Evaluate the Word Error Rate of Binary Block Codes with Square Radius Probability Density Function

TL;DR

This paper introduces the square radius probability density function (SR-PDF) to accurately evaluate the word error rate of binary block codes, providing precise calculations and practical approximations for both optimal and suboptimal decoding.

Contribution

It proposes the SR-PDF concept for exact WER evaluation and demonstrates Gamma distribution approximation for long codes, enabling simple closed-form expressions.

Findings

SR-PDF allows precise WER calculation for ML and suboptimum decoders.

Gamma distribution approximates SR-PDF for long codes with two measurable parameters.

Proposed formulas closely match simulation results.

Abstract

The word error rate (WER) of soft-decision-decoded binary block codes rarely has closed-form. Bounding techniques are widely used to evaluate the performance of maximum-likelihood decoding algorithm. But the existing bounds are not tight enough especially for low signal-to-noise ratios and become looser when a suboptimum decoding algorithm is used. This paper proposes a new concept named square radius probability density function (SR-PDF) of decision region to evaluate the WER. Based on the SR-PDF, The WER of binary block codes can be calculated precisely for ML and suboptimum decoders. Furthermore, for a long binary block code, SR-PDF can be approximated by Gamma distribution with only two parameters that can be measured easily. Using this property, two closed-form approximative expressions are proposed which are very close to the simulation results of the WER of interesting.