Exact Symbol Error Rate for Variable Length Codes Over Binary Symmetric Channel

In this paper, we analyze the error recovery performance of variable length codes (VLCs) transmitted over binary symmetric channel (BSC). Simple expressions for the exact mean symbol error rate (MSER) and the exact variance of symbol error rate (VSER) for any crossover probability p_e are presented. We also prove that the mean error propagation length (MEPE) derived for single bit inversion error case is a scaled value of MSER when p_e tends to zero. Comparisons with simulations demonstrate the accuracy of the MSER and VSER expressions.