We consider the problem of finding the closest lattice point to a vector in n-dimensional Euclidean space when each component of the vector is available at a distinct node in a network. Our objectives are (i) minimize the communication cost and (ii) obtain the error probability. The approximate closest lattice point considered here is the one obtained using the nearest-plane (Babai) algorithm. Assuming a triangular special basis for the lattice, we develop communication-efficient protocols for computing the approximate lattice point and determine the communication cost for lattices of dimension n>1. Based on available parameterizations of reduced bases, we determine the error probability of the nearest plane algorithm for two dimensional lattices analytically, and present a computational error estimation algorithm in three dimensions. For dimensions 2 and 3, our results show that the error probability increases with the packing density of the lattice.
One way to find closest pairs in large datasets is to use hash functions. In recent years locality-sensitive hash functions for various metrics have been given: projecting an n-cube onto k bits is simple hash function that performs well. In this paper we investigate alternatives to projection. For various parameters hash functions given by complete decoding algorithms for codes work better, and asymptotically random codes perform better than projection.
We consider the closest lattice point problem in a distributed network setting and study the communication cost and the error probability for computing an approximate nearest lattice point, using the nearest-plane algorithm, due to Babai. Two distinct communication models, centralized and interactive, are considered. The importance of proper basis selection is addressed. Assuming a reduced basis for a two-dimensional lattice, we determine the approximation error of the nearest plane algorithm. The communication cost for determining the Babai point, or equivalently, for constructing the rectang…
A novel detector for multiple-input multiple-output (MIMO) communications is presented. The algorithm belongs to the class of the lattice detectors, i.e. it finds a reduced complexity solution to the problem of finding the closest vector to the received observations. The algorithm achieves optimal maximum-likelihood (ML) performance in case of two transmit antennas, at the same time keeping a complexity much lower than the exhaustive search-based ML detection technique. Also, differently from the state-of-art lattice detector (namely sphere decoder), the proposed algorithm is suitable for a hi…
In this project, the behavior of Generalized Approximate Message-Passing Decoder for BSC and Z Channel is studied using i.i.d matrices for constructing the codewords. The performance of GAMP in AWGN Channel is already evaluated in the previous scientific work of Jean Barbier, therefore, this project mainly focuses on the performance of GAMP decoder for BSC and Z Channel. We evaluate the performance of the GAMP decoder for sparse superposition codes at various settings and compare the performance of decoder for different channels and parameters.
We consider an energy-harvesting communication system where a transmitter powered by an exogenous energy arrival process and equipped with a finite battery of size $B_{max}$ communicates over a discrete-time AWGN channel. We first concentrate on a simple Bernoulli energy arrival process where at each time step, either an energy packet of size $E$ is harvested with probability $p$, or no energy is harvested at all, independent of the other time steps. We provide a near optimal energy control policy and a simple approximation to the information-theoretic capacity of this channel. Our approximati…
Lattice precoding is an effective strategy for multiantenna broadcast. In this paper, we show that approximate lattice precoding in multiantenna broadcast is a variant of the closest vector problem (CVP) known as $η$-CVP. The proximity factors of lattice reduction-aided precoding are defined, and their bounds are derived, which measure the worst-case loss in power efficiency compared to sphere precoding. Unlike decoding applications, this analysis does not suffer from the boundary effect of a finite constellation, since the underlying lattice in multiantenna broadcast is indeed infinite.
Reconfigurable intelligent surfaces (RISs) have been recently considered as a promising candidate for energy-efficient solutions in future wireless networks. Their dynamic and lowpower configuration enables coverage extension, massive connectivity, and low-latency communications. Due to a large number of unknown variables referring to the RIS unit elements and the transmitted signals, channel estimation and signal recovery in RIS-based systems are the ones of the most critical technical challenges. To address this problem, we focus on the RIS-assisted multi-user wireless communication system a…
In this paper, a communication-efficient multi-processor compressed sensing framework based on the approximate message passing algorithm is proposed. We perform lossy compression on the data being communicated between processors, resulting in a reduction in communication costs with a minor degradation in recovery quality. In the proposed framework, a new state evolution formulation takes the quantization error into account, and analytically determines the coding rate required in each iteration. Two approaches for allocating the coding rate, an online back-tracking heuristic and an optimal allo…
We derive new expressions for the connection probability and the average ergodic capacity to evaluate the performance achieved by multi-connectivity (MC) in an indoor ultra-wideband terahertz (THz) communication system. In this system, the user is affected by both self-blockage and dynamic human blockers. We first build up a three-dimensional propagation channel in this system to characterize the impact of molecular absorption loss and the shrinking usable bandwidth nature of the ultra-wideband THz channel. We then carry out new performance analysis for two MC strategies: 1) Closest line-of-si…
One of the main challenges in diffusion-based molecular communication is dealing with the non-linearity of reaction-diffusion chemical equations. While numerical methods can be used to solve these equations, a change in the input signals or the parameters of the medium requires one to redo the simulations. This makes it difficult to design modulation schemes and practically impossible to prove the optimality of a given transmission strategy. In this paper, we provide an analytical technique for modeling the non-linearity of chemical reaction equations based on the perturbation method. The pert…
Exact analytical channel models for molecular communication via diffusion (MCvD) systems involving multiple fully absorbing receivers (FARs) in a three-dimensional (3- D) medium are hard to obtain due to the mathematical intractability of corresponding diffusion equations. This work, therefore, consider an MCvD system with two spherical FARs in a 3-D diffusion-limited medium and develop several insights using an approximate analytical expression for the hitting probability of information molecule (IM). Further, based on the hitting probability, a novel approximate closed-form analytical expres…
Reconfigurable intelligent surface (RIS) is very promising for wireless networks to achieve high energy efficiency, extended coverage, improved capacity, massive connectivity, etc. To unleash the full potentials of RIS-aided communications, acquiring accurate channel state information is crucial, which however is very challenging. For RIS-aided multiple-input and multiple-output (MIMO) communications, the existing channel estimation methods have computational complexity growing rapidly with the number of RIS units $N$ (e.g., in the order of $N^2$ or $N^3$) and/or have special requirements on t…
This paper analyzes the secrecy performance of a reconfigurable intelligent surface (RIS) assisted wireless communication system with a friendly jammer in the presence of an eavesdropper. The friendly jammer enhances the secrecy by introducing artificial noise towards the eavesdropper without degrading the reception at the destination. Approximate secrecy outage probability (SOP) is derived in closed form. We also provide a simpler approximate closed-form expression for the SOP in order to understand the effect of system parameters on the performance and to find the optimal power allocation fo…
In this paper, an efficient distributed approach for implementing the approximate message passing (AMP) algorithm, named distributed AMP (DAMP), is developed for compressed sensing (CS) recovery in sensor networks with the sparsity K unknown. In the proposed DAMP, distributed sensors do not have to use or know the entire global sensing matrix, and the burden of computation and storage for each sensor is reduced. To reduce communications among the sensors, a new data query algorithm, called global computation for AMP (GCAMP), is proposed. The proposed GCAMP based DAMP approach has exactly the s…
When computing systems can tolerate the effects of errors or erasures in their communicated data values, they can trade this tolerance for improved resource efficiency. One method for enabling this tradeoff in the I/O subsystems of computing systems, is to use channel codes that reduce the power needed to send bits on a channel in exchange for bounded errors and erasures on numeric program values---value-deviation-bounded (VDB) codes. Unlike rate distortion codes, which guarantee a bound on the expected value of channel distortion, the probabilistic VDB codes we present guarantee any desired t…
