Decoding by Embedding: Correct Decoding Radius and DMT Optimality

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. 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).
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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⟩

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