Lowering the error floors of irregular high-rate LDPC codes by graph conditioning

This paper applies a graph conditioning algorithm, called the approximate cycle extrinsic message degree (ACE) algorithm, to design high-rate (R≥1/2) irregular LDPC codes. The algorithm was shown to be an effective tool to lower the error floors of lower-rate (R≤1/2) LDPC codes. However, for high-rate LDPC codes, due to the large number of degree-2 variable nodes in the optimal degree distribution, the error floor is high and it is more difficult to condition the graph. By constraining the number of degree-2 nodes, we found that the ACE algorithm can dramatically lower the error floor with little compromise of the threshold. A rate-3/4, length-10688 LDPC code is proposed whose AWGN channel performance is within 0.67 dB of the Shannon limit at BER=10^-5 and its error floor is lower than 10^-7. Compared to existing semi-regular codes which lower the floor by adopting non-optimal degree distributions, our graph-conditioned codes provides 0.38 dB of performance improvement at BER=10^-5. The same design criteria also apply well to medium-length LDPC code design and are suitable for rate-compatible applications using the information-ing technique. The rate-compatible scheme has consistently good thresholds and low error floors for 1/2≤ R≤ 8/9.