Decoding and Convergence Analysis for Distributed Low Density Lattice Codes
Xuebo Wang, Wai Ho Mow · 2021
Distributed low density lattice codes (D-LDLCs) have been proposed for application in cooperative communication networks. D-LDLCs are able to achieve a higher coding gain than LDLCs under the same code length and transmission power. However, an efficient decoder for D-LDLCs is still lacking. The state-of-the-art message passing decoder for LDLCs can be extended to decode D-LDLCs, but its complexity analysis requires an asymptotic characterization of the decoding behavior in terms of the convergence of the message variances. In this paper, we prove that as the number of iterations tends to infinity, the message variances converge to some constants determined by the code parameters of D-LDLCs. Based on the convergence analysis of message variances, we can further show that the extended decoder achieves linear complexity with respect to the column degree of the D-LDLC check matrix.