Markov Sources Research Articles

Reinforcement Learning for Near-Optimal Design of Zero-Delay Codes for Markov Sources

Reinforcement Learning for Near-Optimal Design of Zero-Delay Codes for Markov Sources

Real-Time Reconstruction of Markov Sources and Remote Actuation Over Wireless Channels

Real-Time Reconstruction of Markov Sources and Remote Actuation Over Wireless Channels

Effective Energy Efficiency under Delay-Outage Probability Constraints and F-Composite Fading.

The paradigm of the Next Generation cellular network (6G) and beyond is machine-type communications (MTCs), where numerous Internet of Things (IoT) devices operate autonomously without human intervention over wireless channels. IoT's autonomous and energy-intensive characteristics highlight effective energy efficiency (EEE) as a crucial key performance indicator (KPI) of 6G. However, there is a lack of investigation on the EEE of random arrival traffic, which is the underlying platform for MTCs. In this work, we explore the distinct characteristics of F-composite fading channels, which specify the combined impact of multipath fading and shadowing. Furthermore, we evaluate the EEE over such fading under a finite blocklength regime and QoS constraints where IoT applications generate constant and sporadic traffic. We consider a point-to-point buffer-aided communication system model, where (1) an uplink transmission under a finite blocklength regime is examined; (2) we make realistic assumptions regarding the perfect channel state information (CSI) available at the receiver, and the channel is characterized by the F-composite fading model; and (3) due to its effectiveness and tractability, application data are found to have an average arrival rate calculated using Markovian sources models. To this end, we derive an exact closed-form expression for outage probability and the effective rate, which provides an accurate approximation for our analysis. Moreover, we determine the arrival and required service rates that satisfy the QoS constraints by applying effective bandwidth and capacity theories. The EEE is shown to be quasiconcave, with a trade-off between the transmit power and the rate for maximising the EEE. Measuring the impact of transmission power or rate individually is quite complex, but this complexity is further intensified when both variables are considered simultaneously. Thus, we formulate power allocation (PA) and rate allocation (RA) optimisation problems individually and jointly to maximise the EEE under a QoS constraint and solve such a problem numerically through a particle swarm optimization (PSO) algorithm. Finally, we examine the EEE performance in the context of line-of-sight and shadowing parameters.

Source Coding for Markov Sources With Partial Memoryless Side Information at the Decoder

Source Coding for Markov Sources With Partial Memoryless Side Information at the Decoder

An Index Policy for Minimizing the Uncertainty-of-Information of Markov Sources

An Index Policy for Minimizing the Uncertainty-of-Information of Markov Sources

State-Aware Timeliness in Energy Harvesting IoT Systems Monitoring a Markovian Source

State-Aware Timeliness in Energy Harvesting IoT Systems Monitoring a Markovian Source

Asymptotic Equipartition Property for a Markov Source Having Ambiguous Alphabet

Asymptotic Equipartition Property for a Markov Source Having Ambiguous Alphabet

Encoding of Messages Generated by an Arbitrary Markov Source with Unknown Message Statistics

The method of universal coding of an arbitrary set of Markov sources with finite memory is proposed. An estimation of the universal coding is obtained depending on the ε-entropy of the set of sources describing the massive of this set.

State-aware real-time tracking and remote reconstruction of a Markov source

State-aware real-time tracking and remote reconstruction of a Markov source

Bayesian denoising of structured sources and its implications on learning-based denoising

Abstract Denoising a stationary process $(X_{i})_{i \in \mathbb{Z}}$ corrupted by additive white Gaussian noise $(Z_{i})_{i \in \mathbb{Z}}$ is a classic, well-studied and fundamental problem in information theory and statistical signal processing. However, finding theoretically founded computationally efficient denoising methods applicable to general sources is still an open problem. In the Bayesian set-up where the source distribution is known, a minimum mean square error (MMSE) denoiser estimates $X^{n}$ from noisy measurements $Y^{n}$ as $\hat{X}^{n}=\mathrm{E}[X^{n}|Y^{n}]$. However, for general sources, computing $\mathrm{E}[X^{n}|Y^{n}]$ is computationally very challenging, if not infeasible. In this paper, starting from a Bayesian set-up, a novel denoising method, namely, quantized maximum a posteriori (Q-MAP) denoiser is proposed and its asymptotic performance is analysed. Both for memoryless sources, and for structured first-order Markov sources, it is shown that, asymptotically, as $\sigma _{z}^{2} $ (noise variance) converges to zero, ${1\over \sigma _{z}^{2}} \mathrm{E}[(X_{i}-\hat{X}^{\mathrm{QMAP}}_{i})^{2}]$ converges to the information dimension of the source. For the studied memoryless sources, this limit is known to be optimal. A key advantage of the Q-MAP denoiser, unlike an MMSE denoiser, is that it highlights the key properties of the source distribution that are to be used in its denoising. This key property leads to a new learning-based denoising approach that is applicable to generic structured sources. Using ImageNet database for training, initial simulation results exploring the performance of such a learning-based denoiser in image denoising are presented.

Modeling Markov sources and hidden Markov models by P systems

Modeling Markov sources and hidden Markov models by P systems

Deep learning based sequence detection with natural redundancy for memory sources

AbstractThe current wireless communication system has higher performance demands for receivers. This paper considers exploiting the natural redundancy (NR) that is widely existed in the transmission sources to improve the receiver's performance of sequence detection. The type of NR discussed in this paper is the inherent redundancy in data caused by the correlation between symbols in the memory sources. Since the correlation between transmitted symbols is too challenging to obtain, deep learning (DL) is introduced into sequence detection, which has a powerful ability to extract complex patterns from data. Specifically, intended for a specific memory source that is convenient for performance analysis, namely the Markov source, an iterative sequence detection algorithm based on the long short‐term memory network is proposed. Simulation results demonstrate that the receiver's performance can be improved by exploiting the NR and the proposed DL‐based sequence detection scheme can obtain optimal bit error rate performance with blind state transition probability of the transmitted Markov source.

Deep Learning for Waveform Level Receiver Design With Natural Redundancy

High-speed information transmission system demands more powerful communication receivers. In this paper, we integrate deep learning algorithms into constructing waveform level receiver, which is capable of harnessing natural redundancy (NR) in raw message sources. Owing to end-to-end learning paradigm of neural network (NN), the proposed NN receiver can accomplish joint symbol timing synchronization and demodulation based on oversampled waveform sequences directly. The prevalent bidirectional LSTM (BiLSTM) and Transformer structures, suitable for excavating sequential correlation of complex sources and waveform sequences, are considered as the backbone of NN receivers. Under the cases of clean label and noisy label, we conceive two novel training algorithms and interpret their principles in theory. The clean label bits are accessible from original source encoding schemes, while noisy label bits are available from the decision results of canonical receivers with independently noised waveform sequences. When noisy labels possess sufficiently small error rates, optimized NN receiver is competitive with that adopting the accurate labels. As for Markov sources and natural language text sources, simulation results show that the proposed NN receivers’ performances are superior to the classical receivers without a priori knowledge, especially when high spectral efficiency modulation schemes are encountered and random noise is significant.

Remote Monitoring of Two-State Markov Sources via Random Access Channels: An Information Freshness vs. State Estimation Entropy Perspective

Remote Monitoring of Two-State Markov Sources via Random Access Channels: An Information Freshness vs. State Estimation Entropy Perspective

Hypergraph-Based Source Codes for Function Computation Under Maximal Distortion

This work investigates functional source coding problems with maximal distortion, motivated by approximate function computation in many modern applications. The maximal distortion treats imprecise reconstruction of a function value as good as perfect computation if it deviates less than a tolerance level, while treating reconstruction that differs by more than that level as a failure. Using a geometric understanding of the maximal distortion, we propose a hypergraph-based source coding scheme for function computation that is constructive in the sense that it gives an explicit procedure for finding optimal or good auxiliary random variables. Moreover, we find that the hypergraph-based coding scheme achieves the optimal rate-distortion function in the setting of coding for computing with side information and achieves the Berger-Tung sum-rate inner bound in the setting of distributed source coding for computing. It also achieves the El Gamal-Cover inner bound for multiple description coding for computing and is optimal for successive refinement and cascade multiple description problems for computing. Lastly, the benefit of complexity reduction of finding a forward test channel is shown for a class of Markov sources.

Rényi Cross-Entropy Measures for Common Distributions and Processes with Memory

Two Rényi-type generalizations of the Shannon cross-entropy, the Rényi cross-entropy and the Natural Rényi cross-entropy, were recently used as loss functions for the improved design of deep learning generative adversarial networks. In this work, we derive the Rényi and Natural Rényi differential cross-entropy measures in closed form for a wide class of common continuous distributions belonging to the exponential family, and we tabulate the results for ease of reference. We also summarise the Rényi-type cross-entropy rates between stationary Gaussian processes and between finite-alphabet time-invariant Markov sources.

Accelerated Simulation Method Involving Markovian and Self-Similar Traffic Sources with Non-Fifo Scheduler

Accelerated Simulation Method Involving Markovian and Self-Similar Traffic Sources with Non-Fifo Scheduler

Zero-Delay Lossy Coding of Linear Vector Markov Sources: Optimality of Stationary Codes and Near Optimality of Finite Memory Codes

Optimal zero-delay coding (quantization) of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathbb {R}^{d}$ </tex-math></inline-formula> -valued linearly generated Markov sources is studied under quadratic distortion. The structure and existence of deterministic and stationary coding policies that are optimal for the infinite horizon average cost (distortion) problem are established. Prior results studying the optimality of zero-delay codes for Markov sources for infinite horizons either considered finite alphabet sources or, for the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathbb {R}^{d}$ </tex-math></inline-formula> -valued case, only showed the existence of deterministic and non-stationary Markov coding policies or those which are randomized. In addition to existence results, for finite blocklength (horizon) <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$T$ </tex-math></inline-formula> the performance of an optimal coding policy is shown to approach the infinite time horizon optimum at a rate <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$O\left({\frac {1}{T}}\right)$ </tex-math></inline-formula> . This gives an explicit rate of convergence that quantifies the near-optimality of finite window (finite-memory) codes among all optimal zero-delay codes.

Detecting State Transitions of a Markov Source: Sampling Frequency and Age Trade-off

We consider a finite-state Discrete-Time Markov Chain (DTMC) source that can be sampled for detecting the events when the DTMC transits to a new state. Our goal is to study the trade-off between sampling frequency and staleness in detecting the events. We argue that, for the problem at hand, using Age of Information (AoI) for quantifying the staleness of a sample is conservative and therefore, study another freshness metric <i>age penalty</i>, which is defined as the time elapsed since the first transition out of the most recently observed state. We study two optimization problems: minimize average age penalty subject to an average sampling frequency constraint, and minimize average sampling frequency subject to an average age penalty constraint; both are Constrained Markov Decision Problems. We solve them using the Lagrangian MDP approach, where we also provide structural results that reduce the search space. Our numerical results demonstrate that the computed Markov policies not only outperform optimal periodic sampling policies, but also achieve sampling frequencies close to or lower than that of an optimal clairvoyant (non-causal) sampling policy, if a small age penalty is allowed.

Complete Characterization of Gorbunov and Pinsker Nonanticipatory Epsilon Entropy of Multivariate Gaussian Sources: Structural Properties

This paper derives the optimal test channel distribution and the complete characterization of the classical Gorbunov and Pinsker (1973), Gorbunov and Pinsker (1974) nonanticipatory epsilon entropy of multivariate Gaussian Markov sources with square-error fidelity, which remained an open problem since 1974. The paper also formulates a state dependent nonanticipatory epsilon entropy, in which past reproductions are available to the decoder and not to the encoder, the test channel is specified with respect to an auxiliary (state) random process, and the reproduction process is a causal function of past reproduction and the auxiliary random process. This variation is analogous to the Wyner and Ziv (1976) and Wyner (1978) rate distortion function (RDF), of memoryless sources. It is shown that the operational rate of zero-delay codes, with past reproductions available to the decoder but not to the encoder is bounded below by the state dependent nonanticipatory epsilon entropy rate. For the case of multivariate Gaussian Markov sources with square-error fidelity, the optimal test channel distribution and the complete characterization of the state dependent of nonanticipatory epsilon entropy are derived, and also shown that that the two nonanticipatory epsilon entropies coincide. The derivations are new; they are based on structural properties of the stochastic realizations of the reproduction process that induce the optimal test channel distributions. They are derived using, achievable lower bounds on information theoretic measures, properties of mean-square estimation theory, Hadamard’s inequality, and canonical correlation coefficients of a tuple of multivariate jointly Gaussian random processes. Applications of the nonanticipatory epsilon entropy and its state dependent variation are discussed to the areas of control of unstable Gaussian systems over limited memory channels, design of causal estimators for Gaussian Markov sources with a fidelity criterion, computation of the rate loss of causal and zero-delay codes of Gaussian Markov sources with respect to non-causal codes.