Analysis and design of turbo-like codes
Abstract
50 years after Shannon determined the capacity of memoryless channels, we finally know of practical encoding and decoding algorithms that closely approach this limit. This remarkable feat was first achieved by the invention of turbo codes by Berrou, Glavieux, and Thitimajshima in 1993 cite{BGT93}. Since then turbo codes have essentially revolutionized the coding field and became one of the central research problems in recent years. While there has been a great deal of excellent theoretical work on turbo codes, it is fair to say practice still leads theory by a considerable margin.
This thesis endeavors to fill some of that gap. The main body of the thesis concerns coding theorems for general turbo codes. We first prove coding theorems for some simple (yet interesting) serial turbo code ensembles on the AWGN channel. Then we generalize the results for a broader class of turbo-like codes on any memoryless channel. To closely estimate the noise threshold when calculate is feasible, we develop a method based on ``typical pairs decoding'. This method is powerful enough to reproduce Shannon's original coding theorems on any memoryless binary-input symmetric channels. Last we introduce a linearly encodable and decodable code, after carefule design, with performance provably close to Shannon's limit.
One main contribution here of both theoretical and practical interests is the introduction of repeat-accumulate (RA) codes. RA codes are structurally simple enough that a rigorous…
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