  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.
