Decoding by Embedding: Correct Decoding Radius and DMT Optimality

Cong Ling (1) , Shuiyin Liu (1) , Laura Luzzi (2) , Damien Stehlé (3)

1 DEEE - Department of Electrical and Electronic Engineering [London]
2 Chaire Radio Flexible - Chaire Radio Flexible Alcatel-Lucent/Supélec
3 Macquarie University

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. 1=(2 )- BDD is referred to as a decoder that finds the closest vector when the noise norm is smaller than 1=(2 ), where 1 is the minimum distance of the lattice. We prove that the Lenstra, Lenstra and Lov'asz (LLL) algorithm can achieve 1=(2 )-BDD for O(2n=4). This substantially improves the existing result = O(2n) for embedding decoding. We also prove that BDD of the regularized lattice is optimal in terms of the diversitymultiplexing gain tradeoff (DMT).

Domains: Information Theory [cs.IT]; Information Theory [math.IT]

Cong Ling, Shuiyin Liu, Laura Luzzi, Damien Stehlé. Decoding by Embedding: Correct Decoding Radius and DMT Optimality. IEEE International Symposium on Information Theory (ISIT'11), Jul 2011, Saint-Petersburg, Russia. 5 p. ⟨hal-00648134⟩