Construction of time-invariant rate-compatible-low-density parity-check convolutional codes

In this study, a family of time-invariant rate-compatible (RC) low-density parity-check (LDPC) convolutional codes with algebraic construction is developed based on the graph-extension method over a given positive integer m, which is considered as the given encoding memory. The base code of this family is first obtained by modifying a given construction of a time-invariant LDPC convolutional code. Afterwards, the authors derive the other extended component codes by successively adding extra information bits into the base code. In particular, each component code in the family not only enables the property of fast encoding that can dramatically reduce the implementation complexity, but has the given encoding memory m for each parity-check bit that can remarkably improve the error performance as well. They also demonstrate that the Tanner graph for all the codes in the family is free of girth 4. Simulation results indicate that the proposed family of RC-LDPC convolutional codes collectively offers a desirable performance improvement as compared with the existing counterparts over the binary-input additive Gaussian noise channels under BP decoding.