Related papers: A Lattice-Theoretic Characterization of Optimal Mi…
Lattices are deceptively simple mathematical structures that have become indispensable for code design for physical layer communications. While lattice-related problems are interesting in their own right, the usefulness of these discrete…
Low density lattice codes (LDLC) are a family of lattice codes that can be decoded efficiently using a message-passing algorithm. In the original LDLC decoder, the message exchanged between variable nodes and check nodes are continuous…
In this paper we show that any sequence of infinite lattice constellations which is good for the unconstrained Gaussian channel can be shaped into a capacity-achieving sequence of codes for the power-constrained Gaussian channel under…
A lattice quantizer approximates an arbitrary real-valued source vector with a vector taken from a specific discrete lattice. The quantization error is the difference between the source vector and the lattice vector. In a classic 1996…
In this paper we investigate the optimal latency of communications. Focusing on fixed rate communication without any feedback channel, this paper encompasses low-latency strategies with which one hop and multi-hop communication issues are…
In Index coding there is a single sender with multiple messages and multiple receivers each wanting a different set of messages and knowing a different set of messages a priori. The Index Coding problem is to identify the minimum number of…
The Erd\H{o}s distance problem concerns the least number of distinct distances that can be determined by $N$ points in the plane. The integer lattice with $N$ points is known as \textit{near-optimal}, as it spans $\Theta(N/\sqrt{\log(N)})$…
Lattice codes with optimal decoding coefficient are capacity-achieving when dimension $N \rightarrow \infty$. In communications systems, finite dimensional lattice codes are considered, where the optimal decoding coefficients may still fail…
In this paper, we propose a new class of lattices constructed from polar codes, namely polar lattices, to achieve the capacity $\frac{1}{2}\log(1+\SNR)$ of the additive white Gaussian-noise (AWGN) channel. Our construction follows the…
A novel technique to optimize the input distribution and compute a lower bound for the capacity of the nonlinear optical fiber channel is proposed. The technique improves previous bounds obtained with the additive white Gaussian noise…
Polar lattices, which are constructed from polar codes, have recently been proved to be able to achieve the capacity of the additive white Gaussian noise (AWGN) channel. In this work, we propose a new construction of polar lattices to solve…
In this paper we are concerned with three lattice problems: the lattice packing problem, the lattice covering problem and the lattice packing-covering problem. One way to find optimal lattices for these problems is to enumerate all finitely…
In this article we revisit smoothing bounds in parallel between lattices $and$ codes. Initially introduced by Micciancio and Regev, these bounds were instantiated with Gaussian distributions and were crucial for arguing the security of many…
In this paper, we propose the explicit construction of a new class of lattices based on polar codes, which are provably good for the additive white Gaussian noise (AWGN) channel. We follow the multilevel construction of Forney \textit{et…
In this paper, we investigate the design of linear precoders for the multiple-input multiple-output (MIMO) multiple access channel (MAC). We assume that statistical channel state information (CSI) is available at the transmitters and…
The design of the precoder the maximizes the mutual information in linear vector Gaussian channels with an arbitrary input distribution is studied. Precisely, the precoder optimal left singular vectors and singular values are derived. The…
It is well-known that the densest lattice sphere packings also typically have large kissing numbers. The sphere packing density maximization problem is known to have a solution among well-rounded lattices, of which the integer lattice…
Linear-assignment Gel'fand-Pinsker coding (LA-GPC) is a coding technique for channels with interference known only at the transmitter, where the known interference is treated as side-information (SI). As a special case of LA-GPC, dirty…
Lattices are important as models for the node locations in wireless networks for two main reasons: (1) When network designers have control over the placement of the nodes, they often prefer a regular arrangement in a lattice for coverage…
Linear codes play a central role in coding theory and have applications in several branches of mathematics. For error correction purposes the minimum Hamming distance should be as large as possible. Linear codes related to applications in…