Connectivity of cycles constrained Root-LDPC codes for block fading channels

The construction and performance of full diversity Root-LDPC codes for block fading channels are the hot spot at present. There are two important factors, the girth and the cycles connectivity, can affect the frame error rate performance of Root-LDPC codes. The original PEG algorithm is an effective method to provide longer girth of cycles, but ignores the cycles connectivity. The contribution of this paper is to present two algorithms to design Root-LDPC codes for block fading channels. The first algorithm is the modified PEG algorithm (MPEG). We apply the Approximated Cycle Extrinsic Message Degree (ACE) metric, which is used to measure the cycles connectivity, to modify the traditional PEG algorithm to ensure having lower frame error rate. However, MPEG algorithm is one of the greedy algorithms. With the increase of code length, the encoding/decoding complexity of MPEG algorithm will enhance. Meanwhile the QC algorithm has low complexity because of its quasi cyclic feature. Then we combine the modified PEG algorithm with QC algorithm, which guarantees not only the code performance but also the quasi cyclic feature. The novel algorithm achieves a tradeoff between the frame error rate performance and the encoding/decoding complexity, so that it is more suitable for the practical application. Simulation results demonstrate that the algorithms we proposed can achieve full diversity and make the average required number of iterations decrease from medium to high SNR, suitable to different fading blocks.