On the Capacity of the Noncausal Relay Channel

TL;DR

This paper investigates the noncausal relay channel, demonstrating that Gelfand--Pinsker coding can improve achievable rates and providing new bounds that establish the channel's capacity for degraded cases.

Contribution

It introduces a novel coding scheme using Gelfand--Pinsker coding and derives tighter capacity bounds for the noncausal relay channel.

Findings

Gelfand--Pinsker coding improves achievable rates.

New upper bounds on capacity surpass cutset bounds.

Capacity is established for degraded noncausal relay channels.

Abstract

This paper studies the noncausal relay channel, also known as the relay channel with unlimited lookahead, introduced 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 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, which can achieve strictly higher rates than existing coding schemes. This paper also provides a new upper bound on the capacity of the noncausal relay that strictly improves upon the 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.