ON APPROXIMATING THE DENSITY FUNCTION OF RELIABILITIES OF THE MAX-LOG-MAP DECODER

Reliabilities at the output of soft-decision decoders are random variables and hence are characterized by their density function. Density functions of reliabilities have been computed based on probabilities involving the projection of the noise in directions corresponding to different error events. Each such projection results in a random variable, and two approaches have been taken to compute probabilities involving these random variables. In the first approach, the random variables are treated as if they are independent; in the second approach, correlations between the random variables are taken into account. The mathematical expressions found using either approach are generally too complicated for further use in analytical work. In this paper, we propose a simple approach to account for the correlation between the random variables resulting from the projection of noise onto directions specified by different error events. Under this approach, we reduce the number of random variables that are considered in the computation of the PDF by eliminating those that are highly correlated. Working with this condensed set of random variables produces results that are close to the true values even if the independence assumption is used. A mathematically tractable closed-form approximation for the PDF is also presented, and the validity of this approximation is demonstrated. This PDF estimate can be used to analyze several communication schemes that utilize reliabilities as a design tool.