Free Distance Bounds for Protograph-Based Regular LDPC Convolutional Codes

In this paper asymptotic methods are used to form lower bounds on the free distance to constraint length ratio of several ensembles of regular, asymptotically good, protograph based LDPC convolutional codes. In particular, the authors show that the free distance to constraint length ratio of the regular LDPC convolutional codes exceeds that of the minimum distance to block length ratio of the corresponding LDPC block codes. LDPC convolutional codes, the convolutional counterparts of LDPC block codes, were introduced, and they have been shown to have certain advantages compared to LDPC block codes of the same complexity.