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In this paper, we study the Nair-El Gamal outer bound and Marton's inner bound for general two-receiver broadcast channels. We show that the Nair-El Gamal outer bound can be made fully computable. For the inner bound, we show that, unlike in the Gaussian case, for a degraded broadcast channel even without a common message, Marton's coding scheme without a superposition variable is in general insufficient for obtaining the capacity region. Further, we prove various results that help to restrict the search space for computing the sum-rate for Marton's inner bound. We establish the capacity region along certain directions and show that it coincides with Marton's inner bound. Lastly, we discuss an idea that may lead to a larger inner bound.

In this paper, we study the achievable rate regions of parallel relay broadcast channels. We present two system models, the parallel unshared-relay broadcast channel and the parallel shared-relay broadcast channel. In the first system, each relay node is peculiar to one of the users and does not assist any other user. In the second system, each relay node is shared by all users and assists all of them. Achievable rate regions for these two different channel models are derived in the discrete memoryless case. We also provide an outer bound on the rate regions, which is tighter than the cut-set bound.

This paper studies the design and analysis of multiresolution vector quantization (MRVQ) for broadcast channels. Given a broadcast system with MRVQ, a random index assignment, and a coded broadcast channel, we first obtain a closed-form formula for the weighted end-to-end distortion (EED) of the system. Based on the formula, an iterative algorithm is then proposed for designing optimal MRVQ for the broadcast system. Experimental results demonstrate that multiresolution quantizers jointly designed with channel conditions by the proposed algorithm significantly reduce the weighted EED in comparison with multiresolution quantizers designed without reference to channel conditions.

In this paper, we obtain an outer bound on the capacity region of the Broadcast-Relay-Channel (BRC). BRC is a four node network with one source, one relay and two destinations. To the best of our knowledge, this work represents the first effort to find an outer bound on the capacity region of the BRC. In the proof, we jointly utilize the ideas of the outer bounds on the Broadcast Channel (BC) and also the cut-set bound. The proposed outer bound looks like the inner bound obtained by Kramer et. al for BRC.