Abstract
Turbo codes, which achieve near Shannon-limit error correction performance, are a combination of parallel concatenated coding and iterative decoding. For the coding part, the reasons why the parallel concatenated coding structure could produce very good codes are now well understood. However, for the decoding part, although a number of researchers have shed a great deal of light on how the turbo decoding algorithm works, there is still no satisfactory theoretical explanation of the excellent performance of the low-complexity, iterative, turbo decoding algorithm. In this thesis, we study the turbo decoding algorithm using Max-Log-MAP instead of MAP as the soft-input/soft-output decoding algorithm for the constituent decoders. It is shown that this iterative decoding algorithm is suboptimal and may not even converge. Moreover, the existence of the fixed points of this iterative decoding algorithm is proved. Finally, we give some sufficient conditions for the convergence of the turbo decoding algorithm using Max-Log-MAP.