Binary Informed Source Codes and Index Codes Using Certain Near-MDS Codes
Anoop Thomas, Balaji Sundar Rajan · IEEE Transactions on Communications · 2018
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.