Fano Decoding of BCH and CRC Codes on BPSK and Noncoherent QFSK Channels

The Fano algorithm for decoding convolutional codes has been shown to have significantly faster decoding speeds than the Viterbi decoder at operational signal-to-noise ratios with nearly identical frame-error rate (FER) performance. We show here that the Fano algorithm can be modified to decode BCH and CRC codes with similarly high throughput and FER performance by treating the BCH (CRC) code as a rate-1 zero-terminated convolutional code. This is the case even for systematic encodings, where only minor post-Fano processing is necessary. This paper considers the case of binary BCH and CRC codes on a standard BPSK/AWGN channel and a binary CRC code on a noncoherent Q-ary FSK channel. The latter case requires the derivation of an appropriate Fano metric and a binary code to Q-ary decoding tree. We demonstrate near-maximum-likelihood performance and several decibels of coding gain. We also include two cases of Chase algorithm decoding on the BPSK channel and make software-based decoding speed comparisons.