High-performance, low-complexity decoding of generalized low-density parity-check codes

A class of pseudo-random compound error-correcting codes, called Generalized Low-Density (GLD) Parity-Check codes, has been proposed recently. As a generalization of Gallager's Low-Density Parity-Check (LDPC) codes, GLD codes are also asymptotically good in the sense of minimum distance criterion and can be effectively decoded based on iterative soft-input soft-output (SISO) decoding of individual constituent codes. The code performance and decoding complexity of GLD code are heavily dependent on the employed SISO decoding algorithm. In this paper, we show that Max-Log-MAP is an attractive SISO decoding algorithm for GLD coding scheme, considering the trade-off between performance and complexity in the practical implementations. A normalized Max-Log-MAP is presented to improve the GLD code performance significantly compared with using conventional Max-Log-MAP. Moreover, we propose two techniques, decoding task scheduling and reduced search Max-Log-MAP, to effectively reduce the decoding complexity without any performance degradation.