We present a systematic technique for obtaining all the input sequences that are mapped by a given permutation either to themselves or to shifted versions of themselves (generically called permutation fixed points). Such sequences or their subsets, represent the primary candidates for examination in connection with obtaining estimates of the minimum distance of parallel concatenated codes, specially for interleaver lengths for which the determination of the actual minimum distance may be very difficult. Subsequently, we present a new class of permutations that nearly achieve the lower bound on the number of possible fixed points associated with a given permutation of prime length p. Preliminary experimental evidence suggests that certain permutations of this class lead to turbo codes with large minimum distances fur short interleaver lengths.
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