The Symmetric Capacity of the K-Receiver Interleaved Broadcast Channel with Symmetric Side Information
Mohamed Salman, Mahesh K. Varanasi · 2019
In this paper, we consider the K-receiver discrete memoryless (DM) broadcast channel (BC) with K private messages of the same rate. Inspired by the decentralized caching problem which has received much interest of late, we consider the case where each message consists of 2Kindependent sub-messages, with each sub-message available at a distinct subset of receivers as side information. We assume that the rates of all the sub-messages available at the same number of receivers are the same. Hence, each receiver has exactly the same amount of information about each message, including its intended message, as side information. For this symmetric side information structure, we establish the symmetric capacity for the interleavable DM BC, a class of channels which subsumes the K-receiver degraded DM BC and the less noisy BC in the three-receiver case. Our coding scheme involves (a) network coding in the form of a bit-wise XOR of two or more messages (b) message merging where multiple messages are bijectively mapped into a single message with a rate that is the sum of the rates of the merged messages (c) superposition coding where the codebooks are generated for the merged messages and (d) successive decoding at each receiver to find its intended message with the aid of the side information.