Low-rate Convolutional Codes Used In Code-Spread CDMA System

The attention to Low-rate convlutional codes is born in Viterbi's research on low-rate orthogonal convolutional codes for spread-spectrum. In the following years, many researches concerned with more common low-rate convolutional codes used for spreading demonstrated that this application can bring much good in improving capacity, BER etc.. Thus, how to effectively find good low-rate convolutional codes is crucial. However, achievements are hardly satisfactory.This thesis is devoted to constructing good low-rate convolutional codes and main harvest is as below:First, based on the analysis of linear properties, we introduce several fundamental concepts for model generating, say, Simple Path, Path Generator Matrix and son on. Via them, we deduce then obtain a standard Linear Programming Problem.Then, Simplex Method of linear programming is used to attain several groups of solutions. But for most code rates, the solutions are non-integer, for the generators composition in fact. However, still they are significant for further integer searching, since they can assure the maximum value of free distances and are optimal in some sense.At last, the Branch and Bound method of Integer Linear Programming is employed, which made the above non-integer solutions as initial ones. Through this, we get satisfactory generator constructions in several ways.First, the free distances are maximal; second, distance spectrum is optimal in the first element; third, we use the least sorts of generators for any code rate; forth, the repetition of each generator is most. The last two points are of great...