On The Limitations of The Naive Lattice Decoding

TL;DR

This paper critically examines the limitations of naive lattice decoding in MIMO systems, revealing significant deficiencies in achieving optimal rate-diversity trade-offs and providing bounds on error probability.

Contribution

It demonstrates that naive lattice decoding cannot attain the optimal rate-diversity trade-off even with perfect codes and establishes a lower bound on error probability, highlighting its suboptimality.

Findings

Naive lattice decoding has significant rate-diversity trade-off deficiencies.

Even with perfect lattice codes, naive decoding cannot achieve optimal trade-offs.

A lower bound on error probability shows unbounded SNR loss compared to ML decoding.

Abstract

In this paper, the inherent drawbacks of the naive lattice decoding for MIMO fading systems is investigated. We show that using the naive lattice decoding for MIMO systems has considerable deficiencies in terms of the rate-diversity trade-off. Unlike the case of maximum-likelihood decoding, in this case, even the perfect lattice space-time codes which have the non-vanishing determinant property can not achieve the optimal rate-diversity trade-off. Indeed, we show that in the case of naive lattice decoding, when we fix the underlying lattice, all the codes based on full-rate lattices have the same rate-diversity trade-off as V-BLAST. Also, we drive a lower bound on the symbol error probability of the naive lattice decoding for the fixed-rate MIMO systems (with equal numbers of receive and transmit antennas). This bound shows that asymptotically, the naive lattice decoding has an unbounded loss in terms of the required SNR, compared to the maximum likelihood decoding.