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的各种问题实例，例如，大规模传感器网络和分布式数据存储系统。分布式信源编码领域考虑以分布式方式利用信源之间的相关性同时允许以尽可能低的比特率将信息传送到终端的编码策略。本研究针对一般性的分布式信源编码问题，研究了实用的编码方案，这一领域的绝大多数先前的工作考虑了两个二进制信源，或具有小字母和限制性相关结构的更多信源的情况。本研究以Reed所罗门（RS）码为基础，探讨分布式源代码的新构造.非二进制源的连续实现被视为有限域上多项式的系数。每个源编码器在来自该字段的某些点处发送该多项式的评估。在终端的源恢复进行多元多项式插值仔细选择根的多重性，然后因式分解。多重性矩阵允许我们在解码过程中捕获不同源序列的联合似然，同时确保解码是易处理的。该方案是为多个非二进制源而设计的。期望以这种方式实现具有任意相关性的源的速率区域的角点。对于一般率点，该方法将被扩展为一个大类的相关结构，概括了一套结构，可以处理当前的最先进的techniques.The研究被集成到研究生/本科课程，并在适当的水平进入高级设计。