Optimal error correcting index codes for two classes of index coding problems
Mahesh Babu Vaddi, Balaji Sundar Rajan · 2018
A single unicast index coding problem (SUICP) with symmetric neighboring interference (SNI) has K receivers, the kth receiver Rkwanting the kth message zkand having the interference D messages after and U messages before its desired message. Maleki, Cadambe and Jafar studied the SUICP-SNI setting. In our previous work, we gave the capacity and optimal index codes for SUICP-SNI with K messages, D interfering messages after and U = gcd(K, D + 1) - 1 interfering messages before the desired message. In this paper, we present optimal length error-correcting index codes for these index coding problems, assuming that the transmissions are error prone. Thapa, Ong and Johnson defined the interlinked cycle (IC) structure, that generalizes cycles and cliques. Interlinked-cycle-cover (ICC) scheme, that leverages IC structures in digraphs to construct scalar linear index codes was proposed and a class of infinitely many digraphs where the proposed scalar linear codes based on ICC scheme are optimal were characterized. In this paper, we present optimal length error-correcting index codes for this class of infinitely many digraphs, assuming that the transmissions are error prone.