- 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. 2013 IEEE.