New results on Construction A Lattices based on Very Sparse Parity-Check Matrices
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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.
author list (cited authors)
di Pietro, N., Zémor, G., & Boutros, J. J.