On the improved sub-code constrained algorithm for the determination of free distance for turbo codes

In this paper, two effective techniques are proposed to improve the computation efficiency of the sub-code constrained algorithm for the determination of free distance for Turbo codes. Firstly, it is known that, the determination of the minimum output Hamming weight of the recursive systematic convolutional (RSC) code under some input constraints is the crucial problem in the constrained sub-code algorithm towards the weight distribution calculation for Turbo codes. And the modified Viterbi algorithm was utilized to solve this problem. In this paper, the backward state transition based (BST) algorithm is introduced to determine the minimum output Hamming weight of the RSC codes for the given input constraints. Although the state transition-based calculation is utilized as well, it is shown that, by making full use of the state transition characteristics of the given RSC codes, multiple step calculations may be merged into one step calculation, thus improving the computation efficiency when determining the minimum output Hamming weight of the RSC code. Secondly, it is proposed to employ the backward computation procedure instead of the forward one when implementing the sub-code algorithm. And it is validated that, the proposed backward computation method could be utilized to speed up the determination of the free distance for Turbo codes. And the 3GPP standard Turbo code is used as an example to validate the applicability of the proposed improved schemes.