Intrinsic multicast region of broadcast channel

Abstract

We address the problem of multicasting individual and common information from a single transmitter (source) to multiple receivers (destinations). We consider the general case where a separate message could be intended for any subset of destinations. We call this problem multicasting in broadcast channel. The multicast achievable rate region of a N-user broadcast channel is 2N − 1 dimensional region while the broadcast achievable rate region is a N dimensional region. Given a broadcast achievable rate tuple there is a set of rate tuple that are achievable for multicasting problem. The multicast rate region obtained by this generator rate tuple consists of rate tuples that are not componentwise smaller than the generator rate tuple. For the general case of N users, we address the following questions (i) Given a generator rate tuple, what is the region achievable for any broadcast channel irrespective of its channel model, (ii) What is the largest achievable rate region, i.e., a region for which no point outside this region is universally achievable by any broadcast channel given a generator rate tuple. For a given generator rate tuple λ, the region which satisfies (i) and (ii) is called λ-intrinsic multicast region due to the fact that it depends on an inherent structure of multicasting and not on the underlying broadcast channel model. In this paper, We derive an achievable multicast rate region for the general N-user broadcast channel which extend the known result for only N = 2 and 3. We show that the obtained region is convex and hence there is no need for convex hull operation. We then show the maximal property of the proposed region under certain conditions and explicitly find the λ-intrinsic multicast region for those cases.