Improving the Sphere-Packing Bound for Binary Codes over Memoryless Symmetric Channels

TL;DR

This paper introduces an improved lower bound on the minimum code length for binary codes over symmetric channels by leveraging a connection with Ulam's liar game and Spencer's optimal solution.

Contribution

It presents a novel bound that refines the classical Sphere-Packing Bound using insights from combinatorial game theory.

Findings

New lower bound surpasses traditional Sphere-Packing Bound

Utilizes Spencer's solution to Ulam's liar game for coding theory

Provides tighter constraints on code length requirements

Abstract

A lower bound on the minimum required code length of binary codes is obtained. The bound is obtained based on observing a close relation between the Ulam's liar game and channel coding. In fact, Spencer's optimal solution to the game is used to derive this new bound which improves the famous Sphere-Packing Bound.