Reduced Dimensional Optimal Vector Linear Index Codes for Index Coding Problems with Symmetric Neighboring and Consecutive Side-information

Vaddi, Mahesh Babu and Rajan, B Sundar (2018) Reduced Dimensional Optimal Vector Linear Index Codes for Index Coding Problems with Symmetric Neighboring and Consecutive Side-information. In: 15th International Symposium on Information Theory and its Applications (ISITA), OCT 28-31, 2018, Singapore, SINGAPORE, pp. 95-99.

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Abstract

A single unicast index coding problem (SUICP) with symmetric neighboring and consecutive side- information (SNCS) has K messages and K receivers, the k th receiver R-k wanting the k th message x(k) and having the side-information K-k = {x(k-U),..., x(k-2), x(k-1)} boolean OR {x(k+1), x(k+2),..., x(k+D)}. Maleki, Cadambe and Jafar obtained the symmetric capacity of this single unicast index coding problem with symmetric neighboring and consecutive side-information (SUICP(SNCS)) and proposed optimal length codes by using Vandermonde matrices. SUICP(SNCS) with arbitrary K, D and U is the only known setting in index coding for which symmetric capacity is known and vector linear index codes are required to achieve capacity. In our earlier work, we gave optimal length (U+1)- dimensional vector linear index codes for SUICP(SNCS) satisfying some conditions on K, D and U. In this paper, for SUICP(SNCS) with arbitrary K, D and U, we construct optimal length U+1/gcd(K, D-U, U+1) - dimensional vector linear index codes. We prove that the constructed vector linear index code is of minimal dimension if gcd(K - D + U, U + 1) is equal to gcd(K, D - U, U + 1). The proposed construction gives optimal length scalar linear index codes for the SUICP(SNCS) if (U + 1) divides both K and D - U. The proposed construction is independent of field size and works over every field. We give encoding matrices and a low- complexity decoding for the proposed construction.

Item Type:	Conference Proceedings
Series.:	ISITA 2018
Publisher:	IEEE
Additional Information:	15th International Symposium on Information Theory and its Applications (ISITA), Singapore, SINGAPORE, OCT 28-31, 2018
Department/Centre:	Division of Electrical Sciences > Electrical Communication Engineering
Date Deposited:	22 Jul 2019 09:37
Last Modified:	25 Aug 2022 12:07
URI:	https://eprints.iisc.ac.in/id/eprint/62905

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