On the Design of Turbo Codes

Abstract: This thesis is about Turbo codes - codes constructed via parallel concatenation of two recursive convolutional encoders linked by an interleaver. The focus of the work is on the understanding and design of Turbo codes. This includes thorough investigation of central components that influence Turbo code performances, such as the constituent encoders and the interleaver, as well as the procedure of iterative decoding. The investigations are carried out for transmission on additive white Gaussian noise channels. Two aspects that influence the performance of Turbo codes are considered: (1) code properties, in terms of Hamming distance spectra, and (2) decoding properties, in terms of the performance of iterative decoding. It is asserted that both these aspects are influenced by both the choice of interleaver and the choice of constituent encoders. An interleaver design algorithm based on these observations is presented. Furthermore, guidelines for the choice of constituent encoders are outlined. As regards the interleaver, it can be designed to result in both good code- and decoding properties. In contrast, the choice of constituent encoders involves a trade off between the two. A measure that comprises the interleaver properties influencing the performance of iterative decoding is presented. This measure is called Iterative Decoding Suitability (IDS), and it is derived using a model that approximates correlation properties of decoder inputs and outputs. The aspect of trellis termination of Turbo codes is also investigated. It is demonstrated that with proper interleaver design, very competitive error rate performances is obtained also without trellis termination. In addition, it is demonstrated that the 'error-floor' that Turbo codes are claimed to suffer from at medium- to high signal-to-noise ratios can be significantly lowered by proper combination of constituent encoders and interleaver design.