Near-ML Decoding of CRC Codes

We study a new bit-flipping algorithm, coupled with an algebraic decoder, for near-ML decoding of cyclic redundancy check (CRC) codes on the binary AWGN channel. The asymptotic coding gain of such codes approaches 6 dB, and the real gain at 10^-4 block error probability is about 4.5 dB. We show that a generalization of Chase´s algorithm, called the {a,b} algorithm, is able to achieve nearly all of this gain at modest complexity. Here a denotes the number of bit positions having lowest confidence, and b denotes the maximum number of bits to be flipped among this low-confidence set. For a 16-bit CRC code of length n=1024, we show a=8, b=3 represents a good design choice.