On decoding product lattices

A product lattice is a high-dimensional lattice constructed using two lower dimensional lattices, in equivalence to binary product block codes constructed from two lower dimensional binary block codes. However, decoding methods typically used for binary product codes do not necessarily apply to product lattices. In this work several approaches for decoding product lattices are presented. In particular, bounded-distance decoding, which relies on the fact that all the rows and columns of the product lattice are points in the component lattices, is detailed. This property of product lattices enables one to efficiently decode the product lattice by employing separate decoders for the (much smaller dimensional) component lattices. Measures for the efficiency of these decoding methods are derived, and it is shown, also by means of computer simulation, that they are comparable to known decoding methods of lattices both in terms of effective coding gain and complexity.