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

Vaddi, Mahesh Babu; Rajan, B. Sundar

doi:10.23919/isita.2018.8664213

Cited by 3 publications

(2 citation statements)

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“…In [8], we constructed optimal length vector linear index codes for SUICP(SNC) by using AIR matrices. In [9], we constructed optimal length scalar linear index codes for SUICP(SNC) for a special case when U + 1 divide both K and D − U . In [10], we gave a low-complexity decoding for SUICP(SNC) with AIR matrix as encoding matrix.…”

Section: A Review Of Air Matricesmentioning

confidence: 99%

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Optimal Scalar Linear Index Codes for One-Sided Neighboring Side-Information Problems

Vaddi

Rajan

2016

2016 IEEE Globecom Workshops (GC Wkshps)

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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-dimensional vector linear index code, the transmitter needs to wait for b realizations of each message and hence the latency introduced at the transmitter is proportional to b. For any given single unicast index coding problem (SUICP) with the side-information graph G, MAIS(G) is used to give a lowerbound on the broadcast rate of the ICP. In this paper, we derive MAIS(G) of SUICP(SNC) with side-information graph G. We construct scalar linear index codes for SUICP(SNC) with length K U +1 − D−U U +1 . We derive the minrank(G) of SUICP(SNC) with side-information graph G and show that the constructed scalar linear index codes are of optimal length for SUICP(SNC) with some combinations of K, D and U . For SUICP(SNC) with arbitrary K, D and U , we show that the length of constructed scalar linear index codes are atmost two index code symbols per message symbol more than the broadcast rate. The given results for SUICP(SNC) are of practical importance due to its relation with topological interference management problem in wireless communication networks.

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Section: A Review Of Air Matricesmentioning

confidence: 99%

“…In G 1 , there exists no edge from x j(U+1) to x 0 follows from the fact that j(U + 1) + D < K for every j ∈ [1 : t − 1] as shown in (9).…”

Section: Maximum Acyclic Induced Subgraph Bound For Suicp(snc) Simentioning

confidence: 99%

Optimal Scalar Linear Index Codes for One-Sided Neighboring Side-Information Problems

Vaddi

Rajan

2016

2016 IEEE Globecom Workshops (GC Wkshps)

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On the Minrank of Symmetric and Neighboring Side-information Index Coding Problems

Vaddi

Rajan

2019

2019 IEEE Information Theory Workshop (ITW)

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