On Convolutional Lattice Codes and Lattice Decoding Using Trellis Structure

Abstract

Constructing hypercubic lattices from convolutional codes based on Constructions A and D is investigated in this paper and their error performance in a point-to-point communication system is studied. Moreover, analogous to Construction A/D, single/multilayer code lattices are proposed. As Construction D requires certain minimum Euclidean distance criteria, we propose methods to guarantee the distance requirements of Construction D, which results in a superior lattice construction compared with Construction A. Due to the key role of soft input soft out decoding algorithms in improving the performance of a code, lattice decoding based on the Bahl, Cocke, Jelinek and Raviv (BCJR) algorithm for lattices constructed from convolutional codes is also proposed in this paper. Moreover, as the BCJR algorithm requires knowledge of the statistical characteristics of modulo lattice additive noise (MLAN), the probability density function of MLAN is derived in closed form.

Keywords

• Lattice encoding/decoding
• convolutional lattices
• BCJR lattice decoder
• construction A/D
• modulo-lattice additive noise