Interleaver design for serially concatenated convolutional codes: theory and application

This paper addresses the problem of interleaver design for serially concatenated convolutional codes (SCCCs) tailored to the constituent codes of the SCCC configuration. We present a theoretical framework for interleaver optimization based on a cost function closely tied to the asymptotic bit-error rate (BER) of the block code C_s resulting from proper termination of the constituent codes in the SCCC code. We define a canonical form of the interleaving engine denoted as the finite state permuter (FSP) and using its structural property, develop a systematic iterative technique for construction of interleavers. The core theoretical results focus on the asymptotic behavior of a class of cost functions and their martingale property, which is then used to develop an order recursive interleaver optimization algorithm. We address the issue of the complexity of the interleaver growth algorithm presented in the paper and demonstrate that it has polynomial complexity. Subsequently, we provide details about the application of the proposed technique and present a modification of the algorithm that employs error pattern feedback for improved performance at a reduced complexity. Sample experimental results are provided for an SCCC code of rate 1/3 and information block length 320 that achieves a minimum distance of d_min=44.