Decoding by Embedding: Correct Decoding Radius and DMT Optimality

Details Decoding by Embedding: Correct Decoding Radius and DMT Optimality Decoding by Embedding: Correct Decoding Radius and DMT Optimality

2011-02-15

arxiv.org/abs/1102.2936v2

Computer Science

Information Theory

5 pages, 1 figure, conference

Scientific paper

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. $1/(2\gamma)$-BDD is referred to as a decoder that finds the closest vector when the noise norm is smaller than $\lambda_1/(2\gamma)$, where $\lambda_1$ is the minimum distance of the lattice. We prove that the Lenstra, Lenstra and Lov\'asz (LLL) algorithm can achieve $1/(2\gamma)$-BDD for $\gamma \approx O(2^{n/4})$. 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).

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