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Low-Complexity Decoding for Symmetric, Neighboring and Consecutive Side-information Index Coding Problems. (arXiv:1705.03192v2 [cs.IT] UPDATED)
来源于:arXiv
The capacity of symmetric, neighboring and consecutive side-information
single unicast index coding problems (SNC-SUICP) with number of messages equal
to the number of receivers was given by Maleki, Cadambe and Jafar. For these
index coding problems, an optimal index code construction by using Vandermonde
matrices was proposed. This construction requires all the side-information at
the receivers to decode their wanted messages and also requires large field
size. In an earlier work, we constructed binary matrices of size $m \times n
(m\geq n)$ such that any $n$ adjacent rows of the matrix are linearly
independent over every field. Calling these matrices as Adjacent Independent
Row (AIR) matrices using which we gave an optimal scalar linear index code for
the one-sided SNC-SUICP for any given number of messages and one-sided
side-information. By using Vandermonde matrices or AIR matrices, every receiver
needs to solve $K-D$ equations with $K-D$ unknowns to obtain its wanted
message, wher 查看全文>>