Turbo Codes and Turbo Principle

This chapter discusses the generation of turbo codes which can be implemented by either serial or parallel concatenation. It presents parallel concatenation for illustration. Maximum a posteriori (MAP) decoding of turbo codes relies on a recursive algorithm that exploits the inherent trellis structures of convolutional codes. Such an algorithm was derived by Bahl, Cocke, Jelinek, and Raviv, and thus has the name BCJR algorithm. To decode a turbo code formed by parallel concatenation of two recursive systematic convolutional (RSC) codes, two constituent decoders perform the BCJR algorithm individually, but exchanging their estimation information to expedite the iteration convergence. The extrinsic information transfer (EXIT) chart intuitively describes the convergence behavior of extrinsic information exchange between the two constituent decoders, thereby providing a guideline for turbo design. The chapter investigates turbo equalization, statistics of log likelihood ratio (LLR) and application of the turbo principle such as turbo CDMA and interleaver-division multiple-access (IDMA).