Decoding by Embedding: Correct Decoding Radius and DMT Optimality

—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 Lov´asz (LLL) algorithm can achieve 1/(2γ)-BDD for γ ≈ O(2n/4 ), yielding a polynomialcomplexity decoding algorithm performing exponentially better than Babai’s which achieves γ = O(2n/2 ). This substantially improves the existing result γ = O(2n ) for embedding decoding. We also prove that BDD of the regularized lattice is optimal in terms of the diversity-multiplexing gain tradeoff (DMT).

• Type: Journal
• Year: 2011
• Where: CORR
• Authors: Cong Ling, Shuiyin Liu, Laura Luzzi, Damien Stehlé
• Keywords: Closest Vector Problem, CORR 2011, Education, Embedding, Optimal Decoding Amounts