2016 IEEE Globecom Workshops (GC Wkshps) 2016
DOI: 10.1109/glocomw.2016.7848993
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Optimal Scalar Linear Index Codes for One-Sided Neighboring Side-Information Problems

Abstract: A single unicast index coding problem (SUICP) is called symmetric neighboring and consecutive (SNC) sideinformation problem if it has K messages and K receivers, the kth receiver R k wanting the kth message x k and having the side-information D messages immediately after x k and U (D ≥ U ) messages immediately before x k . Maleki, Cadambe and Jafar obtained the capacity of this SUICP(SNC) and proposed (U + 1)-dimensional optimal length vector linear index codes by using Vandermonde matrices. However, for a b-d… Show more

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Cited by 23 publications
(19 citation statements)
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“…Theorem 3. Let l 1 = D + 1 + ( a b ) min , where ( a b ) min is the minimum value of a and b such that (a, b) ∈ S given in (9) and a b is minimum. Let l 2 = D + 1 + (a + b) min , where (a + b) min is the minimum value of a and b satisfying (13) and (a + b) min is minimum.…”
Section: Lemmamentioning
confidence: 99%
“…Theorem 3. Let l 1 = D + 1 + ( a b ) min , where ( a b ) min is the minimum value of a and b such that (a, b) ∈ S given in (9) and a b is minimum. Let l 2 = D + 1 + (a + b) min , where (a + b) min is the minimum value of a and b satisfying (13) and (a + b) min is minimum.…”
Section: Lemmamentioning
confidence: 99%
“…In [8], we constructed binary matrices of size m×n(m ≥ n) such that any n adjacent rows of the matrix are linearly independent over every field. We refer these matrices as Adjacent Independent Row (AIR) matrices.…”
Section: A Review Of Adjacent Independent Row (Air) Matricesmentioning
confidence: 99%
“…In [8], we gave an optimal length scalar linear index code for one-sided SUICP(SNCS) using AIR encoding matrices. In [7], we constructed optimal length (U +1) dimensional VLICs for two-sided SUICP(SNCS) satisfying some conditions on K, D and U .…”
Section: A Review Of Adjacent Independent Row (Air) Matricesmentioning
confidence: 99%
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“…In [7], we constructed binary matrices of size m×n(m ≥ n) such that any n adjacent rows of the matrix are linearly independent over every field. We refer these matrices as adjacent row independent (AIR) matrices.…”
Section: A Air Matricesmentioning
confidence: 99%