Related papers: A Lattice-Theoretic Characterization of Optimal Mi…
The so-called "replica method" of statistical physics is employed for the large system analysis of vector precoding for the Gaussian multiple-input multiple-output (MIMO) broadcast channel. The transmitter is assumed to comprise a linear…
The nearest lattice point problem in $\mathbb{R}^n$ is formulated in a distributed network with $n$ nodes. The objective is to minimize the probability that an incorrect lattice point is found, subject to a constraint on inter-node…
Lattice reduction (LR) aided multiple-input-multiple-out (MIMO) linear detection can achieve the maximum receive diversity of the maximum likelihood detection (MLD). By emloying the most commonly used Lenstra, Lenstra, and L. Lovasz (LLL)…
In this paper, we propose a new approach to proving results regarding channel coding schemes based on construction-A lattices for the Additive White Gaussian Noise (AWGN) channel that yields new characterizations of the code construction…
In this paper, the problem of designing a linear precoder for Multiple-Input Multiple-Output (MIMO) systems in conjunction with Quadrature Amplitude Modulation (QAM) is addressed. First, a novel and efficient methodology to evaluate the…
It is shown why the discriminant of a maximal order within a cyclic division algebra must be minimized in order to get the densest possible matrix lattices with a prescribed nonvanishing minimum determinant. Using results from class field…
Lattice-linearity was introduced as a way to model problems using predicates that induce a lattice among the global states (Garg, SPAA 2020). A key property of \textit{the predicate} representing such problems is that it induces…
A lattice of integers is the collection of all linear combinations of a set of vectors for which all entries of the vectors are integers and all coefficients in the linear combinations are also integers. Lattice reduction refers to the…
We construct explicit rate-one, full-diversity, geometrically dense matrix lattices with large, non-vanishing determinants (NVD) for four transmit antenna multiple-input single-output (MISO) space-time (ST) applications. The constructions…
We propose a new method to construct maximin distance designs with arbitrary number of dimensions and points. The proposed designs hold interleaved-layer structures and are by far the best maximin distance designs in four or more…
This work focuses on distributed linear precoding when users transmit correlated information over a fading Multiple-Input and Multiple-Output Multiple Access Channel. Precoders are optimized in order to minimize the sum-Mean Square Error…
In this paper, the design of robust linear precoders for the massive multi-input multi-output (MIMO) downlink with imperfect channel state information (CSI) is investigated. The imperfect CSI for each UE obtained at the BS is modeled as…
In this paper, we investigate the optimal precoding scheme for relay networks with finite-alphabet constraints. We show that the previous work utilizing various design criteria to maximize either the diversity order or the transmission rate…
Lattices and partially ordered sets have played an increasingly important role in coding theory, providing combinatorial frameworks for studying structural and algebraic properties of error-correcting codes. Motivated by recent works…
The design of lattice coset codes for wiretap channels is considered. Bounds on the eavesdropper's correct decoding probability and information leakage are first revisited. From these bounds, it is explicit that both the information leakage…
Discrete barycenters are the optimal solutions to mass transport problems for a set of discrete measures. Such transport problems arise in many applications of operations research and statistics. The best known algorithms for exact…
Optimal physical layer multicasting (PLM) is an NP-hard problem that for simplicity has been studied under idealistic assumptions, e.g., availability of perfect channel state information (CSI), both at the base station (BS) and at the user…
In this work, we investigate the simultaneous goodness of polar codes and polar lattices. The simultaneous goodness of a lattice or a code means that it is optimal for both channel coding and source coding simultaneously. The existence of…
The work identifies the first general, explicit, and non-random MIMO encoder-decoder structures that guarantee optimality with respect to the diversity-multiplexing tradeoff (DMT), without employing a computationally expensive…
Motivated by linear network coding, communication channels perform linear operation over finite fields, namely linear operator channels (LOCs), are studied in this paper. For such a channel, its output vector is a linear transform of its…