Computing the probability of undetected error for shortened cyclic codes

The authors present a general technique for computing P/sub e/ for all possible shortened versions of cyclic codes generated by any given polynomial. The technique is recursive, i.e. computes P/sub e/ for a given code block length n from that of the code block length n-1. The proposed computation technique for determining P/sub e/ does not require knowledge of the code weight distributions. For a generator polynomial of degree r, and mod g mod nonzero coefficients, the technique yields P/sub e/ for all code block lengths up to length n in time complexity O(n mod g mod 2/sup r+ mod g mod /). Channels with variable bit error probabilities can be analyzed with the same complexity. This enables the performance of the code generator polynomials to be analyzed for burst errors.<
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