Optimal CRC Design and Serial List Viterbi Decoding for Multi-Input Convolutional Codes

Abstract

We introduce a process for designing the optimal cyclic redundancy check (CRC) code for each input of a given $\kappa$ input convolutional code $(\kappa \ge 1)$. Using the free distance on each input and considering that each input sequence can correspond to multiple error events in a $\kappa -$ input CC, the process efficiently narrows down from the set of polynomials with the same degree the best CRC that provides the minimum frame error rate (FER) for each input. We also extend the efficient and low complexity serial list Viterbi algorithm (SLVA) for single-input CCs in [1] to the $\kappa -$ input case. We discuss different ways of integrating CRCs in a $\kappa -$ input CC and derive the truncated union bound on the FER for each input. Numerical examples on a two-input CC illustrate the effectiveness of the proposed CRC design and SLVA decoder for $\kappa -$ input CCs.