Hybrid decoding of irregular LDPC codes

Time-invariant hybrid (ℋTI) decoding of irregular low-density parity-check (LDPC) codes is studied. Focusing on ℋTI algorithms with majority-based (MB) binary message-passing constituents, we use density evolution and finite-length simulation to analyze the performance and the convergence properties of these algorithms. Tight upper bounds on the threshold of MB ℋTI algorithms are derived, and it is proven that the asymptotic error probability for these algorithms tends to zero at least exponentially with the number of iterations. We devise optimal MB ℋTI algorithms for irregular LDPC codes, and show that these algorithms outperform Gallager's algorithm A applied to optimized irregular LDPC codes. We also show that compared to switch-type algorithms, such as Gallager's algorithm B, where a comparable improvement is obtained by switching between different MB algorithms, MB ℋTI algorithms are more robust, and can better cope with unknown channel conditions, and thus can be practically more attractive