Research On The Distributions Of Low-Weight Codewords Of Turbo Codes

The Turbo Codes, which can approach the Shannon limits, are taken as a mark stone in the development history of channel coding theory. It changes the ideas of designing channel codes by the means of geometric to increase the minimum weight to that of designing channel codes by the means of random coding to decrease the multiplicities of the low weight codewords. In this dissertation, a deep study is taken on the distributions of low weight codewords of Turbo codes and the applications. Some positive results are obtained and summarized as follow:1. Various factors that have impacts on the distributions of low weight codewords have been examined. Especially as the interleaving length is shorter and the period of the feedback polynomial in the generating matrix is longer the impacts produced by the input sequences weighted more than 2, such as weight 3, weight 4 sequences have been analyzed deeply.2. An algorithm of computing the distributions of the weight of codewords of Turbo codes, named statistics per weight, based on the statistics is presented. Its' complexity is not dependent on the constructions of the Turbo coders; therefore it is very convenient to apply. When the interleaving length is not very long, such as no longer than 500 bits, it can bring out very accurate results, especially for the distributions of low weight codewords.3. The features of the self-terminating sequences have been studied thoroughly and deeply. Two theorems, called decomposing theory and constructing weight-equally theory respectively, and several properties about the self-terminating sequences are derived. A method based on the theorem of constructing weight-equally to computing the distributions of low weight codewords is presented. Also the concept of pseudo-self terminating sequence is presented and discussed.4. The transform features of multiple-period for interleavers, including the various factors that have impacts on the features, are analyzed. It is pointed out that when the distributions of the low-weight codewords are dominated by the weight-2 or combinations of weight-2 self-terminating sequences, the transform features of multiple-period have great affections on the distributions. Under these cases, a method of designing interleavers that can produce sparse distributions of low weight codewords without transform of lowmultiple-period is derived.5. A concept of full-correlation, developed from the general concept of correlation, is brought forward to describe the correlation properties of the correlated sequence, such as the punctured sequences of Turbo codes. It is helpful to understand the mechanism of puncturing in turbo codes theoretically.6. The unequal protections of Turbo codes are studied further more under the distributions of low weight codewords. Three improved methods are presented. All of them are easy to design and simple to implement without nearly any changes in the original encoding constructions. The improvements will be more noticeable as the distributions of low weight codewords are sparser.