Turbo Code, The Max-log-map Algorithm

Turbo code was first discovered in 1993. Because of its near Shannon limit performance, Turbo code had once been the focus of the channel coding area. After more than one decade's continuous efforts poured into the research aiming at a theoretical explanation behind the mask of the exceptionable Turbo performance, the intrinsic nature of the Turbo code has been, little by little, thrust into the spotlight of the public. As a result, the frontier of Turbo code is undergoing a fundamental swift toward implementation and it has been recommended or employed in enormous adopted communication standards, such as CDMA2000, WCDMA, 3GPP etc.Roughly speaking, implementation should strive to make a compromise between the hardware complexity and the corresponding performance. This dissertation elaborates the complexity reduction of the Max-Log-MAP-Based Turbo decoder. As we know, the addition and taking the maximum (max) operations, as well as all the quantized data involved in the Max-Log-MAP Turbo decoding algorithm form a commutative max-sum semiring. In this paper, it will be shown that when the distributive law is properly applied to this semiring, not only a considerable computational saving is achieved, but also the shift operations are removed. Simulation result for a (21,37) Turbo code shows that by taking the advantage of removing shift operations, precision bit of all the data involved in the decoder can be safely reduced from 3 to 2 with negligible performance degradation.This is the outline of this dissertation: In chapter 1, the excellent performance of the Turbo code and the research frontier are elaborated.Chapter 2 recalls the structure of the Turbo encoder and decoder, as well as the skeleton of some famous decoding algorithms.Given some peculiar features owned by Max-Log-MAP decoding algorithm, the structure of Turbo decoder could be further simplified, which is the main topic of Chapter 3.In Chapter 4, the introduction of the quantization and the max-sum semiring are given, serving as a knowledge background for derivations in the subsequent chapters.Chapter 5 is the main part to solve the problems tendered above. We will see the beneficial merits by properly applying the distributive law to the max-sum semiring, which is formed by Max-Log-MAP algorithm. And the corresponding simulation results are given in the last chapter to substantiate the conclusions.