On the capacity of index coding problems with symmetric neighboring interference

Abstract

A single unicast index coding problem (SUICP) with symmetric neighboring interference (SNI) has equal number of K messages and K receivers, the kth receiver R k wanting the kth message x k and having the side-information. , x k+D } is the interference with D messages after and U messages before its desired message. Maleki, Cadambe and Jafar obtained the capacity of this symmetric neighboring interference single unicast index coding problem (SNI-SUICP) with (K) tending to infinity and Blasiak, Kleinberg and Lubetzky for the special case of (D = U = 1) with K being finite. In this work, for any finite K and arbitrary D we obtain the capacity for the case U = gcd(K, D + 1) − 1. Our proof is constructive, i.e., we give an explicit construction of a linear index code achieving the capacity.• If L(j, k) is present in I D+1 , then j R = j and k R = k.

Reduced Complexity Index Codes and Improved Upperbound on Broadcast Rate for Neighboring Interference Problems

“…In this section, we give scalar linear index codes for SUICP(SNI) with arbitrary K, D and U . In [13], we proved Lemma 1 by proving the capacity of SUICP(SNI) with arbitrary K, D and U = gcd(K, D + 1) − 1. This lemma is useful to derive Theorem 2 of this section.…”

“…Proof. Let a and b be the non negative integers satisfying (13). Consider an SUICP(SNI) with K + a messages [x 0 x 1 .…”

A New Upperbound on the Broadcast Rate and Near-Optimal Vector Linear Codes for Index Coding Problems with Symmetric Neighboring Interference

“…In [18], we showed that the capacity of SUICP-SNI for arbitrary K and D with U = gcd(K, D + 1) − 1 is…”

An Approximation Algorithm for Optimal Clique Cover Delivery in Coded Caching

“…In our problem, the total number of subfiles that the server needs to send can be exponential in the number K of users and further, the size of subfiles can be distinct in general. Therefore, existing algorithms [17]- [19] for the conventional index coding problem and the recent algorithms for the index coding problems with interlinked cycles [20] and symmetric neighboring interference [21] are not appropriate for our setting.…”