Universal Random Access Error Exponents for Codebooks of Different Word-Lengths

TL;DR

This paper generalizes Csiszár's channel coding theorem to multiple codebooks with different word lengths, achieving optimal error exponents even without channel knowledge, and improves performance when the sender knows the channel.

Contribution

It extends the channel coding theorem to diverse codebook lengths and demonstrates error exponent achievement without channel knowledge, with improvements when the sender is informed.

Findings

Error exponents match single codebook case for multiple codebooks

Error probability tends to zero even without channel knowledge

Significant performance gains when sender knows the channel

Abstract

Csisz\'ar's channel coding theorem for multiple codebooks is generalized allowing the codeword lenghts differ across codebooks. Also in this case, for each codebook an error exponent can be achieved that equals the random coding exponent for this codebook alone, in addition, erasure detection failure probability tends to 0. This is proved even for sender and receiver not knowing the channel. As a corollary, a substantial improvement is obtained when the sender knows the channel.