Input-Output Weight Distribution of Terminated Recursive Systematical Convolutional Codes

摘要

In this paper, we provide an evaluation of the input-parity weight distribution of terminated recursive systematic convolutional (RSC) codes with a constraint length of 3 as an example of code with a generating polynomial G = 1,1+ D~2/1+D+D~2- After L information bits, the paths of the codewords are ended at any state of the code. The number of paths ended at zero-state can be described by the number of error events, which is a sequence of code segments that diverges from an all-zero state at a given time and re-merges to the all-zero state at the same time and can be easily obtained. We provide the number of paths, that have ended at non-zero states based on the number of sets of error events. Using the number of paths that ended at each of the states, we provide the input-parity weight distribution of terminated RSC codes. This is the precise weight distribution that is necessary for the performance analysis of convolutional codes.