Information Theory (cs.IT)

Abstract: In this paper, we investigate the achievable rate of a diffusive Molecular Communication (MC) channel with fully absorbing receiver, which counts particles absorbed along each symbol interval and resets the counter at every interval (reset-counting). The MC channel is affected by a memory effect and thus inter-symbol interference (ISI), due to the delayed arrival of molecules. To reduce complexity, our analysis is based on measuring the channel memory as an integer number of symbol intervals and on a single-sample memoryless detector. Thus, in our model the effect of released particles remains effective for a limited number of symbol intervals. We optimize the detector threshold for maximizing capacity, approximate as Gaussian the received signal distribution, and calculate the channel mutual information affected by ISI, in the case of binary concentration shift keying modulation. To the best of our knowledge, in literature there are no previous investigations on the achievable rate in this type of system. Our results demonstrate that, in general, the optimal input probability distribution achieving the maximum achievable rate may be not uniform. In particular, when the symbol interval is small (strong ISI), the maximum achievable rate does not occur with equiprobable transmission of bits.

Abstract: Utilizing low-resolution analog-to-digital converters (ADCs) in uplink massive multiple-input multiple-output (MIMO) systems is a practical solution to decrease power consumption. The performance gap between the low and high-resolution systems is small at low signal-to-noise ratio (SNR) regimes. However, at high SNR and with high modulation orders, the achievable rate saturates after a finite SNR value due to the stochastic resonance (SR) phenomenon. This paper proposes a novel pseudo-random quantization (PRQ) scheme by modifying the quantization thresholds that can help compensate for the effects of SR and makes communication with high-order modulation schemes such as $1024$-QAM in one-bit quantized uplink massive MIMO systems possible. Moreover, modified linear detectors for non-zero threshold quantization are derived, and a two-stage uplink detector for single-carrier (SC) multi-user systems is proposed. The first stage is an iterative method called Boxed Newton Detector (BND) that utilizes Newton's Method to maximize the log-likelihood with box constraints. The second stage, Nearest Codeword Detector (NCD), exploits the first stage solution and creates a small set of most likely candidates based on sign constraints to increase detection performance. The proposed two-stage method with PRQ outperforms the state-of-the-art detectors from the literature with comparable complexity while supporting high-order modulation schemes.

Abstract: In this letter, we study the channel estimation for wireless communications with movable antenna (MA), which requires to reconstruct the channel response at any location in a given region where the transmitter/receiver is located based on the channel measurements taken at finite locations therein, so as to find the MA's location for optimizing the communication performance. To reduce the pilot overhead and computational complexity for channel estimation, we propose a new successive transmitter-receiver compressed sensing (STRCS) method by exploiting the efficient representation of the channel responses in the given transmitter/receiver region (field) in terms of multi-path components. Specifically, the field-response information (FRI) in the angular domain, including the angles of departure (AoDs)/angles of arrival (AoAs) and complex coefficients of all significant multi-path components are sequentially estimated based on a finite number of channel measurements taken at random/selected locations by the MA at the transmitter and/or receiver. Simulation results demonstrate that the proposed channel reconstruction method outperforms the benchmark schemes in terms of both pilot overhead and channel reconstruction accuracy.

Abstract: Using low-resolution analog-to-digital converters (ADCs) is a valuable solution to decrease power consumption and cost in massive MIMO systems. Previous studies show that the performance gap between low and high-resolution systems gets more prominent as the signal-to-noise ratio (SNR) increases since the detection performance starts to saturate at some point due to the stochastic resonance (SR) phenomenon. In our previous work, we proposed new quantization and detection schemes for one-bit massive MIMO systems operating under frequency-flat fading. This paper offers a new frequency domain equalization (FDE) scheme that can work with the previously proposed pseudo-random quantization (PRQ) scheme to mitigate the effects of SR to support high-order modulation schemes such as $64$-QAM and $256$-QAM. Our equalizer is based on a projected quasi-Newton method for one-bit uplink massive MIMO systems applicable for orthogonal frequency division multiplexing (OFDM) and single carrier (SC) transmission under frequency-selective fading. The proposed low-complexity detector can outperform the benchmark detector from the literature with very similar complexity. We analyze the effects of PRQ under frequency-selective fading for different scenarios and show that the PRQ scheme can close the performance gap between SC and OFDM systems by simulations.

Abstract: In this paper we address the problem of decoding linearized Reed-Solomon (LRS) codes beyond their unique decoding radius. We analyze the complexity in order to evaluate if the considered problem is of cryptographic relevance, i.e., can be used to design cryptosystems that are computationally hard to break. We show that our proposed algorithm improves over other generic algorithms that do not take into account the underlying code structure.

Abstract: The Blahut-Arimoto algorithm is a well known method to compute classical channel capacities and rate-distortion functions. Recent works have extended this algorithm to compute various quantum analogs of these quantities. In this paper, we show how these Blahut-Arimoto algorithms are special instances of mirror descent, which is a well-studied generalization of gradient descent for constrained convex optimization. Using new convex analysis tools, we show how relative smoothness and strong convexity analysis recovers known sublinear and linear convergence rates for Blahut-Arimoto algorithms. This mirror descent viewpoint allows us to derive related algorithms with similar convergence guarantees to solve problems in information theory for which Blahut-Arimoto-type algorithms are not directly applicable. We apply this framework to compute energy-constrained classical and quantum channel capacities, classical and quantum rate-distortion functions, and approximations of the relative entropy of entanglement, all with provable convergence guarantees.

Abstract: In this paper, we study a secure integrated sensing and communication (ISAC) system where one multi-antenna base station (BS) simultaneously serves a downlink communication user and senses the location of a target that may potentially serve as an eavesdropper via its reflected echo signals. Specifically, the location information of the target is unknown and random, while its a priori distribution is available for exploitation. First, to characterize the sensing performance, we derive the posterior Cram\'er-Rao bound (PCRB) which is a lower bound of the mean squared error (MSE) for target sensing exploiting prior distribution. Due to the intractability of the PCRB expression, we further derive a novel approximate upper bound of it which has a closed-form expression. Next, under an artificial noise (AN) based beamforming structure at the BS to alleviate information eavesdropping and enhance the target's reflected signal power for sensing, we formulate a transmit beamforming optimization problem to maximize the worst-case secrecy rate among all possible target (eavesdropper) locations, under a sensing accuracy threshold characterized by an upper bound on the PCRB. Despite the non-convexity of the formulated problem, we propose a two-stage approach to obtain its optimal solution by leveraging the semi-definite relaxation (SDR) technique. Numerical results validate the effectiveness of our proposed transmit beamforming design and demonstrate the non-trivial trade-off between secrecy performance and sensing performance in secure ISAC systems.

Abstract: We consider a statistical model for matrix factorization in a regime where the rank of the two hidden matrix factors grows linearly with their dimension and their product is corrupted by additive noise. Despite various approaches, statistical and algorithmic limits of such problems have remained elusive. We study a Bayesian setting with the assumptions that (a) one of the matrix factors is symmetric, (b) both factors as well as the additive noise have rotational invariant priors, (c) the priors are known to the statistician. We derive analytical formulas for Rotation Invariant Estimators to reconstruct the two matrix factors, and conjecture that these are optimal in the large-dimension limit, in the sense that they minimize the average mean-square-error. We provide numerical checks which confirm the optimality conjecture when confronted to Oracle Estimators which are optimal by definition, but involve the ground-truth. Our derivation relies on a combination of tools, namely random matrix theory transforms, spherical integral formulas, and the replica method from statistical mechanics.