Closest point search in lattices using sequential decoding

Abstract

The problem of finding the closest lattice point arises in several communication problems, and is known to be NP-hard. Existing methods to solve the problem are based on the sphere decoder, which searches for all the lattice points in a sphere around the received point. The sphere decoder is general and does not exploit the noise properties of the communication channel. In this paper we suggest to use sequential decoding algorithms for this problem. In particular, we propose an algorithm based on the well known Fano algorithm that naturally exploits the noise structure, hence offers a significant complexity reduction with respect to the sphere decoder with only a small penalty in error performance. Two further improvements are suggested. The first is bidirectional stack decoding, where the stack is implemented using a heap data structure to avoid sorting. The second is interleaved decoding, where the possibility to choose an arbitrary search order along the lattice coordinates is used to interleave noise bursts at the receiver. Finally, a lower bound is found for the computational cutoff rate of sequential lattice decoding