Iterative encoding with Gauss-Seidel method for spatially-coupled low-density lattice codes

While it is known that spatially-coupled low-density lattice codes (SC-LDLC) have better decoding performance than conventional (non-coupled) LDLC lattices, in this paper it is shown that their encoding complexity is also lower. Since nonzero elements are mainly in lower triangular entries of the sparse inverse generator matrix of SC-LDLC, iterative encoding with the Gauss-Seidel method performs well. The convergence speed of iterative encoding is evaluated by both the mean square error (MSE) and the symbol error rate between a given integer vector b and the inversely generated integer vector from the codeword of b. Numerical experiments show that the convergence of encoding for SC-LDLC is 3 times faster than that of the conventional LDLC, at an MSE of 10^-10 for dimension n = 10000.