In this paper, we explore the fine-grained channel state information (CSI) obtained through the sensing function in an reconfigurable intelligent surface (RIS)-assisted integrated sensing and communication (ISAC) system to support the efficient covert communications in the system. We first construct a new fine-grained CSI model for the RIS-assisted ISAC system and propose a novel covert communication scheme based on the new CSI model. We then develop theoretical models for the detection error probability, Cramér-Rao Bound and covert rate to depict the covertness, sensing and covert communication performances under the proposed scheme. Based on these theoretical models, we further formulate an optimization problem for covert rate maximization through optimizing the reflection coefficient in RIS and the transmit powers for covert/probing signals. With the help of the homogenization for quadratic constrained quadratic programming, semi-definite relaxation and Dinkelbach transform, an efficient alternating optimization (AO) algorithm is devised to tackle this complex optimization problem. Finally, extensive numerical results are presented to demonstrate the performance enhancement for covert communication in the RIS-assisted ISAC system from exploring the fine-grained CSI and AO-based parameter optimization therein.

In this paper, we design the wideband hybrid-analog-digital (HAD) beamforming for integrated sensing and communication (ISAC) systems. Specifically, we incorporate the phase shifters (PSs) and true-time delay lines (TTDs) to combat the wideband beam squint effect, which are able to provide frequency-dependent phase shift in the analog beamforming stage. The fully-digital (FD) beamformers with guaranteed sensing and communication signal-to-interference-plus-noise ratios (SINRs) are first designed. Then, the HAD beamforming is formulated as a least squares (LS) problem to approximate the designed FD beamformers with constant-modulus constraints, whose main challenges are the complicated objective function and the non-convex constraints. To tackle these issues, we majorize the objective function to decouple the optimization variables. Then, the beamformer for PSs can be solved with a closed-form solution, whereas the beamformer for TTDs can be obtained by a simple grid-search. Finally, we adjust the PS and TTD beamformers by the Riemannian conjugate gradient method (RCGM) to improve the performance. Simulation results demonstrate the superior performance of the proposed algorithm over the conventional algorithm.

In this paper, we propose a novel function named Rate Distortion-in-Distortion (RDD) function as an extension of the classical rate-distortion (RD) function, where the expected distortion constraint is replaced by a Gromov-type distortion. This distortion, integral to the Gromov-Wasserstein (GW) distance, effectively defines the similarity in spaces of possibly different dimensions even without a direct metric between them. While the RDD function qualifies as an informational RD function, encoding theorems substantiate its status as an operational RD function, thereby underscoring its potential applicability in real-world source coding. Due to the high computational complexity associated with Gromov-type distortion, in general, the RDD function cannot be evaluated analytically. Consequently, we develop an alternating mirror descent algorithm that significantly reduces computational complexity by employing decomposition, linearization, and relaxation techniques. Numerical results on classical sources and different grids demonstrate the effectiveness of the developed algorithm. By exploring the relationship between the RDD function and the RD function, we suggest that the RDD function may have potential applications in future scenarios.

We consider the computation of the entanglement-assisted quantum rate-distortion function, which plays a central role in quantum information theory. We propose an efficient alternating minimization algorithm based on the Lagrangian analysis. Instead of fixing the multiplier corresponding to the distortion constraint, we update the multiplier in each iteration. Hence the algorithm solves the original problem itself, rather than the Lagrangian relaxation of it. Moreover, all the other variables are iterated in closed form without solving multidimensional nonlinear equations or multivariate optimization problems. Numerical experiments show the accuracy of our proposed algorithm and its improved efficiency over existing methods.

The rate-distortion (RD) theory is one of the key concepts in information theory, providing theoretical limits for compression performance and guiding the source coding design, with both theoretical and practical significance. The Blahut-Arimoto (BA) algorithm, as a classical algorithm to compute RD functions, encounters computational challenges when applied to high-dimensional scenarios. In recent years, many neural methods have attempted to compute high-dimensional RD problems from the perspective of implicit generative models. Nevertheless, these approaches often neglect the reconstruction of the optimal conditional distribution or rely on unreasonable prior assumptions. In face of these issues, we propose an innovative energy-based modeling framework that leverages the connection between the RD dual form and the free energy in statistical physics, achieving effective reconstruction of the optimal conditional distribution. The proposed algorithm requires training only a single neural network and circumvents the challenge of computing the normalization factor in energy-based models using the Markov chain Monte Carlo (MCMC) sampling. Experimental results demonstrate the significant effectiveness of the proposed algorithm in estimating high-dimensional RD functions and reconstructing the optimal conditional distribution.

The error exponent in lossy source coding characterizes the asymptotic decay rate of error probability with respect to blocklength. The Marton’s error exponent provides the theoretically optimal bound on this rate. However, computation methods of the Marton’s error exponent remain underdeveloped due to its formulation as a non-convex optimization problem with limited efficient solvers. While a recent grid search algorithm can compute its inverse function, it incurs prohibitive computational costs from two-dimensional brute-force parameter grid searches. This paper proposes a composite maximization approach that effectively handles both Marton’s error exponent and its inverse function. Through a constraint decoupling technique, the resulting problem formulations admit efficient solvers driven by an alternating maximization algorithm. By fixing one parameter via a one-dimensional line search, the remaining subproblem becomes convex and can be efficiently solved by alternating variable updates, thereby significantly reducing search complexity. Therefore, the global convergence of the algorithm can be guaranteed. Numerical experiments for simple sources and the Ahlswede’s counterexample, demonstrates the superior efficiency of our algorithm in contrast to existing methods.

This paper investigates the joint relay and transmission mode selection for covert communication in a wireless relay system with amplify-and-forward (AF) forwarding mode, which consists of one source, multiple AF relays, one destination, one friendly jammer and one warden, and each relay can switch between the half-duplex (HD) and full-duplex (FD) transmission modes. We first explore the fundamental covert performance of the system when it works in either the fixed HD or fixed FD mode. Based on this result, we then investigate the covert performance of the system with optimal (resp. random) relay selection and random (resp. optimal) mode selection, so as to reveal the achievable covert performance in the system with solely the relay selection or mode selection. Building upon above results, we further design the optimal joint relay and mode selection scheme, and develop related theoretical models for performance analysis. Finally, we provide extensive numerical results to conduct a comprehensive comparison between the relay selection and mode selection on their achievable covert performance and to illustrate the performance enhancement from adopting the joint relay and mode selection in the relay system.

A protograph low-density parity-check (P-LDPC) code-based lossy coding system is proposed for compressing the Gaussian mixture model source, as a particular case of shipping transportation systems. The compression performance is benchmarked against the rate-distortion bounds for this source. Some effective methods are developed to improve both the encoder and the decoder to reduce the compression distortion. Experimental results demonstrate that the proposed methods achieve good performance while maintaining low complexity.

In this paper, we study the deep learning (DL) based channel extrapolation problem and conduct the over-the-air (OTA) antenna extrapolation and frequency channel interpolation test for the 3rd generation partnership project (3GPP) long-term evolution (LTE) time-division duplex (TDD)-like orthogonal frequency division multiplexing (OFDM) massive MIMO prototype. We first present measurement campaigns using universal software radio peripherals (USRP) at 3.5 GHz, where the base station (BS) is composed of a 64-element antenna array. A DL-based antenna extrapolation network is then designed to approximate the inner deterministic function among antennas from the attained channel data within the “training” pilots. We present an antenna selection network (ASN) that can select a limited number of antennas for the best extrapolation, which outperforms the uniform antenna selection in terms of channel reconstruction and signal detection. We also design a deep residual neural network for channel interpolation. The performance of the extrapolated channel is evaluated in terms of normalized mean squared error (NMSE) in comparison to the measured channels on all antenna ports or the full pilot-aided channels in all OFDM subcarriers. Experimental results show that ASN can reduce an average of 87.5% antenna ports and maintain channel estimation NMSE by$10^{-2}$when compared to 3GPP channel estimation protocols.

Information Bottleneck (IB) is a technique to extract information about one target random variable through another relevant random variable. This technique has garnered significant interest due to its broad applications in information theory and deep learning. Hence, there is a strong motivation to develop efficient numerical methods with high precision and theoretical convergence guarantees. In this paper, we propose a semi-relaxed IB model, where the Markov chain and transition probability condition are relaxed from the relevance-compression function. Based on the proposed model, we develop an algorithm, which recovers the relaxed constraints and involves only closed-form iterations. Specifically, the algorithm is obtained by analyzing the Lagrangian of the relaxed model with alternating minimization in each direction. The convergence property of the proposed algorithm is theoretically guaranteed through descent estimation and Pinsker's inequality. Numerical experiments across classical and discrete distributions corroborate the analysis. Moreover, our proposed algorithm demonstrates notable advantages in terms of computational efficiency, evidenced by significantly reduced run times compared to existing methods with comparable accuracy.

An approach is established for maximizing the Lower bound on the Mismatch capacity (hereafter abbreviated as LM rate), a key performance bound in mismatched decoding, by optimizing the channel input probability distribution. Under a fixed channel input probability distribution, the computation of the corresponding LM rate is a convex optimization problem. When optimizing the channel input probability distribution, however, the corresponding optimization problem adopts a max-min formulation, which is generally non-convex and is intractable with standard approaches. To solve this problem, a novel dual form of the LM rate is proposed, thereby transforming the max-min formulation into an equivalent double maximization formulation. This new formulation leads to a maximization problem setup wherein each individual optimization direction is convex. Consequently, an alternating maximization algorithm is established to solve the resultant maximization problem setup. Each step of the algorithm only involves a closed-form iteration, which is efficiently implemented with standard optimization procedures. Numerical experiments show the proposed approach for optimizing the LM rate leads to noticeable rate gains.

Computing the rate-distortion function for continuous sources is commonly regarded as a standard continuous optimization problem. When numerically addressing this problem, a typical approach involves discretizing the source space and subsequently solving the associated discrete problem. However, existing literature has predominantly concentrated on the convergence analysis of solving discrete problems, usually neglecting the convergence relationship between the original continuous optimization and its associated discrete counterpart. This neglect is not rigorous, since the solution of a discrete problem does not necessarily imply convergence to the solution of the original continuous problem, especially for non-linear problems. To address this gap, our study employs rigorous mathematical analysis, which constructs a series of finite-dimensional spaces approximating the infinite-dimensional space of the probability measure, establishing that solutions from discrete schemes converge to those from the continuous problems.

The privacy funnel (PF) gives a framework of privacy-preserving data release, where the goal is to release useful data while also limiting the exposure of associated sensitive information. This framework has garnered significant interest due to its broad applications in characterization of the privacy-utility tradeoff. Hence, there is a strong motivation to develop numerical methods with high precision and theoretical convergence guarantees. In this paper, we propose a novel relaxation variant based on Jensen's inequality of the objective function for the computation of the PF problem. This model is proved to be equivalent to the original in terms of optimal solutions and optimal values. Based on our proposed model, we develop an accurate algorithm which only involves closed-form iterations. The convergence of our algorithm is theoretically guaranteed through descent estimation and Pinsker's inequality. Numerical results demonstrate the effectiveness of our proposed algorithm.

The information bottleneck (IB) method is a technique designed to extract meaningful information related to one random variable from another random variable, and has found extensive applications in machine learning problems. In this paper, neural network based estimation of the IB problem solution is studied, through the lens of a novel formulation of the IB problem. Via exploiting the inherent structure of the IB functional and leveraging the mapping approach, the proposed formulation of the IB problem involves only a single variable to be optimized, and subsequently is readily amenable to data-driven estimators based on neural networks. A theoretical analysis is conducted to guarantee that the neural estimator asymptotically solves the IB problem, and the numerical experiments on both synthetic and MNIST datasets demonstrate the effectiveness of the neural estimator.

Reliable communication over a discrete memoryless channel with the help of a relay has aroused interest due to its widespread applications in practical scenarios. By considering the system with a mismatched decoder, previous works have provided optimization models to evaluate the mismatch capacity in these scenarios. The proposed models, however, are difficult due to the complicated structure of the mismatched decoding problem with the information flows in hops given by the relay. Existing methods, such as the grid search, become impractical as they involve finding all roots of a nonlinear system, with the growing size of the alphabet. To address this problem, we reformulate the max-min optimization model as a consistent maximization form, by considering the dual form of the inner minimization problem and the Lagrangian with a fixed multiplier. Based on the proposed formulation, an alternating maximization framework is designed, which provides the closed-form solution with simple iterations in each step by introducing a suitable variable transformation. The effectiveness of the proposed approach is demonstrated by the simulations over practical scenarios, including Quaternary and Gaussian channels. Moreover, the simulation results of the transitional probability also shed light on the promising application attribute to the quantizer design in the relay node.

In this paper, we consider the moving target sensing problem for integrated sensing and communication (ISAC) sys-tems in clutter environment. Scatterers produce strong clutter, deteriorating the performance of ISAC systems in practice. Given that scatterers are typically stationary and the targets of interest are usually moving, we here focus on sensing the moving targets. Specifically, we adopt a scanning beam to search for moving target candidates. For the received signal in each scan, we employ high-pass filtering in the Doppler domain to suppress the clutter within the echo, thereby identifying candidate moving targets according to the power of filtered signal. Then, we adopt root-MUSIC-based algorithms to estimate the angle, range, and radial velocity of these candidate moving targets. Subsequently, we propose a target detection algorithm to reject false targets. Simulation results validate the effectiveness of these proposed methods.

In this paper, we propose a practical integrated sensing and communications (ISAC) framework to sense dynamic targets from clutter environment while ensuring users communications quality. We design multiple communications beams that can communicate with users while one rotating sensing beam can scan entire space, and then we propose the supporting beam-forming design and power allocation strategies for such design. Unlike most existing ISAC studies that ignore the interference of static environmental clutter on target sensing, we construct a mixed sensing channel that includes both static environment and dynamic targets. When base station receives echo signals, we first provide a practical clutter filtering method to filter out static environmental clutter. Then dynamic target detection and angle estimation are realized through angle-Doppler spectrum estimation (ADSE) and joint detection over multiple subcarriers (MSJD), while distance and velocity estimation are realized through the extended subspace algorithm. Simulation results are provided to demonstrate the effectiveness of the proposed scheme.

In this paper, we investigate the covertness and secrecy guarantees of wireless communications in an active attacker scenario where attackers perform detection/eavesdropping and jamming simultaneously. Both detection and eavesdropping attacks need to be counteracted, such that the covertness and secrecy guarantees in wireless communications can be achieved. To understand the covertness and secrecy performances, we provide theoretical modeling for covertness outage probability and secrecy outage probability, respectively. Based on the the-oretical model, we conduct theoretical analysis to identify the covert secrecy rate (CSR) under power control (PC)-based secure transmission scheme. Extensive numerical results are provided to illustrate the achievable performances and also reveal the impact of the active attackers on the CSR.

This paper explores a new secure wireless communication scenario for the data collection in the Internet of Things (IoT) where the physical layer security technology is applied to counteract both the detection and eavesdropping attacks, such that the critical covertness and secrecy properties of the communication are jointly guaranteed. We first provide theoretical modeling for covertness outage probability (COP), secrecy outage probability (SOP) and transmission probability (TP) to depict the covertness, secrecy and transmission performances of the wireless communication system. To understand the fundamental security performance under the wireless communication system, we then define a new metric -covert secrecy rate (CSR), which characterizes the maximum transmission rate subject to the constraints of COP, SOP and TP. We further conduct detailed theoretical analysis to identify the CSR under various scenarios determined by the detector-eavesdropper relationships and the secure transmission schemes adopted by transmitters. Finally, numerical results are provided to illustrate the achievable performances under the secure wireless communication system.

This paper investigates the fundamental covert rate performance in a D2D-enabled cellular network consisting of a cellular user Alice, a base station BS, an active warden Willie, and a D2D pair with a transmitter$D_{t}$and a full-duplex receiver$D_{r}$. To conduct covert communication between Alice and BS, the full-duplex$D_{r}$transmits jamming signal to confuse the active Willie and also receives signal from$D_{t}$simultaneously. With spectrum sharing,$D_{t}$can operate over either an underlay mode reusing cellular spectrum or an overlay mode using dedicated spectrum. With power control,$D_{r}$can send jamming signal to confuse Willie's detection of the transmission from Alice. We first provide theoretical results for the outage probabilities of the cellular and D2D transmissions, the average minimum detection error probability at Willie, and the achievable covert rate from Alice to BS. We then explore the power control for covert rate maximization (CRM) under the underlay mode as well as the joint designs of power control and spectrum partition for CRM under the overlay mode. We further consider a mode selection that flexibly switches between these two modes with a probability, and also investigate the covert rate modeling and joint designs of power control, spectrum partition and mode selection probability for CRM. Finally, numerical results are presented to illustrate the covert rate performances of the network under the underlay mode, overlay mode and mode selection.

In this paper, we propose a practical integrated sensing and communications (ISAC) framework to sense dynamic targets from clutter environment while ensuring users communications quality. To implement communications function and sensing function simultaneously, we design multiple communications beams that can communicate with the users as well as one sensing beam that can rotate and scan the entire space. To minimize the interference of sensing beam on existing communications systems, we divide the service area intosensing beam for sensing (S4S) sectorandcommunications beam for sensing (C4S) sector, and provide beamforming design and power allocation optimization strategies for each type sector. Unlike most existing ISAC studies that ignore the interference of static environmental clutter on target sensing, we construct a mixed sensing channel model that includes both static environment and dynamic targets. When base station receives the echo signals, it first filters out the interference from static environmental clutter and extracts the effective dynamic target echoes. Then a complete and practical dynamic target sensing scheme is designed to detect the presence of dynamic targets and to estimate their angles, distances, and velocities. In particular, dynamic target detection and angle estimation are realized through angle-Doppler spectrum estimation (ADSE) and joint detection over multiple subcarriers (MSJD), while distance and velocity estimation are realized through the extended subspace algorithm. Simulation results demonstrate the effectiveness of the proposed scheme and its superiority over the existing methods that ignore environmental clutter.

Information bottleneck (IB) is a paradigm to extract information in one target random variable from another relevant random variable, which has aroused great interest due to its potential to explain deep neural networks in terms of information compression and prediction. Despite its great importance, finding the optimal bottleneck variable involves a difficult nonconvex optimization problem due to the nonconvexity of mutual information constraint. The Blahut-Arimoto algorithm and its variants provide an approach by considering its Lagrangian with fixed Lagrange multiplier. However, only the strictly concave IB curve can be fully obtained by the BA algorithm, which strongly limits its application in machine learning and related fields, as strict concavity cannot be guaranteed in those problems. To overcome the above difficulty, we derive an entropy regularized optimal transport (OT) model for IB problem from a posterior probability perspective. Correspondingly, we use the alternating optimization procedure and generalize the Sinkhorn algorithm to solve the above OT model. The effectiveness and efficiency of our approach are demonstrated via numerical experiments.

This paper presents a low-complexity lossy compression scheme for Gaussian vectors, using sparse regression codes (SRC) and a novel decimated approximate message passing (AMP) encoder. The sparse regression codebook is characterized by a design matrix and each codeword is a linear combination of selected columns of the matrix. In order to enable the convergence of AMP for lossy compression, we incorporate the concept of decimation into the AMP algorithm for the first time. Further, we show that the power allocation technique is beneficial for improving the rate-distortion performance. The computational complexity of the proposed encoding is O(log n) per source sample for a length-n source vector, using a sub-Fourier design matrix. Moreover, the proposed AMP encoder inherently supports successively refinable compression. Simulation results show that the proposed decimated AMP encoder significantly outperforms the existing successive-approximation encoding [1] and approaches the rate-distortion limit in low-rate regime.

In this paper, we propose a new framework named Communication Optimal Transport (CommOT) for computing the rate distortion (RD) function. This work is motivated by observing the fact that the transition law and the relative entropy in communication theory can be viewed as the transport plan and the regularized objective function in the optimal transport (OT) model. However, unlike in classical OT problems, the RD function only possesses one-side marginal distribution. Hence, to maintain the OT structure, we introduce slackness variables to fulfill the other-side marginal distribution and then propose a general framework (CommOT) for the RD function. The CommOT model is solved via the alternating optimization technique and the well-known Sinkhorn algorithm. In particular, the expected distortion threshold can be converted into finding the unique root of a one-dimensional monotonic function with only a few steps. Numerical experiments show that our proposed framework (CommOT) for solving the RD function with given distortion threshold is efficient and accurate.

Mismatch capacity characterizes the highest information rate for a channel under a prescribed decoding metric, and is thus a highly relevant fundamental performance metric when dealing with many practically important communication scenarios. Compared with the frequently used generalized mutual information (GMI), the LM rate has been known as a tighter lower bound of the mismatch capacity. The computation of the LM rate,11To our best knowledge, the name LM rate first appeared in the reference [1]. The capital letter LM seems to be the abbreviation of Lower bound on the Mismatch capacity. however, has been a difficult task, due to the fact that the LM rate involves a maximization over a function of the channel input, which becomes challenging as the input alphabet size grows, and direct numerical methods (e.g., interior point methods) suffer from intensive memory and computational resource requirements. Noting that the computation of the LM rate can also be formulated as an entropy-based optimization problem with constraints, in this work, we transform the task into an optimal transport (OT) problem with an extra constraint. This allows us to efficiently and accurately accomplish our task by using the well-known Sinkhorn algorithm. Indeed, only a few iterations are required for convergence, due to the fact that the formulated problem does not contain additional regularization terms. Moreover, we convert the extra constraint into a root-finding procedure for a one-dimensional monotonic function. Numerical experiments demonstrate the feasibility and efficiency of our OT approach to the computation of the LM rate.

We consider a semantic cipher system, in which we protect only the semantic information of the source. The optimal tradeoff is characterized among the coding rate, the secret key rate, the semantic information leakage rate, the source reconstruction distortion, and the semantic distortion. It is shown that an efficient key with a small size suffices to protect the semantic information.

In this paper, we investigate the performance of space-time block-coded multiple-input-multiple-output (STBCMIMO) LoRa system over Nakagami-m and Ricean fading channels with perfect and imperfect channel state information (CSI). Specifically, we derive the closed-form bit-error-rate expressions and analyze the diversity order of the STBC-MIMO LoRa system with perfect and imperfect CSI, where two common channel estimation error models are considered. Moreover, we perform simulations to evaluate the coverage performance of the system and to verify the accuracy of the theoretical analyses.

Abstract Self-driving cars over the last decade have achieved significant progress like driving millions of miles without any human intervention. However, behavioral safety in applying deep-neural-network-based (DNN based) systems for self-driving cars could not be guaranteed. Several real-world accidents involving self-driving cars have already happened, some of which have led to fatal collisions. In this paper, we present a novel and automated technique for verifying steering angle safety for self-driving cars. The technique is based on deep learning verification (DLV), which is an automated verification framework for safety of image classification neural networks. We extend DLV by leveraging neuron coverage and slack relationship to solve the judgement problem of predicted behaviors, and thus, to achieve verification of steering angle safety for self-driving cars. We evaluate our technique on the NVIDIA’s end-to-end self-driving architecture, which is a crucial ingredient in many modern self-driving cars. Experimental results show that our technique can successfully find adversarial misclassifications (i.e., incorrect steering decisions) within given regions if they exist. Therefore, we can achieve safety verification (if no misclassification is found for all DNN layers, in which case the network can be said to be stable or reliable w.r.t. steering decisions) or falsification (in which case the adversarial examples can be used to fine-tune the network).

This article presents a novel way to reduce blockchain nodes’ memory requirements using error correcting codes. In particular, LDPC codes are taken as examples to explicitly demonstrate the scheme. The proposed coding scheme encodes data across multiple blocks, respectively, block headers, in the blockchain. This leads to a significant reduction in required memory at each node. We then apply the proposed coding technique to blockchains organized in two different ways. Our first scheme has the same protocol for mining, broadcasting, and verification of blocks, as Bitcoin-type blockchains. Our scheme is different in thatfull nodesdo not have to store all blocks. Instead they will need to store only one block of a group of$t$blocks. In the second scheme, we consider a new block verification protocol and an account-based model under the assumption that transmission between any two nodes can be established, as well as the broadcast transmission. Our block verification protocol uses the Byzantine fault tolerance algorithm and requires sending a newly mined block to only a small number of verification nodes, instead of broadcasting it to the entire network, which leads to a reduction of the network load.

This paper presents an algorithm for the optimal design of general entropy-constrained successively refinable unrestricted polar quantizer, i.e., with arbitrary number L of refinement levels, for bivariate circularly symmetric sources. The optimization problem is formulated as the minimization of a weighted sum of distortions and entropies for the scenario where the magnitude quantizers' thresholds are confined to a predefined finite set. The proposed solution algorithm is globally optimal. It involves L stages, where each stage corresponds to an unrestricted polar quantizer (UPQ) level, and includes solving the minimum-weight path problem for multiple node pairs in a series of weighted directed acyclic graphs. Additionally, we derive an upper bound Pmax(l), l ∈ [1 : L], on the possible number of phase levels in any phase quantizer of the l-th level UPQ, which grows linearly with l. The time complexity of the proposed approach is O(L2K3Pmax(l)), where K is the cardinality of the predefined set of possible magnitude thresholds. Finally, the experimental results for L = 3 demonstrate the effectiveness in practice of the proposed scheme.

This paper addresses the design of a sequential scalar quantizer (SSQ) for finite-alphabet correlated sources in the fixed-rate (FR) and entropy-constrained (EC) cases. The optimization problem is formulated as the minimization of a weighted sum of distortions and rates. The proposed solution is globally optimal for the class of SSQs with convex cells and is based on solving the minimum-weight path (MWP) problem in the EC case, respectively, a length-constrained MWP problem in the FR case, in a series of weighted directed acyclic graphs. The asymptotic time complexity is O(K12K22), where K1and K2are the respective sizes of the alphabets of the two sources. Additionally, it is proved that, by applying the proposed algorithms to discretizations of correlated sources with continuous joint probability density function, the performance approaches that of the optimal EC-SSQ, respectively, FR-SSQ, with convex cells for the original sources as the accuracy of the discretization increases. Extensive experiments performed with correlated Gaussian sources validate the effectiveness in practice of the proposed approach in approximating the optimal SSQ for the case of continuous-alphabet sources.

This paper addresses the design of two-stage successively refinable unrestricted polar quantizers for bivariate circularly symmetric sources in the entropy-constrained and fixed-rate cases. The proposed solutions are globally optimal when the thresholds of the magnitude quantizers are confined to finite discretizations of the interval [0, ∞). The algorithm developed for the entropy-constrained case involves a series of stages, including solving the minimum-weight path problem for multiple node pairs in certain weighted directed acyclic graphs. The asymptotical time complexity is O(K1K22Pmax), where K1and K2are the sizes of the sets of possible magnitude thresholds of the coarse and refined unrestricted polar quantizers (UPQs), respectively, while Pmaxis an upper bound on the number of phase levels in any phase quantizer of the coarse UPQ. The solution algorithm for the fixed-rate case is based on solving a succession of dynamic programming problems for multiple coarse quantizer bins. The time complexity in the fixed-rate case amounts to O(K1K2N2N1), where N1is the number of cells of the coarse UPQ and N is the ratio between the number of bins of the fine and coarse UPQs. The extensive experimental results on a bivariate circularly symmetric Gaussian source show the effectiveness of the proposed schemes.

This paper proposes an algorithm for the design of entropy-constrained unrestricted polar quantizer (ECUPQ) for bivariate circularly symmetric sources. The algorithm is globally optimal for the class of ECUPQs with magnitude quantizer thresholds confined to a finite set. The optimization problem is formulated as the minimization of a weighted sum of the distortion and entropy and the proposed solution is based on modeling the problem as a minimum-weight path problem in a certain weighted directed acyclic graph. The proposed algorithm enables solving the overall problem in O(K2log|P̂|) time, where K is the size of the set of possible magnitude thresholds and P̂ is the set of the number of phase levels for the uniform phase quantizers.

This letter presents an algorithm for the design of fixed-rate unrestricted polar quantizer (FUPQ) for bivariate circularly symmetric sources. The proposed algorithm is globally optimal for the class of FUPQs with the magnitude quantizer thresholds restricted to some predefined finite set. The solution algorithm is based on dynamic programming, which is further accelerated by exploiting the monotonicity property of the cost function. The time complexity of the accelerated algorithm is O(KN2 ), where N is the number of target qunatizer levels and K is the size of the predefined set of possible thresholds. The experimental results show that our approach outperforms the previous tractable designs when the total number of quantizer levels ranges between 25 and 256.

This paper proposes an algorithm for the design of entropy-constrained unrestricted polar quantizer (ECUPQ) for bivariate circularly symmetric sources. The algorithm is globally optimal for the class of ECUPQs with magnitude quantizer thresholds confined to a finite set. The optimization problem is formulated as the minimization of a weighted sum of distortion and entropy, and the proposed solution is based on modeling the problem as a minimum-weight path problem in a certain weighted directed acyclic graph. Each graph edge corresponds to a possible magnitude quantizer bin and computing its weight involves solving another optimization problem. We develop a fast strategy for evaluating all edge weights, leading to a O(K2+ KPmax) time solution algorithm, where K is the size of the set of possible magnitude thresholds and Pmax is the maximum number of phase levels. The practical performance of the proposed algorithm is assessed for a bivariate circularly symmetric Gaussian source, at rates ranging from 0.5 to 6 bits/sample. Our results demonstrate that the proposed approach achieves performance very close to the asymptotically optimal ECUPQ at all rates, while at low rates it significantly outperforms all previous UPQ schemes. Notably, peak improvement of 0.755 dB can be achieved for rates below 2.5.

This work addresses the design of a sequential code for correlated sources using entropy-constrained scalar quantization at each encoder. We consider discrete sources and propose a globally optimal algorithm to minimize a weighted sum of distortions and rates. Our algorithm is based on solving the minimum weight path problem in a series of appropriately constructed weighted directed acyclic graphs. Its asymptotical time complexity is O(N21N22), where N1and N2denote the alphabet sizes of the two sources, respectively.

This paper addresses the design of symmetric entropy-constrained multiple description scalar quantizers (EC-MDSQ) with linear joint decoders, i.e., where some of the decoders compute the reconstruction by averaging the reconstructions of individual descriptions. Thus, the use of linear decoders reduces the space complexity at the decoder since only a subset of the codebooks needs to be stored. The proposed design algorithm locally minimizes the Lagrangian, which is a weighted sum of the expected distortion and of the side quantizers' rates. The algorithm is inspired by the EC-MDSQ design algorithm proposed by Vaishampayan and Domaszewicz, and it is adapted from two to K descriptions. Differently from the aforementioned work, the optimization of the reconstruction values can no longer be performed separately at the decoder optimization step. Interestingly, we show that the problem is a convex quadratic optimization problem, which can be efficiently solved. Moreover, the generalization of the encoder optimization step from two to K descriptions increases drastically the amount of computations. We show how to exploit the special form of the cost function conferred by the linear joint decoders to significantly reduce the time complexity at this step. We compare the performance of the proposed design with multiple description lattice vector quantizers (MDLVQ) and with the multiple description scheme based on successive refinement and unequal erasure protection (UEP). Our experiments show that the proposed approach outperforms MDLVQ with dimension 1 quantization, as expected. Additionally, when more codebooks are added our scheme even beats MDLVQ with quantization dimension approaching ∞, for rates sufficiently high. Furthermore, the proposed approach is also superior to UEP with dimension 1 quantization when the rates are low.

This paper introduces a linear permutation module before the inner encoder of the iteratively decoded product coding structure, for the transmission of scalable bit streams over error-prone channels1. This can improve the error correction ability of the inner code when some source bits are known from the preceding outer code decoding stages. The product code consists of a protograph low-density parity-check code (inner code) and Reed-Solomon (RS) codes of various strengths (outer code). Further, an algorithm relying on protograph-based extrinsic information transfer analysis is devised to design good base matrices from which the linear permutations are constructed. In addition, an analytical formula for the expected fidelity of the reconstructed sequence is derived and utilized in the optimization of the RS codes redundancy assignment. The experimental results reveal that the proposed approach consistently outperforms the scheme without the linear permutation module, reaching peak improvements of 1.98 dB and 1.30 dB over binary symmetric channels (BSC) and additive white Gaussian noise (AWGN) channels, respectively.

As the demand for e-Health care increases quickly, the transmission of medical images has been a crucial problem which needs to be solved as soon as possible. In the last decade, joint source-channel coding (JSCC), which combines the source coding with the channel coding reasonably to build an integral system so as to obtain significant improvement of system performance has attracted much attention. A framework of transmitting medical images by a P-JSCC scheme constructed from protograph low-density parity-check (P-LDPC) codes is proposed in this paper. Without loss of generality, we exploit a typical radiography image for simulation, and experimental results show that the receiver can recover the transmitted radiography image with good quality even at a very low signal-to-noise ratio (SNR); the P-JSCC scheme outperforms irregular-JSCC and regular-JSCC.