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

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. Index Terms Binary block codes, bounds, decision region, square radius probability density function, word error rate.