COMPUTER-SEARCH OF THE BEST CONVOLUTIONAL-CODES ON THE BASIS OF WEIGHT DISTRIBUTION

As the efficient methods to determine the weight distribution of the c onvolutional code, there have been proposed the high-speed algorithm b ased on the tree search on the trellis [1] and the variational method based on the variation of the weight of the code word [2]. This paper proposes a method to determine the weight distribution of the convolut ional code with the coding ratio 1:2 where an algorithm (called modifi ed variational method), which is efficient and can easily be realized on the computer, is derived by modifying the variational method. It is shown that the modified algorithm has a better performance than the c onventional method. Then an efficient method is proposed which searche s the best nonsystematic convolutional code with the coding ratio 1:2, assuming the maximum likelihood decoding. The best codes are sought f or the constraint length from 6 to 19 using the proposed method, and a large number of the best codes is shown which heretofore have not bee n known.