New results on Construction A lattices based on very sparse parity-check matrices

We address the problem of transmission of information over the AWGN channel using lattices. In particular, we will deal with previously introduced LDA lattices which are obtained by Construction A from LDPC codes over the finite field F_p. We will show how to build a particular ensemble of LDA lattices related to bipartite graphs with good expansion properties. We investigate the quality of this family under lattice decoding and show that a random member in it can be reliably decoded for any value of the channel noise variance up to Poltyrev limit. Values of p and the parameters for which optimal performance is guaranteed under lattice decoding are in accordance with the optimal parameters found experimentally under iterative decoding.