On the Reliability Function of the Discrete Memoryless Relay Channel

TL;DR

This paper derives bounds on the reliability function for the discrete memoryless relay channel using types, introducing achievable error exponents based on known coding schemes and analyzing their performance.

Contribution

It presents new bounds on the relay channel's reliability function and evaluates error exponents for partial decode-forward and compress-forward schemes.

Findings

Decode-forward error exponent evaluated on Sato's relay channel

Optimal number of blocks improves error decay rate

Upper bound derived using feedback-based techniques

Abstract

Bounds on the reliability function for the discrete memoryless relay channel are derived using the method of types. Two achievable error exponents are derived based on partial decode-forward and compress-forward which are well-known superposition block-Markov coding schemes. The derivations require combinations of the techniques involved in the proofs of Csisz\'ar-K\"orner-Marton's packing lemma for the error exponent of channel coding and Marton's type covering lemma for the error exponent of source coding with a fidelity criterion. The decode-forward error exponent is evaluated on Sato's relay channel. From this example, it is noted that to obtain the fastest possible decay in the error probability for a fixed effective coding rate, one ought to optimize the number of blocks in the block-Markov coding scheme assuming the blocklength within each block is large. An upper bound on the reliability function is also derived using ideas from Haroutunian's lower bound on the error probability for point-to-point channel coding with feedback.