Efficient Decoding of Low Density Lattice Codes

Abstract

This letter describes a low complexity belief propagation decoder for low density lattice codes (LDLC). Compared with the fastest decoder in the literature, the memory usage and computational complexity at each variable node is reduced from O(2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</sup> ) to O(d), where d is the degree of LDLC. The cost at each check node remains at O(d). The key idea is to compute each variable message based on 2d - 2 Gaussian functions, rather than 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d-1</sup> Gaussian functions in the previous decoders. A novel convergence analysis is given for Gaussian approximation (GA)-based LDLC decoders. Simulation results confirm that the proposed decoder can lower the error floor of the fastest GA-based decoder.