Binary Informed Source Codes and Index Codes Using Certain Near-MDS Codes

作     者：Thomas, Anoop Rajan, B. Sundar 

作者机构：Indian Inst Sci Dept Elect Commun Engn Bangalore 560012 Karnataka India 

出 版 物：《IEEE TRANSACTIONS ON COMMUNICATIONS》 (IEEE Trans Commun)

年 卷 期：2018年第66卷第5期

页      面：2181-2190页

核心收录：

学科分类：0810[工学-信息与通信工程] 0808[工学-电气工程] 08[工学] 

基　　金：Science and Engineering Research Board (SERB) of Department of Science and Technology (DST)  Government of India through J. C. Bose National Fellowship 

主　　题：Index coding informed source codes MDS codes side-information 

摘      要：A source coding problem in which a central source has to satisfy the demands of several receivers, with each receiver having some subset of the messages (side-information) held by the source is considered. The source has knowledge of only the cardinality of the side-information at each receiver. The encoding scheme used by the source to transmit at a higher throughput is referred to as an informed source code. A technique to obtain informed source codes by using l-th Near Maximum Distance Separable (Near-MDS) Codes is presented. The advantage of using l-th Near-MDS codes is the reduction in field size required. For certain informed source coding problems, the code obtained from l-th Near-MDS codes is shown to be of the minimum length under certain field size restrictions. The same technique can be used for a given index coding problem to obtain index codes. The index codes obtained through this technique are optimal for, but not limited to, special cases of index coding problems discussed in the paper. Finding an optimal solution to a general index coding problem is NP hard and this technique helps in finding binary suboptimal solutions. Using the Gilbert-Varshamov bound, an upper bound on the lengths of optimal binary informed source codes is obtained.