Capacity Upper Bound and Minimum Energy-per-Bit for AWGN Relay Channel with Channel Side Information

In the following paper, we will analyze and study over a subset of channels including relay with channel side information. First, it has been derived an upper bound on the capacity for this AWGN relay channel when the channel side information is non-causally accessible at both, the transmitter and the relay. In the following, a minimization problem for the energy-per-bit for this type of channel has been presented. After that, by using derived results for the capacity of this channel, we evaluate a lower bound for the problem of the minimum energy-per-bit. We investigate that this bound could be less than the bound founded of the classical AWGN relay channels.

I. Introduction

The well-known relay channel (RC) at first was introduced at 1971 by Van-der Meulen in [1]. Then, Sato in 1976 introduced a degraded RC and derived two different capacity lower bounds and an upper bound, also for capacity, for RC in [2]. The substantial findings on the capacity of the RCs have been reported in [3]. They presented different coding techniques and a considerable upper bound on the capacity of these channels. Following the proposed coding technique, introduced in [3], a series of new capacity results over RCs as the capacity of the physically degraded RCs [4], additive white Gaussian noise (AWGN) degraded RCs with power constraints [5], deterministic RC [6] were established. Also, the capacity of RC with orthogonal components, for a special class, was studied in [7]. The authors in [8] presented an achievable rate region and a coding scheme in order to achieve this rate for the multiple-level RC. Some other works as [9] and [10] have been down upon RCs.