FFT Based Sum-Product Algorithm for Decoding LDPC Lattices

LDPC lattices were introduced by Sadeghi et al. in [13] and have a good performance under generalized minsum and sum-product algorithms. The high complexity of these algorithms is mainly due to the search for local valid codewords in each check node process. In addition, when the dimension of such lattices is increased, these decoding algorithms are very time-consuming. In this paper, we propose an FFT based sum-product algorithm to decode LDPC lattices. In the check node process, using the FFT method reduces the check node complexity from O(d_cg²) to O(d_cg log g) where d_c is the degree of a check equation and g is the alphabet size of an LDPC lattice. As a result, with almost the same complexity cost, we have a significant improvement over the performance of the minsum based decoding 2-level LDPC lattices with the symbol error probability smaller than 10^-5 at SNR = 1.5 dB.