On the Capacity of the Noncausal Relay Channel

Abstract

This paper studies the noncausal relay channel, also known as the relay channel with unlimited look ahead, introduced by by El Gamal, Hassanpour, and Mammen. Unlike the standard relay channel model, where the relay encodes its signal based on the previous received output symbols, the relay in the noncausal relay channel encodes its signal as a function of the entire received sequence. In the existing coding schemes, the relay uses this noncausal information solely to recover the transmitted message or part of it and then cooperates with the sender to communicate this message to the receiver. However, it is shown in this paper that by applying the Gelfand–Pinsker coding scheme, the relay can take further advantage of the noncausally available information and achieve rates strictly higher than those of the existing coding schemes. This paper also provides a new upper bound on the capacity of the noncausal relay channel that strictly improves upon the existing cutset bound. These new lower and upper bounds on the capacity coincide for the class of degraded noncausal relay channels and establish the capacity for this class.