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首页> 外文期刊>Information Theory, IEEE Transactions on >Decoding by Embedding: Correct Decoding Radius and DMT Optimality
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Decoding by Embedding: Correct Decoding Radius and DMT Optimality

机译：嵌入解码：正确的解码半径和DMT最优性

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摘要

The closest vector problem (CVP) and shortest (nonzero) vector problem (SVP) are the core algorithmic problems on Euclidean lattices. They are central to the applications of lattices in many problems of communications and cryptography. Kannan's embedding technique is a powerful technique for solving the approximate CVP; yet, its remarkable practical performance is not well understood. In this paper, the embedding technique is analyzed from a bounded distance decoding (BDD) viewpoint. We present two complementary analyses of the embedding technique: we establish a reduction from BDD to Hermite SVP (via unique SVP), which can be used along with any Hermite SVP solver (including, among others, the Lenstra, Lenstra and Lovász (LLL) algorithm), and show that, in the special case of LLL, it performs at least as well as Babai's nearest plane algorithm (LLL-aided successive interference cancellation). The former analysis helps us to explain the folklore practical observation that unique SVP is easier than standard approximate SVP. It is proven that when the LLL algorithm is employed, the embedding technique can solve the CVP provided that the noise norm is smaller than a decoding radius $lambda_{1}/(2gamma)$ , where $lambda_{1}$ is the minimum distance of the lattice, and $gammaapprox O(2^{n/4})$. This substantially improves the previously best known correct decoding bound $gammaapprox{O}(2^{n})$ . Focusing on the applications of BDD to decoding of multiple-input multiple-output systems, we also prove that BDD of the regularized lattice is optimal in terms of the diversity–multiplexing gain tradeoff, and propose practical variants of embedding decoding which require no knowled- e of the minimum distance of the lattice and/or further improve the error performance.
机译：<？Pub Dtl？>最近的向量问题（CVP）和最短的（非零）向量问题（SVP）是欧几里得格上的核心算法问题。在许多通信和密码学问题中，它们对于晶格的应用至关重要。 Kannan的嵌入技术是解决近似CVP的强大技术。然而，其出色的实际性能尚未得到很好的理解。本文从有界距离解码（BDD）的角度分析了嵌入技术。我们对嵌入技术进行了两个补充分析：我们将BDD还原为Hermite SVP（通过唯一的SVP），可以将其与任何Hermite SVP求解器（包括Lenstra，Lenstra和Lovász（LLL）等一起使用）算法），并表明，在LLL的特殊情况下，它的性能至少与Babai最接近的平面算法（LLL辅助的连续干扰消除）相同。以前的分析帮助我们解释了民间传说的实践观察，即独特的SVP比标准的近似SVP更容易。已经证明，当采用LLL算法时，如果噪声范数小于解码半径，则嵌入技术可以解决CVP问题。<公式公式类型=“ inline”> $ lambda_ {1} /（2gamma）$ ，其中 $ lambda_ {1} $ 是格和 $ gammaapprox O（2 ^ {n / 4}）$ 。这大大改善了以前最著名的正确解码范围 $ gammaapprox {O}（2 ^ {n}）$ 。着眼于BDD在多输入多输出系统的解码中的应用，我们还证明了正则化格的BDD就分集复用增益的折衷而言是最佳的，并提出了不需要实际知识的嵌入解码的实际变体， e最小的晶格距离和/或进一步提高了误差性能。

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