Non-Systematic LDPC Codes for Redundant Data

Non-systematic channel encoding can be superior to systematic encoding in the presence of redundancy in the transmitted data. We consider classes of non-systematic lowdensity parity-check (LDPC) codes based on scrambling or splitting redundant data bits into coded bits. Scrambling and splitting are achieved by cascading a sparse matrix or an inverse of a sparse matrix, respectively, with an LDPC code. Such codes exhibit excellent performance in the presence of redundancy in the transmitted data, which is far superior to that of systematic LDPC codes. We study the theoretical limits of such codes, and present a density evolution (DE) method to find the threshold values of splitting based codes. We show that the advantage of these codes is even more significant for high channel rate transmission. Simulations, supporting the results, are presented.