The Sphere Packing Bound for DSPCs with Feedback a la Augustin

TL;DR

This paper provides a complete proof of the sphere packing bound for discrete stationary product channels with feedback, building on Augustin's 1978 sketch and introducing novel proof techniques.

Contribution

It offers a full proof of the sphere packing bound with feedback, incorporating new ideas like averaging and subblocks that may benefit other communication theory problems.

Findings

Complete proof of the sphere packing bound with feedback

Introduction of Augustin's averaging technique

Use of subblocks in the proof

Abstract

Establishing the sphere packing bound for block codes on the discrete stationary product channels with feedback ---which are commonly called the discrete memoryless channels with feedback--- was considered to be an open problem until recently, notwithstanding the proof sketch provided by Augustin in 1978. A complete proof following Augustin's proof sketch is presented, to demonstrate its adequacy and to draw attention to two novel ideas it employs. These novel ideas (i.e., the Augustin's averaging and the use of subblocks) are likely to be applicable in other communication problems for establishing impossibility results.