy
• 金额: $ 35.06万
• 依托单位: Iowa State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-09-01 至 2014-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1018148&HistoricalAwards=false
• 关键词: CIF; Small; Algebraic; Approach; Distributed

There are various instances of problems where correlated sources need to be transmitted from remote sources to a set of terminals, e.g., large scale sensor networks and distributed data storage systems. The field of distributed source coding considers coding strategies that leverage the correlation between the sources in a distributed manner while allowing the information to be communicated at a bitrate as low as possible to the terminals. This research studies practical coding schemes for the general distributed source coding problem.The vast majority of prior work in this area considers the case of two binary sources, or a higher number of sources with small alphabets and restrictive correlation structures. This research investigates novel constructions of distributed source codes based on Reed Solomon (RS) codes. Consecutive realizations of the nonbinary sources are viewed as coefficients of polynomials over a finite field. Each source encoder transmits evaluations of this polynomial at certain points from the field. Source recovery at the terminal is performed by multivariate polynomial interpolation with carefully chosen root multiplicities, followed by factorization. The multiplicity matrices allow us to capture the joint likelihood of the different source sequences in the decoding process, while ensuring that the decoding is tractable. The scheme is designed for multiple nonbinary sources. Corner points of the rate region for sources with arbitrary correlation are expected to be achieved in this manner. For general rate points, the approach will be extended for a large class of correlation structures that generalizes the set of structures that can be handled by current state of the art techniques.The research is integrated into the graduate/undergraduate curriculum and into senior-design at appropriate levels.

存在需要将相关源从远程源传输到一组终端（例如大规模传感器网络和分布式数据存储系统）的问题的各种实例。分布式源编码领域考虑以分布式方式利用源之间的相关性同时允许以尽可能低的比特率向终端传送信息的编码策略。这项研究研究了一般分布式源编码问题的实用编码方案。该领域的绝大多数先前工作考虑了两个二进制源或具有小字母表和限制性相关结构的大量源的情况。本研究研究了基于里德所罗门（RS）代码的分布式源代码的新颖构造。非二元源的连续实现被视为有限域上多项式的系数。每个源编码器在现场的某些点传输该多项式的计算值。终端的源恢复是通过仔细选择根重数的多元多项式插值来执行的，然后进行因式分解。多重性矩阵使我们能够捕获解码过程中不同源序列的联合似然，同时确保解码易于处理。该方案是为多个非二进制源设计的。具有任意相关性的源的速率区域的角点预计将以这种方式实现。对于一般评分点，该方法将扩展到一大类相关结构，这些结构概括了当前最先进技术可以处理的一组结构。该研究已融入研究生/本科生课程和高级设计中在适当的水平。