The theoretical capacity of the Parity Source Coder

TL;DR

This paper analyzes the theoretical capacity of the Parity Source Coder, showing it approaches the Shannon limit with minimal corrections for large parameters, indicating near-optimal data compression performance.

Contribution

It provides a theoretical analysis demonstrating that the Parity Source Coder's capacity saturates the Shannon limit at large K, with exponentially small finite-size corrections.

Findings

Capacity saturates the Shannon limit at large K

Finite K corrections are exponentially small

Behavior at finite K is nearly optimal

Abstract

The Parity Source Coder is a protocol for data compression which is based on a set of parity checks organized in a sparse random network. We consider here the case of memoryless unbiased binary sources. We show that the theoretical capacity saturate the Shannon limit at large K. We also find that the first corrections to the leading behavior are exponentially small, so that the behavior at finite K is very close to the optimal one.