Non-systematic channel encoding is superior to systematic encoding in the presence of source redundancy. We show analytically that for high rate codes the advantage of non-systematic encoding over systematic encoding becomes even more significant. We then consider classes of non-systematic low-density 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 source redundancy, which is far superior to that of systematic LDPC codes. The advantage of such codes is even more significant for high rate coding. Simulation results demonstrate this advantage.
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