CIF: Small: An Algebraic Approach to Distributed Source Coding

存在各种各样的问题实例，其中相关源需要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。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的编码策略，同时允许以尽可能低的比特率将信息传输到终端。针对一般的分布式源编码问题，研究了实用的编码方案。该领域的绝大多数先前工作考虑了两个二进制源的情况，或者具有小字母和限制性相关结构的更高数量的源。本文研究了基于RS码的分布式源代码的新结构。非二元源的连续实现被视为有限域上多项式的系数。每个源编码器在字段的某些点上传输该多项式的评估值。在终端源恢复是执行多元多项式插值与精心选择的根多重，其次是因式分解。多重矩阵允许我们在解码过程中捕获不同源序列的联合似然，同时确保解码是可处理的。该方案设计用于多个非二进制源。对于具有任意相关性的源，期望用这种方式实现速率区域的角点。对于一般速率点，该方法将扩展到一个大的相关结构类，它概括了可以由当前技术状态处理的结构集。该研究被纳入研究生/本科课程和高级设计在适当的水平。

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.