# Decoding by Embedding: Correct Decoding Radius and DMT
Optimality

### Laura Luzzi, Shuiyin Liu, Cong Ling and Damien Stehlé

Abstract: In lattice-coded multiple-input multiple-output (MIMO)
systems, optimal decoding amounts to solving the closest vector
problem (CVP). Embedding is a powerful technique for the approximate
CVP, yet its remarkable performance is not well understood. In this
paper, we analyze the embedding technique from a bounded distance
decoding (BDD) viewpoint. We prove that the Lenstra, Lenstra and
Lovász (LLL) algorithm can achieve 1/(2gamma) -BDD for gamma \approx
O(2^(n/4)), yielding a polynomial-complexity decoding
algorithm performing exponentially better than Babai's which achieves
gamma = O(2^(n/2)). This substantially improves the existing result
gamma = O(2^(n)) for embedding decoding. We also prove that BDD of
the regularized lattice is optimal in terms of the
diversity-multiplexing gain tradeoff (DMT).
Download: pdf.

Homepage