Upper Bounds on the Mismatched Reliability Function and Capacity Using a Genie Receiver

TL;DR

This paper introduces a new framework using a genie-aided approach to establish upper bounds on the mismatch capacity and reliability function of discrete memoryless channels, simplifying computations and providing tighter bounds.

Contribution

The paper presents a novel genie-based technique for deriving upper bounds on mismatch capacity and reliability functions, incorporating symmetry considerations for improved bounds.

Findings

New upper bounds on mismatch capacity and reliability function.

Relaxed bounds that are easier to compute.

Conditions for tightness of the bounds in certain rate ranges.

Abstract

We develop a novel framework for proving converse theorems for channel coding, which is based on the analysis technique of multicast transmission with an additional auxiliary receiver, which serves as a genie to the original receiver. The genie provides the original receiver a certain narrowed list of codewords to choose from that includes the transmitted one. This technique is used to derive upper bounds on the mismatch capacity of discrete memoryless channels as well as the reliability function with a mismatched decoding metric. Unlike previous works, our bounding technique exploits also the inherent symmetric requirement from the codewords, leading to these new upper bounds. Since the computations of most of the known bounds on the mismatch capacity are rather complicated, we further present a method to obtain relaxed bounds that are easier to compute. As an example, we analyze the obtained bounds in the binary-input channels case. We conclude by presenting simpler bounds on the reliability function, and provide sufficient conditions for their tightness in certain ranges of rates.