Capacity of a Class of Deterministic Relay Channels

TL;DR

This paper determines the capacity of a specific class of deterministic relay channels, introduces two optimal coding schemes, and confirms a related conjecture on channels with rate-limited state information.

Contribution

It derives the exact capacity formula for deterministic relay channels and presents two novel coding schemes that achieve this capacity.

Findings

Capacity is given by max over p(x) of min {I(X;Y)+R_0, I(X;Y,Y_1)}.

Introduces 'hash-and-forward' and 'compress-and-forward' coding schemes.

Confirms a conjecture on channels with rate-limited state information.

Abstract

The capacity of a class of deterministic relay channels with the transmitter input X, the receiver output Y, the relay output Y_1 = f(X, Y), and a separate communication link from the relay to the receiver with capacity R_0, is shown to be C(R_0) = \max_{p(x)} \min \{I(X;Y)+R_0, I(X;Y, Y_1) \}. Thus every bit from the relay is worth exactly one bit to the receiver. Two alternative coding schemes are presented that achieve this capacity. The first scheme, ``hash-and-forward'', is based on a simple yet novel use of random binning on the space of relay outputs, while the second scheme uses the usual ``compress-and-forward''. In fact, these two schemes can be combined together to give a class of optimal coding schemes. As a corollary, this relay capacity result confirms a conjecture by Ahlswede and Han on the capacity of a channel with rate-limited state information at the decoder in the special case when the channel state is recoverable from the channel input and the output.