Punctured turbo code ensembles

We analyze the asymptotic performance of punctured turbo codes. The analysis is based on the union bound on the word error probability of maximum likelihood decoding for punctured turbo code ensembles averaged over all possible puncturing patterns and interleavers. By using special probabilistic puncturing, we prove that, for a given mother turbo code ensemble, [C], with a finite noise threshold, c/sub 0//sup [C]/, if the asymptotic puncturing turing rate, /spl lambda/, satisfies log /spl lambda/ < -c/sub 0//sup [C]/, there exists a finite noise threshold, c/sub 0//sup [Cp]/, for the punctured turbo code ensemble which is bounded by a function of c/sub 0//sup [C]/ and /spl lambda/. Based on this result, we prove that, on any binary-input memoryless channel whose Bhattacharyya noise distance is greater than c/sub 0//sup [Cp]/, the average ML decoding word error probability of the punctured turbo code ensemble approaches zero at least as fast as n/sup -/spl beta//, where /spl beta/ is the well known "interleaver gain" exponent. This enables us to answer an important question in the practice of HARQ (hybrid ARQ) schemes, namely, up to which puncturing rate "good" turbo codes give rise to "good" punctured codes.