Constructing convolutional lattices and its application in Compute and Forward

Constructing lattices from convolutional codes based on Construction A is studied; analogous to Construction A, a single layer code lattice is proposed in this paper which outperforms Construction A. As an application for the proposed convolutional lattices, they are exploited in a multi-user relay network where the relay node employs Compute and Forward as its relaying function. We adopt the BCJR algorithm for lattice decoding convoutional lattices; moreover, as the BCJR algorithm requires the knowledge of the statistical characteristics of modulo lattice additive noise (MLAN), the probability density function of MLAN is derived in closed form.