On capacity region of certain classes of three‐receiver broadcast channels with side information

Abstract

The fact that the results for 2-receiver broadcast channels (BCs) are not generalized to the 3-receiver ones is of information theoretical importance. In this paper we study two classes of discrete memoryless BCs with non-causal side information (SI), i.e. multilevel BC (MBC) and 3-receiver less noisy BC. First, we obtain an achievable rate region and a capacity outer bound for the MBC. Second, we prove a special capacity region for the 3-receiver less noisy BC. Third, the obtained special capacity region for the 3-receiver less noisy BC is extended to continuous alphabet fading Gaussian version. It is worth mentioning that the previous works are special cases of our works. Index TermsThree-receiver broadcast channel, multilevel broadcast channel, less noisy broadcast channel, fading channel. I. INTRODUCTION BROADCAST channel is an important multiuser channel, first introduced by Cover [1]. Bergmans obtained an achievable rate region for degraded 2-receiver BC [2] using superposition coding and Gallager [3] and Ahlswede-Körner [4] showed that it is optimal. Special classes of BCs have been studied in [5] and [6]. By now, the best known capacity bounds for general 2-receiver BC are given by Marton [7] and Nair-El Gamal [8]. The results for BCs with two receivers are not generalizable to the BCs with more than two receivers and finding a closed form result for a broadcast channel with arbitrary number of receivers is not a straightforward problem. So some works focused on some special classes of BCs with more than two receivers such as multilevel broadcast channel [9] and 3-receiver less noisy broadcast channel [10]. For the first time, Borade et al.studied BCs with more than two receivers [11]. They guessed the straightforward extension of capacity region for 2-receiver BC with degraded message sets obtained by Körner and Marton [6], to multilevel broadcast channel, however Nair and El Gamal [9] showed that it is not in general optimal. Later, Nair and Wang [10] obtained the capacity region of the 3-receiver less noisy BC.Sajjad Bahrami is with the ). 2Shannon studied channels with side information (SI) [12], and found the capacity region of the single user channel when causal SI is available at the transmitter. Single user channel, when non-causal SI is available only at the transmitter, was studied by Gel'fand-Pinsker [13]. The results of [13] was generalized by Cover and Chiang [14] to the case where non-causal SI is available at both transmitter and receiver. Also single user channel with partial channel state information at the transmitter (CSIT) was studied in [15]. Multiuser channels e.g. multiple access channels, BCs, interference channels and relay channels in presence of SI were studied in [16], [17], [18] and [19], respectively and some works on multiuser channels with partial SI can be found in [20], [21], [22] and [23]. BC with SI was investigated in [17], in which inner and outer capacity bounds and capacity region for different cases of SI presence in degraded BC were obtained. The authors in [24] ...