An Analytical Method for Performance Evaluation of Binary Linear Block Codes

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An analytical method for performance evaluation of binary linear block codes using an Additive White Gaussian Noise (AWGN) channel model with Binary Phase Shift Keying (BPSK) modulation is presented. We focus on the probability distribution function (pdf) of the bit LogLikelihood Ratio (LLR) which is expressed in terms of the Gram-Charlier series expansion. This expansion requires knowledge of the statistical moments of the bit LLR. We introduce an analytical method for calculating these moments. This is based on some straight-forward recursive calculations involving certain weight enumerating functions of the code. It is shown that the estimate of the bit error probability provided by the proposed method will asymptotically converge to the true bit error performance. Numerical results are provided for the (15,11) Cyclic code which demonstrate close agreement with the simulation results.

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