Error and Erasure Exponents for the Broadcast Channel with Degraded Message Sets

TL;DR

This paper analyzes error and erasure exponents for the broadcast channel with degraded message sets, proposing a two-step decoding algorithm that improves decoding reliability based on confidence levels.

Contribution

It introduces a novel two-step decoding scheme for degraded broadcast channels and derives error and erasure exponents using the method of types.

Findings

Derived error and erasure exponents for the proposed decoding scheme.

The two-step decoding algorithm adapts to confidence levels in message decoding.

Expressed exponents in terms of a penalized modified random coding error exponent.

Abstract

Error and erasure exponents for the broadcast channel with degraded message sets are analyzed. The focus of our error probability analysis is on the main receiver where, nominally, both messages are to be decoded. A two-step decoding algorithm is proposed and analyzed. This receiver first attempts to decode both messages, failing which, it attempts to decode only the message representing the coarser information, i.e., the cloud center. This algorithm reflects the intuition that we should decode both messages only if we have confidence in the estimates; otherwise one should only decode the coarser information. The resulting error and erasure exponents, derived using the method of types, are expressed in terms of a penalized form of the modified random coding error exponent.