Performance Analysis and Design of Punctured Turbo Codes

Turbo codes, formed by the parallel concatenation of two recursive systematic convolutional component codes separated by an interleaver, have been proposed for use in a variety of wireless applications, including mobile, satellite and fixed wireless systems. Analysis of their performance requires knowledge of their transfer function, which conveys their distance properties. Using the transfer function, a tight upper bound on their bit error probability, averaged over all interleavers of a given size, can be evaluated. The upper bound closely reflects the actual bit error rate performance of a turbo code on additive white Gaussian noise (AWGN) channels, if maximum-likelihood decoding is used. In practice, however, suboptimal iterative decoding is employed, nevertheless the bit error rate performance of a turbo code converges towards low bit error probabilities for an increasing number of iterations and coincides with the upper bound, when the turbo code operates in the error floor region. This dissertation is concerned initially with the determination of the transfer function of turbo codes. We first introduce the augmented state diagram, a novel approach for the evaluation of the transfer function of rate-1/3 turbo codes. We then extend the concept of the augmented state diagram to account for turbo codes, whose output is periodically punctured according to a selected pattern, thus achieving rates higher than 1/3. Furthermore, we demonstrate that our technique can be used not only to determine the transfer function of turbo codes and, subsequently, compute their performance upper bound, but also to identify good puncturing patterns that lead to punctured turbo codes yielding a low error floor. As the input block length, or equivalently, the size of the constituent interleaver increases, computation of the full transfer function of a turbo code becomes intensive. However, turbo codeword sequences generated by input information sequences having small Hamming weight, start playing a significant role in the error rate performance of the turbo code. Motivated by this observation, we present a simple method to quickly enumerate only the codeword sequences having low information weight, instead of all codeword sequences composing the full transfer function. Consequently, we obtain an accurate approximation of the performance upper bound of punctured and non-punctured turbo codes, when large interleavers are used.