On the maximum path metric difference in Viterbi decoders of punctured rate (n-1)/n codes

The relationship between code parameters for full and punctured code rates, the maximum candidate path metric difference, and the wordsize of path metrics for modulo normalization is examined. The maximum difference between the candidate path metrics must be known to efficiently implement the modulo normalization technique for accommodating the growth of path metrics in a Viterbi decoder. For rate 1/n and the rate (n-1)/n punctured codes derived therefrom, the smallest number of bits necessary to represent each path metric is a function of the maximum difference between path metrics and hence the minimum free distance (d_free) of the code. The authors examine these relationships and present code parameters and deletion maps for several punctured codes of interest derived from maximum d_free rate 1/2 codes with memory 8 through 13. A modification to J.A. Heller´s (1968) upper bound on d_free for rate 1/n codes is presented which yields an upper bound on d_free for punctured rate (n-1)/n codes