Source Coding Problem Research Articles

Rate Region of the One-Help-Two Quadratic Gaussian Source-Coding Problem With Markovity

We study the quadratic Gaussian one-help-two source-coding problem with Markovity, in which three encoders separately encode the components of a memoryless vector-Gaussian source that form a Markov chain and the central decoder aims to reproduce the first and the second components in the chain subject to individual mean-squared distortion constraints. We determine the rate region under a high-resolution assumption for the middle source.

Private Key and Decoder Side Information for Secure and Private Source Coding.

We extend the problem of secure source coding by considering a remote source whose noisy measurements are correlated random variables used for secure source reconstruction. The main additions to the problem are as follows: (1) all terminals noncausally observe a noisy measurement of the remote source; (2) a private key is available to all legitimate terminals; (3) the public communication link between the encoder and decoder is rate-limited; and (4) the secrecy leakage to the eavesdropper is measured with respect to the encoder input, whereas the privacy leakage is measured with respect to the remote source. Exact rate regions are characterized for a lossy source coding problem with a private key, remote source, and decoder side information under security, privacy, communication, and distortion constraints. By replacing the distortion constraint with a reliability constraint, we obtain the exact rate region for the lossless case as well. Furthermore, the lossy rate region for scalar discrete-time Gaussian sources and measurement channels is established. An achievable lossy rate region that can be numerically computed is also provided for binary-input multiple additive discrete-time Gaussian noise measurement channels.

On Universal D-Semifaithful Coding for Memoryless Sources With Infinite Alphabets

The problem of variable length and fixed-distortion universal source coding (or D-semifaithful source coding) for stationary and memoryless sources on countably infinite alphabets ($\infty$-alphabets) is addressed in this paper. The main results of this work offer a set of sufficient conditions (from weaker to stronger) to obtain weak minimax universality, strong minimax universality, and corresponding achievable rates of convergences for the worse-case redundancy for the family of stationary memoryless sources whose densities are dominated by an envelope function (or the envelope family) on $\infty$-alphabets. An important implication of these results is that universal D-semifaithful source coding is not feasible for the complete family of stationary and memoryless sources on $\infty$-alphabets. To demonstrate this infeasibility, a sufficient condition for the impossibility is presented for the envelope family. Interestingly, it matches the well-known impossibility condition in the context of lossless (variable-length) universal source coding. More generally, this work offers a simple description of what is needed to achieve universal D-semifaithful coding for a family of distributions $\Lambda$. This reduces to finding a collection of quantizations of the product space at different block-lengths -- reflecting the fixed distortion restriction -- that satisfy two asymptotic requirements: the first is a universal quantization condition with respect to $\Lambda$, and the second is a vanishing information radius (I-radius) condition for $\Lambda$ reminiscent of the condition known for lossless universal source coding.

On Smooth Rényi Entropies: A Novel Information Measure, One-Shot Coding Theorems, and Asymptotic Expansions

This study considers the unconditional smooth Rényi entropy proposed by Renner and Wolf [ASIACRYPT, 2005], the smooth conditional Rényi entropy proposed by Kuzuoka [IEEE Trans. Inf. Th., 66(3), 1674–1690, 2020], and a novel quantity which we term the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">conditional smooth</i> -⋆ <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">entropy.</i> The latter two quantities can be specialized to the first in the absence of side-information. We explore the operational roles of these smooth Rényi entropies by establishing one-shot coding theorems for several information-theoretic problems, including Campbell’s source coding problem, the Arıkan–Massey guessing problem, and the Bunte–Lapidoth task encoding problem. We consider these problems in cases where the errors are non-vanishing and for each problem, we consider two error formalisms: the average and maximum error criteria, where the averaging and maximization are taken with respect to the side-information. Using the one-shot coding theorems, we conclude that Kuzuoka’s smooth conditional Rényi entropy and the conditional smooth-⋆ entropy are the solutions to the problems involving the average and maximum error criteria, respectively. Furthermore, we examine asymptotic expansions of these entropies when the underlying source with its side-information is stationary and memoryless. Applying our asymptotic expansions to the one-shot coding theorems, we derive various fundamental limits for these problems. We show that, under non-degenerate settings, the first-order fundamental limits differ under the average and maximum error criteria. This is in contrast to a different but related setting considered by the present authors [IEEE Trans. Inf. Th., 66(12), 7565–7587, 2020], for variable-length conditional source coding allowing errors, in which the first-order terms are identical but the second-order terms are different under these error criteria.

An Equivalent Expression for the Wyner-Ziv Source Coding Problem

We consider the coding problem for lossy source coding with side information at the decoder, which is known as the Wyner-Ziv source coding problem. The goal of the coding problem is to find the minimum rate such that the probability of exceeding a given distortion threshold is less than the desired level. We give an equivalent expression of the minimum rate by using the chromatic number and a notion of covering of a set. This allows us to analyze the coding problem in terms of graph coloring and covering.

Towards a taxonomy of code review smells

Code review is a crucial step of the software development life cycle in order to detect possible problems in source code before merging the changeset to the codebase. Although there is no consensus on a formally defined life cycle of the code review process, many companies and open source software (OSS) communities converge on common rules and best practices. In spite of minor differences in different platforms, the primary purpose of all these rules and practices leads to a faster and more effective code review process. Non-conformance of developers to this process does not only reduce the advantages of the code review but can also introduce waste in later stages of the software development.

Generating Software Product Line Model by Resolving Code Smells in the Products’ Source Code

Software Product Lines (SPLs) refer to some software engineering methods, tools and techniques for creating a collection of similar software systems from a shared set of software assets using a common means of production. This concept is recognized as a successful approach to reuse in software development. Its purpose is to reduce production costs by reusing existing features and managing the variability between the different products with respect of particular constraints. Software Product Line engineering is the production process in product lines and the development of a family of systems by reusing core assets. It exploits the commonalities between software products and preserves the ability to vary the functionalities and features between these products. The adopted strategy for building SPL can be a top-down or bottom-up. Depending from the selected strategy, it is possible to face an inappropriate implementation in the SPL Model or the derived products during this process. The code can contain code smells or code anomalies. Code smells are considered as problems in source code which can have an impact on the quality of the derived products of an SPL. The same problem can be present in many derived products from an SPL due to reuse or in the obtained product line when the bottom-up strategy is selected. A possible solution to this problem can be the refactoring which can improve the internal structure of source code without altering external behavior. This paper proposes an approach for building SPL from source code using the bottom-up strategy. Its purpose is to reduce code smells in the obtained SPL using refactoring source code. This approach proposes a possible solution using reverse engineering to obtain the feature model of the SPL.

Generating Software Product Line Model by Resolving Code Smells in the Products' Source Code

Software Product Lines (SPLs) refer to some software engineering methods, tools and techniques for creating a collection of similar software systems from a shared set of software assets using a common means of production. This concept is recognized as a successful approach to reuse in software development. Its purpose is to reduce production costs by reusing existing features and managing the variability between the different products with respect of particular constraints. Software Product Line engineering is the production process in product lines and the development of a family of systems by reusing core assets. It exploits the commonalities between software products and preserves the ability to vary the functionalities and features between these products. The adopted strategy for building SPL can be a top-down or bottom-up. Depending from the selected strategy, it is possible to face an inappropriate implementation in the SPL Model or the derived products during this process. The code can contain code smells or code anomalies. Code smells are considered as problems in source code which can have an impact on the quality of the derived products of an SPL. The same problem can be present in many derived products from an SPL due to reuse or in the obtained product line when the bottom-up strategy is selected. A possible solution to this problem can be the refactoring which can improve the internal structure of source code without altering external behavior. This paper proposes an approach for building SPL from source code using the bottom-up strategy. Its purpose is to reduce code smells in the obtained SPL using refactoring source code. This approach proposes a possible solution using reverse engineering to obtain the feature model of the SPL.

Universal Decoding for Asynchronous Slepian-Wolf Encoding

We consider the problem of (almost) lossless source coding of two correlated memoryless sources using separate encoders and a joint decoder, that is, Slepian-Wolf (S-W) coding. In our setting, the encoding and decoding are asynchronous, i.e., there is a certain relative delay between the two sources. Neither the source parameters nor the relative delay are known to the encoders and the decoder. Since we assume that both encoders implement standard random binning, which does not require such knowledge anyway, the focus of this work is on the decoder. Our main contribution is in proposing a universal decoder, that independent of the unknown source parameters and the relative delay, and at the same time, is asymptotically as good as the optimal maximum a posteriori probability (MAP) decoder in the sense of the random coding error exponent achieved. Consequently, the achievable rate region is also the same as if the source parameters and the delay were known to the decoder.

Message and Causal Asymmetric State Transmission Over the State-Dependent Degraded Broadcast Channel

We study data transmission and asymmetric state communication over a state-dependent two-user discrete memoryless degraded broadcast channel. In our model the encoder, to whom the state information is available either strictly-causally or causally, in addition to transmitting data reliably to each of the users must also provide the “higher quality” user with a description of the memoryless state sequence with some defined fidelity. The capacity region-i.e. the set of attainable rate-pairs given a maximal-allowed distortion when the state reconstruction fidelity is measured using a single-letter distortion function-is computed in the absence as well as in the presence of feedback from the “higher quality” output to the encoder. In the no-feedback cases we also study the constrained source-coding problem wherein the encoder is required to form a reconstruction that should predict the decoder's reconstruction within a given distortion, and establish the respective capacity regions. Finally, in the strictly-causal setting without feedback and when the encoder is required to form a reconstruction that should coincide with the decoder's reconstruction with probability close to one we characterize the Common-Reconstruction capacity region.

Engrossing Prosecution of Code Smells Type Identification and Rectification using Machine Learning AdaBoost Classifier

Software code smells are the structural features which reside in a software source code. Code smell detection is an established method to discover the problems in source code and reorganize the inner structure of object-oriented software for improving the quality of such software, particularly in terms of maintainability, reusability and cost minimization. The developer identified where the code smell is identified and rectified within a system is a major challenging issue. The various code smell detection technique has been designed but it failed to classify the code type and minimum rectification cost. In order to perform classification with minimum cost, an efficient technique called Machine Learning Ada-Boost Classifier (MLABC) technique is introduced. The MLABC technique improves the software quality by identifying and rectifying the different types of software code smell in source code. Initially, MLABC technique uses decision tree as base classifier to identify the code smell type. The decision tree is used to classify the code smell type based on the certain rule. After that, the base classifiers are combined to make a strong classifier using adaboost machine learning technique. The output of strong classifier is used to identify the code smell type. Finally, the code smell type rectification is performed by applying the refactoring technique where the code smell is identified with minimum cost and space complexity. Experimental results shows that the proposed MLABC technique improves the software code quality in terms of code smell type identification accuracy, false positive rate, code smell type rectification cost and space complexity with the source code.

Non-Asymptotic Converse Bounds and Refined Asymptotics for Two Source Coding Problems

In this paper, we revisit two multi-terminal lossy source coding problems: the lossy source coding problem with side information available at the encoder and one of the two decoders, which we term as the Kaspi problem (Kaspi, 1994), and the multiple description coding problem with one semi-deterministic distortion measure, which we refer to as the Fu-Yeung problem (Fu and Yeung, 2002). For the Kaspi problem, we first present the properties of optimal test channels. Subsequently, we generalize the notion of the distortion-tilted information density for the lossy source coding problem to the Kaspi problem and prove a non-asymptotic converse bound using the properties of optimal test channels and the well-defined distortion-tilted information density. Finally, for discrete memoryless sources, we derive refined asymptotics which includes the second-order, large, and moderate deviations asymptotics. In the converse proof of second-order asymptotics, we apply the Berry-Esseen theorem to the derived non-asymptotic converse bound. The achievability proof follows by first proving a type-covering lemma tailored to the Kaspi problem, then properly Taylor expanding the well-defined distortion-tilted information densities and finally applying the Berry-Esseen theorem. We then generalize the methods used in the Kaspi problem to the Fu-Yeung problem. As a result, we obtain the properties of optimal test channels for the minimum sum-rate function, a non-asymptotic converse bound and refined asymptotics for discrete memoryless sources. Since the successive refinement problem is a special case of the Fu-Yeung problem, as a by-product, we obtain a non-asymptotic converse bound for the successive refinement problem, which is a strict generalization of the non-asymptotic converse bound for successively refinable sources (Zhou, Tan, and Motani, 2017).

Remote Source Coding Under Gaussian Noise: Dueling Roles of Power and Entropy Power

The distributed remote source coding (so-called CEO) problem is studied in the case where the underlying source, not necessarily Gaussian, has finite differential entropy and the observation noise is Gaussian. The main result is a new lower bound for the sum-rate-distortion function under arbitrary distortion measures. When specialized to the case of mean-squared error, it is shown that the bound exactly mirrors a corresponding upper bound, except that the upper bound has the source power (variance) whereas the lower bound has the source entropy power. Bounds exhibiting this pleasing duality of power and entropy power have been well known for direct and centralized source coding since Shannon's work. While the bounds hold generally, their value is most pronounced when interpreted as a function of the number of agents in the CEO problem.

Guessing with Distributed Encoders.

Two correlated sources emit a pair of sequences, each of which is observed by a different encoder. Each encoder produces a rate-limited description of the sequence it observes, and the two descriptions are presented to a guessing device that repeatedly produces sequence pairs until correct. The number of guesses until correct is random, and it is required that it have a moment (of some prespecified order) that tends to one as the length of the sequences tends to infinity. The description rate pairs that allow this are characterized in terms of the Rényi entropy and the Arimoto–Rényi conditional entropy of the joint law of the sources. This solves the guessing analog of the Slepian–Wolf distributed source-coding problem. The achievability is based on random binning, which is analyzed using a technique by Rosenthal.

Binary Data Gathering With a Helper in Internet of Things: Distortion Analysis and Performance Evaluation

This paper focuses on one-helper assisted binary data gathering networks, for example, such as in Internet of Things, where a destination makes estimates of binary data relying on a number of agents and one helper. Due to the noise, corrupting errors already exist in the agent observations. To analyze the performance of this system, we formulate this system as a binary chief executive officer (CEO) problem with a helper. Initially, we use a successive decoding scheme to decompose the binary CEO problem with a helper into the multiterminal source coding and final decision problems. Then, we present an outer bound on the rate-distortion region for multiterminal source coding with binary sources and a helper. After solving a convex optimization problem formulated from the derived outer bound, we obtain the final distortion by substituting the minimized distortions of observation into the distortion propagating function, which is derived to bridge the relationship between the joint decoding results and final decision. Finally, we analyze the trade-off of rate-distortion through theoretical calculation and simulations. Both the theoretical and simulation results demonstrate that a helper can obviously reduce the signal-to-noise ratio threshold. We also have an in-depth discussion on the differences of system performance improvement between locating a helper and including an additional agent.

Fundamental Distortion Limits of Analog-to-Digital Compression

Representing a continuous-time signal by a set of samples is a classical problem in signal processing. We study this problem under the additional constraint that the samples are quantized or compressed in a lossy manner under a limited bitrate budget. To this end, we consider a combined sampling and source coding problem in which an analog stationary Gaussian signal is reconstructed from its encoded samples. These samples are obtained by a set of bounded linear functionals of the continuous-time path, with a limitation on the average number of samples per unit time given in this setting. We provide a full characterization of the minimal distortion in terms of the sampling frequency, the bitrate, and the signal's spectrum. Assuming that the signal's energy is not uniformly distributed over its spectral support, we show that for each compression bitrate there exists a critical sampling frequency smaller than the Nyquist rate, such that the distortion in signal reconstruction when sampling at this frequency is minimal. Our results can be seen as an extension of the classical sampling theorem for bandlimited random processes in the sense that they describe the minimal amount of excess distortion in the reconstruction due to lossy compression of the samples and provide the minimal sampling frequency required in order to achieve this distortion. Finally, we compare the fundamental limits in the combined source coding and sampling problem to the performance of pulse code modulation, where each sample is quantized by a scalar quantizer using a fixed number of bits.

A Study on Code Smell Detection with Refactoring Tools in Object Oriented Languages

A code smell is an indication in the source code that hypothetically indicates a design problem in the equivalent software. The Code smells are certain code lines which makes problems in source code. It also means that code lines are bad design shape or any code made by bad coding practices. Code smells are structural characteristics of software that may indicates a code or drawing problem that makes software hard to evolve and maintain, and may trigger refactoring of code. In this paper, we proposed some success issues for smell detection tools which can assistance to develop the user experience and therefore the acceptance of such tools. The process of detecting and removing code smells with refactoring can be overwhelming.

On the Capacity of Cloud Radio Access Networks With Oblivious Relaying

We study the transmission over a network in which users send information to a remote destination through relay nodes that are connected to the destination via finite-capacity error-free links, i.e., a cloud radio access network. The relays are constrained to operate without knowledge of the users’ codebooks, i.e., they perform oblivious processing. The destination, or central processor, however, is informed about the users’ codebooks. We establish a single-letter characterization of the capacity region of this model for a class of discrete memoryless channels in which the outputs at the relay nodes are independent given the users’ inputs. We show that both relaying a-la Cover–El Gamal, i.e., compress-and-forward with joint decompression and decoding, and “noisy network coding” are optimal. The proof of the converse part establishes, and utilizes, connections with the Chief Executive Officer source coding problem under logarithmic loss distortion measure. Extensions to general discrete memoryless channels are also investigated. In this case, we establish the inner and outer bounds on the capacity region. For memoryless Gaussian channels within the studied class of channels, we characterize the capacity region when the users are constrained to time-share among Gaussian codebooks. Furthermore, we also discuss the suboptimality of separate decompression and decoding and the role of time sharing.

The Distortion Rate Function of Cyclostationary Gaussian Processes

A general expression for the quadratic distortion rate function (DRF) of cyclostationary Gaussian processes in terms of their spectral properties is derived. This expression can be seen as the result of orthogonalization over the different components in the polyphase decomposition of the process. We use this expression to derive, in a closed form, the DRF of several cyclostationary processes arising in practice. We first consider the DRF of a combined sampling and source coding problem. It is known that the optimal coding strategy for this problem involves source coding applied to a signal with the same structure as one resulting from pulse amplitude modulation (PAM). Since a PAM-modulated signal is cyclostationary, our DRF expression can be used to solve for the minimal distortion in the combined sampling and source coding problem. We also analyze in more detail the DRF of a source with the same structure as a PAM-modulated signal, and show that it is obtained by reverse waterfilling over an expression that depends on the energy of the pulse and the baseband process modulated to obtain the PAM signal. This result is then used to explore the effect of the symbol rate in PAM on the DRF of its output. In addition, we also study the DRF of sources with an amplitude-modulation structure, and show that the DRF of a narrow-band Gaussian stationary process modulated by either a deterministic or a random phase sine-wave equals the DRF of the baseband process.

JET: Joint source and channel coding for error resilient virtual reality video wireless transmission

Virtual reality (VR) provides users extraordinary viewing experience and draws more and more attentions from both industry and academia. In this paper, we propose JET: Joint source and channel coding for Error resilient virtual reality video wireless Transmission, where we jointly investigate how to conquer the problem of source video’s huge size, how to efficiently satisfy a user’s view switch request and how to handle packet loss. Specifically, we first divide a VR video into smaller video tiles. Upon a user’s view switch request, the tiles corresponding to the part that the user is requesting, referred to as the field of view (FoV), and the part that the user may switch to before new video can be received, are delivered over a wireless network. We consider unequal error protection (UEP) for FoV and the rest part and formulate the inherent error resilient VR video transmission problem into a joint source and channel coding problem. In particular, we optimize the tile partition, quantization parameter and Forward Error Correction (FEC) packet allocation to maximize a user’s received video quality. We also propose a low-complexity heuristic algorithm to solve this optimization problem. Extensive simulations are conducted and simulation results verify the superior performance.