Optimal Coding Strategies for Bidirectional Broadcast Channels Under Channel Uncertainty

Abstract

Bidirectional relaying is a promising approach to improve the performance in wireless networks such as sensor, ad-hoc, and even cellular systems. Bidirectional relaying applies to three-node networks, where a relay establishes a bidirectional communication between two other nodes using a decode-andforward protocol. First, the two nodes transmit their messages to the relay which decodes them. Then, the relay broadcasts a reencoded message in such a way that both nodes can decode their intended message using their own message as side information. We consider uncertainty in the channel state information (CSI) and assume that all nodes only know that the channel over which the transmission takes place is from a pre-specified set of channels. In this work, we concentrate on the second phase, which is called the compound bidirectional broadcast channel. We present a robust coding strategy which enables reliable communication under channel uncertainty and show that this strategy actually achieves the compound capacity. Further, we analyze scenarios where either the receivers or the transmitter have perfect CSI. We show that CSI at the receivers does not affect the maximal achievable rates, while CSI at the transmitter improves the capacity region. A numerical example and a gametheoretic interpretation complete this work.

Impact of Interference in Coexisting Wireless Networks with Applications to Arbitrarily Varying Bidirectional Broadcast Channels

“…[27]. Together with (3) this immediately implies that for C det (W) the average probability of a successful transmission over the compound BBC W is bounded from below by…”

“…Bidirectional relaying for compound channels is studied in [27,28], while [29] discusses adaptive bidirectional relaying with quantized channel state information. Besides the decode-and-forward protocol [20][21][22][23][24][25][26][27][28][29][30][31][32] there are also amplify-and-forward [32][33][34][35][36] or compress-and-forward [37][38][39] approaches similarly as for the classical relay channel. A newer approach is compute-and-forward [40][41][42][43][44][45][46], where the relay decodes a certain function of both individual messages.…”

“…The capacity region of the compound BBC is known and can be found in [27]. It is shown that for given input distribution P X all rate pairs…”

“…In more detail, in [27] it is shown that there exists a deterministic code C det (W) for the compound BBC W such that all rate pairs (R 1 , R 2 ) ∈ R(P X |Λ) are achievable while the average probability of error can be bounded from above bȳ…”

“…The deterministic rates of the compound channel can be found in [27]. Additionally, as in [57] for the single-user compound channel, it can be easily shown that for the compound BBC W the achievable rates for deterministic and random codes are equal.…”