Exact Free Distance and Trapping Set Growth Rates for LDPC Convolutional Codes
Ensembles of (J,K)-regular Low-Density Parity Check Convolutional (LDPCC) codes are known to be asymptotically good, in the sense that the minimum free distance grows linearly with the constraint length. In this paper, the authors use a protograph-based analysis of terminated LDPCC codes to obtain an upper bound on the free distance growth rate of ensembles of periodically time-varying LDPCC codes. This bound is compared to a lower bound and evaluated numerically. It is found that, for a sufficiently large period, the bounds coincide. This approach is then extended to obtain bounds on the trapping set numbers, which define the size of the smallest, non-empty trapping sets, for these asymptotically good, periodically time-varying LDPCC code ensembles.