A Union Bound Of Turbo Codes On Block-fading Channels

In1993, the French scholars, C.Berrou, put forward a new kind of codes called Turbo codes which was produced by using two recursion systematical convolution encoders connecting with an interleaver. Turbo codes, also known as cascaded convolutional codes, it take the soft-input、soft-output iterative decoding algorithm. Owing to its superior performance closed to Shannon limitation, Turbo codes were paid attention to widely. From then on, estimating the performance of the Turbo codes becomes a very important research direction.The paper systematically describes the encoding and decoding algorithm of Turbo codes and the structure of Turbo code, and then given several common performance bound, deduce the Turbo code’s performance bound and simulate it based on AWGN channel. At the last mainly for the wireless channel characteristics deduce the Turbo codes’ union bound based on Block-fading channel. The main content of this article include:1, An overview on the status of modern communication system theory and introduce the Background and Research status of Turbo Codes.2, Introduce the Turbo Codes and Decoding Principles in detail and it’s basic structure, list several commonly used interleaver and decoding algorithm, then compare the Advantages and disadvantages of various interleaver and the decoding algorithm. Analysis the factors that affecting the performance of Turbo codes, and take simulation.3, Give several common performance bounds, Union bound、Gallager bound、 Sphere bound. Deduce the Turbo code’s bit error rate on AWGN channel by using of those techniques. And compare the advantages and disadvantages of these three methods.4, mainly for the wireless channel characteristics deduce the Turbo codes’ union bound based on Block-fading channel. At the last compared with the M&L bound and the DS2bound. 5, Finally summarize this article, and prospect the development of Turbo code.