Sequential decoding of systematic and nonsystematic convolutional codes with arbitrary decoder bias

Abstract

This paper presents several results involving Fano's sequential decoding algorithm for convolutional codes. An upper bound to the a th moment of decoder computation is obtained for arbitrary decoder bias B and a \leq 1 . An upper bound on error probability with sequential decoding is derived for both systematic and nonsystematic convolutional codes. This error bound involves the exact value of the decoder bias B . It is shown that there is a trade-off between sequential decoder computation and error probability as the bias B is varied. It is also shown that for many values of B , sequential decoding of systematic convolutional codes gives an exponentially larger error probability than sequential decoding of nonsystematic convolutional codes when both codes are designed with exponentially equal optimum decoder error probabilities.