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The capacity of symmetric, neighboring and consecutive side-informationsingle unicast index coding problems (SNC-SUICP) with number of messages equalto the number of receivers was given by Maleki, Cadambe and Jafar. For theseindex coding problems, an optimal index code construction by using Vandermondematrices was proposed. This construction requires all the side-information atthe receivers to decode their wanted messages and also requires large fieldsize. 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 linearlyindependent over every field. Calling these matrices as Adjacent IndependentRow (AIR) matrices using which we gave an optimal scalar linear index code forthe one-sided SNC-SUICP for any given number of messages and one-sidedside-information. By using Vandermonde matrices or AIR matrices, every receiverneeds to solve $K-D$ equations with $K-D$ unknowns to obtain its wantedmessage, where $K$ is the number of messages and $D$ is the size of theside-information. In this paper, we analyze some of the combinatorialproperties of the AIR matrices. By using these properties, we present alow-complexity decoding which helps to identify a reduced set ofside-information for each users with which the decoding can be carried out. Bythis method every receiver is able to decode its wanted message symbol bysimply adding some index code symbols (broadcast symbols). We explicitly giveboth the reduced set of side-information and the broadcast messages to be usedby each receiver to decode its wanted message. For a given pair or receiversour decoding identifies which one will perform better than the other when thebroadcast channel is noisy.

Low-Complexity Decoding for Symmetric, Neighboring and Consecutive Side-information Index Coding Problems