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 \emph{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 \emph{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 SIC). The former analysis helps 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 $λ_1/(2γ)$, where $λ_1$ is the minimum distance of the lattice, and $γ\approx O(2^{n/4})$. This substantially improves the previously best known correct decoding bound $γ\approx {O}(2^{n})$. Focusing on the applications of BDD to decoding of multiple-input multiple-output (MIMO) systems, we also prove that BDD of the regularized lattice is optimal in terms of the diversity-multiplexing gain tradeoff (DMT), and propose practical variants of embedding decoding which require no knowledge of the minimum distance of the lattice and/or further improve the error performance.
LR-aided MMSE lattice decoding is DMT optimal for all approximately universal codes
目前对于nt × nr MIMO信道，已知实现关于分集复用折衷（DMT）的最优性的任何显式构造的空时（ST）设计仅在使用最大似然（ML）解码进行解码时才这样做，这可能导致过高的解码复杂度。在本文中，我们证明了MMSE正则化格解码，以及计算高效的格约简（LR）辅助MMSE解码器，允许有效的和DMT最佳解码的任何近似通用的基于格的代码。该结果首次确定了一个明确构造的编码器和一个计算效率高的解码器，实现DMT最优的所有复用增益和所有信道尺寸。无论衰落的统计结果。
On the achievable diversity-multiplexing tradeoff in interference channels
分析了具有理想接收信道状态信息和无发射信道状态信息的两用户单天线衰落干扰信道。对于非常强的干扰的情况，我们证明了解码干扰，同时将预期信号视为噪声，减去结果，然后解码期望信号，这一过程称为“剥离”，实现了在Akuiyibo和Leveque，Int.Zurich Seminar on Commun.，2008.证明是建设性的意义上说，它提供了相应的代码设计准则DMT最优。对于一般的干扰水平，我们计算的DMT的固定功率分裂韩和小林型叠加编码方案，提供相应的叠加码的设计标准，并发现，该方案是DMT最优的某些复用速率。
A Local Tree Structure is NOT Sufficient for the Local Optimality of Message-Passing Decoding in Low Density Parity Check Codes
我们解决的问题，“是一个局部树结构足够的局部最优性的消息传递算法在低密度奇偶检验码？结果表明，答案是否定的。利用这一观察，我们指出了Thomas J. Richardson和Rüdiger L.Urbanke \cite{RUCapacity}的论文“消息传递解码下低密度奇偶校验码的容量”中定理1证明的一个缺陷。我们进一步提供了一个新的证明该定理的基础上不同的论点。
