Cooperative Strategies for Simultaneous and Broadcast Relay Channels

Abstract

Abstract-Consider the simultaneous relay channel (SRC) which consists of a set of relay channels where the source wishes to transmit common and private information to each of the destinations. This problem is recognized as being equivalent to that of sending common and private information to several destinations in presence of helper relays where each channel outcome becomes a branch of the broadcast relay channel (BRC). Cooperative schemes and capacity region for a set with two memoryless relay channels are investigated. The proposed coding schemes, based on Decode-and-Forward (DF) and Compress-andForward (CF) must be capable of transmitting information simultaneously to all destinations in such set.Depending on the quality of source-to-relay and relayto-destination channels, inner bounds on the capacity of the general BRC are derived. Three cases of particular interest are considered: cooperation is based on DF strategy for both users -referred to as DF-DF region-, cooperation is based on CF strategy for both users -referred to as CF-CF region-, and cooperation is based on DF strategy for one destination and CF for the other -referred to as DF-CF region-. These results can be seen as a generalization and hence unification of previous works. An outer-bound on the capacity of the general BRC is also derived. Capacity results are obtained for the specific cases of semi-degraded and degraded Gaussian simultaneous relay channels. Rates are evaluated for Gaussian models where the source must guarantee a minimum amount of information to both users while additional information is sent to each of them.

Marton-Marton coding for a broadcast relay network

“…Our outer bound can be shown to perform as good as that of the outer bound given in Theorem 5 in [8].…”

“…In [7], the relay only decodes the common message and forwards it to both destinations and the transmitter applies Marton's scheme for broadcasting. In [8], this was generalized such that the relay also decodes and forwards one of the private messages. For the combination of Marton's scheme at the source and compress-and-forward at the receiver, an achievable rate region is provided in [9].…”

On the Gaussian Fading Broadcast Relay Channel With Causal State Feedback

“…Therefore, the proofs are quite standard and omitted here. Proofs for similar settings can be found, e.g., in [4], [5], [24].…”

Cooperative broadcasting with successive refinement based compression

“…In [4], the rate region given in [3] is improved via another DF relaying based achievable scheme. In [5], an achievability scheme based on superposition coding together with DF relaying is discussed.…”

“…The capacity region of the physically degraded Gaussian BRC, in the sense that the destinations are physically degraded with respect to the relay and the destinations are stochastically degraded with respect to each other, is known due to [9]. Other capacity results are for the discrete memoryless physically degraded BRC [8] and semi-degraded BRC [4].…”