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This paper addresses the problem of exponentially increasing sub-packetization with the number of users in a centralized coded caching system by introducing a new coded caching scheme inspired by the symmetric neighboring consecutive side information index coding problem. The scheme has a placement policy where the number of sub-packets required grows only linearly with the number of users, with no restriction on file size, and a delivery policy which is instantaneously decodable. Further, an application of the new delivery scheme in a multi-access coded caching set-up is studied and a few results in that direction are presented. In particular, in the multiaccess set-up, for cases where optimality rate-memory trade-off characterizations are available, it is shown that the new delivery scheme achieves optimal or near-optimal rates.

Abstract-In this paper we consider noisy index coding problem over AWGN channel. We give an algorithm to map the index coded bits to appropriate sized PSK symbols such that for the given index code, in general, the receiver with large amount of side information will gain in probability of error performance compared to the ones with lesser amount, depending upon the index code used. We call this the PSK side information coding gain. Also, we show that receivers with large amount of side information obtain this coding gain in addition to the bandwidth gain whereas receivers with lesser amount of side information trade off this coding gain with bandwidth gain. Moreover, in general, the difference between the best and worst performance among the receivers is shown to be proportional to the length of the index code employed.

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This paper deals with embedded index coding problem (EICP), introduced by A. Porter and M. Wootters, which is a decentralized communication problem among users with side information. An alternate definition of the parameter minrank of an EICP, which has reduced computational complexity compared to the existing definition, is presented. A graphical representation for an EICP is given using directed bipartite graphs, called bipartite problem graph, and the side information alone is represented using an undirected bipartite graph called the side information bipartite graph. Inspired by the well-studied single unicast index coding problem (SUICP), graphical structures, similar to cycles and cliques in the side information graph of an SUICP, are identified in the side information bipartite graph of a single unicast embedded index coding problem (SUEICP). Transmission schemes based on these graphical structures, called tree cover scheme and bi-clique cover scheme are also presented for an SUEICP. Also, a relation between connectedness of the side information bipartite graph and the number of transmissions required in a scalar linear solution of an EICP is established.