Asymptotically Good LDPC Convolutional Codes Based on Protographs

LDPC convolutional codes have been shown to be capable of achieving the same capacity-approaching performance as LDPC block codes with iterative message-passing decoding. In this paper, asymptotic methods are used to calculate a lower bound on the free distance for several ensembles of asymptotically good protograph-based LDPC convolutional codes. Further, we show that the free distance to constraint length ratio of the LDPC convolutional codes exceeds the minimum distance to block length ratio of corresponding LDPC block codes.