Distributed Source Coding

This paper considers the use of punctured quasiarithmetic (QA) codes for the Slepian-Wolf problem. These entropy codes are defined by finite state machines for memoryless and first-order memory sources. Puncturing an entropy coded bit-stream leads to an ambiguity at the decoder side. The decoder makes use of a correlated version of the original message in order to remove this ambiguity. A complete distributed source coding (DSC) scheme based on QA encoding with side information at the decoder is presented, together with iterative structures based on QA codes. The proposed schemes are adapted to memoryless and first-order memory sources. Simulation results reveal that the proposed schemes are efficient in terms of decoding performance for short sequences compared to well-known DSC solutions using channel codes.

This paper addresses the problem of wireless transmission of a captured scene from multiple cameras, which do not communicate among each other, to a joint decoder. Correlation among different camera views calls for distributed source coding for efficient multiview image compression. The fact that cameras are placed within a short range of each other results in a high level of interference, multipath fading, and noise effects during communications. We develop a novel two-camera system, that employs multiterminal source coding and complete complementary data spreading, so that while the former technique exploits the statistical correlation between camera views, and performs joint compression to reduce transmission rates, the spreading technique will protect transmitted data by mitigating the effects of wireless fading channels. Our results indicate that the proposed system is competitive when compared to two independently JPEG encoded streams at low to medium transmission rates.

The use of biometrics (e.g., fingerprints, irises, faces) for recognizing individuals is becoming increasingly popular and many applications are already available. Biometrics are intrinsically associated with individuals and cannot be forgotten or shared with others. However, one of the most relevant vulnerabilities of biometrics is that once a biometric template is compromised, it cannot be reissued, updated or destroyed. An attacker could then gain access to all the accounts/services/applications using that same biometric trait. This paper proposes a biometric verification system using distributed source coding principles, with enhanced security with respect to traditional biometric verification systems. The generation of different templates from the same biometric data is supported, as well as cancelable templates. Furthermore, it will not be possible to recover the original biometric data from the stored data, thus guaranteeing its privacy.

This paper presents an efficient structured binning scheme for solving the noiseless distributed source coding problem with parallel concatenated convolutional codes, or turbo codes. The novelty in the proposed scheme is the introduction of a syndrome former and an inverse syndrome former to efficiently and optimally exploit an existing turbo code without the need to redesign or modify the code structure and/or decoding algorithms. Extension of the proposed approach to serially concatenated codes is also briefed and examples including conventional turbo codes and asymmetric turbo codes are given to show the efficiency and the general applicability of the approach. Simulation results reveal good performance which is close to theoretic limit.

This paper considers the problem of scalable distributed coding of correlated sources that are communicated to a central unit. The general setting is typically encountered in sensor networks. The conditions of communication channels between the source encoders and fusion center may be time-varying and it is often desirable to guarantee a base layer of coarse information during channel fades. In addition the desired system should be robust to various scenarios of channel failure and should utilize all the available information to attain the best possible compression efficiency. Although a standard 'Lloyd-style' distributed coder design algorithm can be generalized to scalable distributed source coding, the resulting algorithm depends heavily on initialization and will virtually always converge to a poor local minimum on the distortion-cost surface. We propose an efficient initialization scheme for such a system, which employs a properly designed multi-stage distributed coder. In our prior work, we highlighted the fundamental conflict that arises when multi-stage coding is directly combined with distributed quantization. Here we use the multi-stage distributed coding system to initialize a scalable distributed coder and propose an iterative algorithm for joint design of all system components once the structural constraint is removed. Simulation results show considerable gains over randomly initialized scalable distributed coder design.

In this paper, the problem of distributed source coding of image data using symmetric and asymmetric turbo codes has been addressed. Both symmetric and asymmetric turbo codes are promising for distributed source coding (DSC) because of their simple encoding implementation and impressive decoding performance. We evaluate bit error rate (BER) and peak signal to noise ratio (PSNR) performance of a reconstructed image data using the side information transmitted through a Rayleigh flat fading channel unlike earlier proposals which assume perfect side information at the decoder. It is observed that Log-MAP and SOVA decoders perform very well with DSC. This observation is true in symmetric turbo code as well as in asymmetric turbo code configuration. Further the Log-MAP decoder performs marginally better than SOVA decoder in distributed source coding environment. All simulation results are presented for image data in a Rayleigh flat fading channel.

In many multiterminal communication problems, constructions of good source codes involve finding distributed partitions (into bins) of a collection of quantizers associated with a group of source encoders. Further, computationally efficient procedures to index these bins are also required. In this work, we consider a constructive approach for distributed binning in an algebraic framework. Several application scenarios fall under the scope of this paper including the CEO problem, distributed source coding, and n-channel symmetric multiple description source coding with n>2. Specifically, in this exposition we consider the case of two codebooks while focusing on the Gaussian CEO problem with mean squared error reconstruction and with two symmetric observations. This problem deals with distributed encoding of correlated noisy observations of a source into descriptions such that the joint decoder having access to them can reconstruct the source with a fidelity criterion. We employ generalized coset codes constructed in a group-theoretic setting for this approach, and analyze the performance in terms of distance properties and decoding algorithms.

n recent years, sensor research has been undergoing a quiet revolution, promising to have a significant impact throughout society that could quite possibly dwarf previous milestones in the information revolution. MIT Technology Review ranked wireless sensor networks that consist of many tiny, low-power and cheap wireless sensors as the number one emerging technology. Unlike PCs or the Internet, which are designed to support all types of applications, sensor networks are usually mission driven and application specific (be it detection of biological agents and toxic chemicals; environmental measurement of temperature, pressure and vibration; or realtime area video surveillance). Thus they must operate under a set of unique constraints and requirements. For example, in contrast to many other wireless devices (e.g., cellular phones, PDAs, and laptops), in which energy can be recharged from time to time, the energy provisioned for a wireless sensor node is not expected to be renewed throughout its mission. The limited amount of energy available to wireless sensors has a significant impact on all aspects of a wireless sensor network, from the amount of information that the node can process, to the volume of wireless communication it can carry across large distances. Realizing the great promise of sensor networks requires more than a mere advance in individual technologies; it relies on many components working together in an efficient, unattended, comprehensible, and trustworthy manner. One of the enabling technologies for sensor networks is distributed source coding (DSC), which refers to the compression of multiple correlated sensor outputs [1]-[4] that do not communicate with each other (hence distributed coding). These sensors send their compressed outputs to a central point [e.g., the base station (BS)] for joint decoding. I

8 th International Conference on Signal and Image Processing (SIGL 2021) is a forum for presenting new advances and research results in the fields of Digital Image Processing. The conference will bring together leading researchers, engineers and scientists in the domain of
interest from around the world. The scope of the conference covers all theoretical and practical aspects of the Signal, Image Processing & Pattern Recognition.
Authors are solicited to contribute to the Conference by submitting articles that illustrate arch results, projects, surveying works and industrial experiences that describe significant advances in
the areas of Signal and Image Processing. Topics of interest include, but are not limited to, the following

The Slepian-Wolf theorem states that the output of two correlated sources can be compressed to the same extent without loss, whether they communicate with each other or not, provided that decompression takes place at a joint decoder. We present a distributed source coding scheme for correlated images which uses modulo encoding of pixel values and encoding (compression) of the resulting symbols with binary and nonbinary turbo-codes, so that larger rate savings than using modulo encoding alone are achieved, practically without loss.

In this Part II of a two-part paper, we present a new achievable rate-distortion region for the symmetric n-channel multiple-descriptions coding problem (n>2) where the rate of every description is the same, and the reconstruction distortion depends only on the number of descriptions received. Using a new approach for the random coding constructions, along with a generalization of the technique used in the two-channel El Gamal and Cover region to any n, the rate region presented here achieves points that have not been known in the literature previously. This rate region is derived from a concatenation of source-channel erasure codes developed in Part I of this work by deploying the framework of source coding with side information ("random binning"). The key idea is that by using the framework of source coding with side information, multiple statistically identical realizations representing the coarse version of a source can be simultaneously refined by a single encoding. We point out that there is an important conceptual difference in random coding construction for the multiple-descriptions coding problem between the case of n=2 and n>2. To illustrate the framework, we also present the important case of the Gaussian source in detail.

We address the problem of distributed source coding, i.e. compression of correlated sources that are not co-located and/or cannot communicate with each other to minimize their joint description cost. In this work we tackle the related problem of compressing a source that is correlated with another source which is available only at the decoder. In contrast to prior information-theoretic approaches, we introduce a new construction and practical framework for tackling the problem based on the judicious incorporation of channel coding principles into this source coding problem. We dub our approach as distributed source coding using syndromes (DISCUS). We focus in this paper on trellis-structured constructions of the framework to illustrate its utility. Simulation results confirm the power of DISCUS, opening up a new and exciting constructive playing-ground for the distributed source coding problem. For the distributed coding of correlated i.i.d. Gaussian sources that are noisy versions of each other with “correlation-SNR” in the range of 12 to 20 dB, the DISCUS method attains gains of 7-15 dB in SNR over the Shannon-bound using “naive” independent coding of the sources

1 -The use of biometrics (e.g., fingerprints, irises, faces) for recognizing individuals is becoming increasingly popular and many applications are already available. Biometrics are intrinsically associated with individuals and cannot be forgotten or shared with others. However, one of the most relevant vulnerabilities of biometrics is that once a biometric template is compromised, it cannot be reissued, updated or destroyed. An attacker could then gain access to all the accounts/services/applications using that same biometric trait. This paper proposes a biometric verification system using distributed source coding principles, with enhanced security with respect to traditional biometric verification systems. The generation of different templates from the same biometric data is supported, as well as cancelable templates. Furthermore, it will not be possible to recover the original biometric data from the stored data, thus guaranteeing its privacy.

Symmetric distributed source coding has made great progress in the past several years. However, few attempts have been tried to use the symmetric distributed source coding schemes in real data compression scenarios. In this paper, with the inspiration of previous symmetric distributed source coding schemes, we first put forward a novel syndrome-based symmetric distributed coding scheme which can achieve the whole Slepian-Wolf rate region. Then we propose a general architecture for symmetric distributed multiview video schemes. Our experiments show very encouraging results. In the high-rate case, our scheme can achieve great rate saving from separate H.264 coding scheme at the same video quality. Index Terms-symmetric distributed multiview video coding, distributed source coding, LDPC, nonuniform channel, H.264

In this paper we consider the problem of lossy coding of correlated vector sources with uncoded side information available at the decoder. In particular, we consider lossy coding of vector source x ∈ R N which is correlated with vector source y ∈ R N , known at the decoder. We propose two compression schemes, namely, distributed adaptive compression (DAC) and distributed universal compression (DUC) schemes. The DAC algorithm is inspired by the optimal solution for Gaussian sources and requires computation of the conditional Karhunen-Loève transform (CKLT) of the data at the encoder. The DUC algorithm, however, does not require knowledge of the CKLT at the encoder. The DUC algorithms are based on the approximation of the correlation model between the sources y and x through a linear model y = Hx + n in which H is a matrix and n is a random vector and independent of x. This model can be viewed as a fictitious communication channel with input x and output y. Utilizing channel equalization at the receiver, we convert the original vector source coding problem into a set of manageable scalar source coding problems. Furthermore, inspired by bit loading strategies employed in wireless communication systems, we propose for both compression schemes a rate allocation policy which minimizes the decoding error rate under a total rate constraint. Equalization and bit loading are paired with a quantization scheme for each vector source entry (a slightly simplified version of the so called DISCUS scheme). The merits of our work are as follows: 1) it provides a simple, yet optimized, implementation of Wyner-Ziv quantizers for correlated vector sources, by using the insight gained in the design of communication systems; 2) it provides encoding schemes that, with or without the knowledge of the correlation model at the encoder, enjoy distributed compression gains.

This paper investigates the performance and proposes modifications to earlier methods for image authentication using distributed source coding. This approach works well on images that have undergone affine geometric transformations such as rotation and resizing and intensity transformations such as contrast and brightness adjustment. The results show that the improvements proposed here can be used to make the original scheme for image authentication robust to affine geometric and intensity transformations. The modifications are of much lesser computational complexity when compared with other schemes for estimation of channel parameters.

In this paper, we consider how polar codes can be used for distributed source coding configuration regardless of the statistical dependency of correlated binary sources. The polar code encoder transmits the syndrome bits which have high entropy first to the decoder for optimal compression. However, the optimal order for transmitting syndrome bits varies with the dependency of correlated sources. It means that the encoder needs to know the correlation of sources for optimal compression. In this point of view, we propose the construction method of the optimal sequence for syndrome bits. The sequence constructed with the proposed method shows the optimal compression rate without knowledge of correlation of sources at the polar code encoder.

In a wireless sensor network (WSN), nodes are battery powered, therefore, there are energy constrained. Network lifetime is one of the most important characteristics of performance for wireless sensor networks. A number of routing schemes, energy efficient and energy-aware, have been proposed to maximize the network lifetime. These schemes typically try to find the minimum energy path to optimize energy usage at a node. In this paper, we consider the lifetime maximization problem, we propose a routing protocols that take into account the battery residual energy in sensor nodes and the energy required for transmission along the path. For each transmission round, only the nodes which have their remaining energies greater than a threshold can participate as relays for other nodes data in addition to sensing the environment. This choice allows the distribution of energy load among any sensor nodes, thus extends network lifetime. Simulation results show that the network lifetimes is increased largely comparable to direct and MTE schemes.

We address the problem of compressing correlated distributed sources, i.e., correlated sources which are not co-located or which cannot cooperate to directly exploit their correlation. We consider the related problem of compressing a source which is correlated with another source that is available only at the decoder. This problem has been studied in the information theory literature under the name of the Slepian-Wolf (1973) source coding problem for the lossless coding case, and as "rate-distortion with side information" for the lossy coding case. We provide a constructive practical framework based on algebraic trellis codes dubbed as DIstributed Source Coding Using Syndromes (DISCUS), that can be applicable in a variety of settings. Simulation results are presented for source coding of independent and identically distributed (i.i.d.) Gaussian sources with side information available at the decoder in the form of a noisy version of the source to be coded. Our results reveal the promise of this approach: using trellis-based quantization and coset construction, the performance of the proposed approach is 2-5 dB from the Wyner-Ziv (1976) bound.

Distributed source coding (DSC) has been proven in theory that it can be used to compress correlated signals with or without loss. Recently this coding method has been used for the application of remote signal estimation in wireless sensor networks (WSN), where multiple sensor nodes compress their correlated observations without inter-node communications. Energy and bandwidth are therefore efficiently saved. Challenges remain, however, in the design of practical and adaptive DSC schemes for WSN. In this paper, we study the problem of a random-binning based DSC scheme for remote source estimation in WSN. We design a DSC scheme and analyze its performance on the estimated signal to distortion ratio (SDR), in which observation noise, quantization distortion, DSC decoding errors and network packet losses are all taken into account. With the introduction of a detailed power consumption model for wireless sensor communications, we quantitatively analyze the overall network energy consumption. We further propose a novel adaptive control mechanism for the DSC scheme, which flexibly optimizes the DSC performance in terms of either SDR or energy consumption by adapting the source coding and transmission parameters to the network conditions. Simulations show the proposed DSC scheme and adaptive control mechanism can either save up to 31.6% energy consumption without decreasing the SDR or maximize the SDR with saving up to 9.4% energy consumption. r

This paper presents a distributed coding scheme for the representation of 3D scenes captured by a pair of omnidirectional cameras with equivalent computational resources and transmission capabilities. The images are captured at different viewpoints and are encoded independently. A joint decoder exploits the correlation between images for improved decoding quality. The distributed coding is built on the multi-resolution representation of spherical images, whose information is split into two partitions. The encoder then transmits one partition after entropy coding, as well as the syndrome bits resulting from the channel encoding of the other partition. The joint decoder exploits the intra-view correlation by predicting one partition from the other partition. At the same time, it exploits the interview correlation using block-based disparity estimation between images from different cameras. Experiments demonstrate that the distributed coding solution performs better than a scheme where images are handled independently. Furthermore, the coding rate stays balanced between the different cameras, which permits to avoid hierarchical relations between vision sensors in camera networks.

A simple but powerful scheme exploiting the binning concept for asymmetric lossless distributed source coding is proposed. The novelty in the proposed scheme is the introduction of a syndrome former (SF) in the source encoder and an inverse syndrome former (ISF) in the source decoder to efficiently exploit an existing linear channel code without the need to modify the code structure or the decoding strategy. For most channel codes, the construction of SF-ISF pairs is a light task. For parallelly and serially concatenated codes and particularly parallel and serial turbo codes where this appears less obvious, an efficient way for constructing linear complexity SF-ISF pairs is demonstrated. It is shown that the proposed SF-ISF approach is simple, provenly optimal, and generally applicable to any linear channel code. Simulation using conventional and asymmetric turbo codes demonstrates a compression rate that is only 0.06 bit/symbol from the theoretical limit, which is among the best results reported so far.

We describe a practical method for distributed compression of q-ary sources using multi-level seriallyconcatenated-accumulate codes. Our approach works well at high compression rates, and allows for graceful and incremental rate-adaptivity. Simulations show that the compression efficiency is near the information-theoretic limits for correlations between sources that obey a Gaussian or Laplacian distribution.

In this paper, we consider multiple access schemes with correlated sources. Distributed source coding is not used; rather, the correlation is exploited at the access point (AP). In particular, we assume that each source uses a channel code to transmit, through an additive white Gaussian noise (AWGN) channel, its information to the AP, where component decoders, associated with the sources, iteratively exchange soft information by taking into account the correlation. The key goal of this paper is to investigate whether there exist optimized channel codes for this scenario, i.e., channel codes which guarantee a desired performance level (in terms of average bit error rate,

In the context of Distributed Source Coding, we propose a low complexity algorithm for the estimation of the cross-over probability of the Binary Symmetric Channel (BSC) modeling the correlation between two binary sources. The coding is done with linear block codes. We propose a novel method to estimate prior to decoding and show that it is the Maximum Likelihood estimator of with respect to the syndromes of the correlated sources. The method can be utilized for the parameter estimation for channel coding of binary sources over the BSC.

We propose a new technique, compress-spreadforward (CSF), for high-performance wireless streaming from two base stations in parallel. CSF uses multiterminal source coding for efficient source compression and complete complementary sequences for error-free multiple access and synchronization. Our practical design shows significant performance gains due to spatial diversity and distributed source coding.

Communication of quantized information is frequently followed by a computation. We consider situations of distributed functional scalar quantization: distributed scalar quantization of (possibly correlated) sources followed by centralized computation of a function. Under smoothness conditions on the sources and function, companding scalar quantizer designs are developed to minimize mean-squared error (MSE) of the computed function as the quantizer resolution is allowed to grow. Striking improvements over quantizers designed without consideration of the function are possible and are larger in the entropy-constrained setting than in the fixed-rate setting. As extensions to the basic analysis, we characterize a large class of functions for which regular quantization suffices, consider certain functions for which asymptotic optimality is achieved without arbitrarily fine quantization, and allow limited collaboration between source encoders. In the entropy-constrained setting, a single bit per sample communicated between encoders can have an arbitrarily-large effect on functional distortion. In contrast, such communication has very little effect in the fixed-rate setting.

In a multi-camera setup, inter-sensor statistical redundancy should be eliminated most significantly to achieve higher compression efficiency. This consequently saves the required bandwidth for the resultant piece of information coming out of a camera sensor network. In this research work, Moving Picture Expert Group (MPEG) a video compression standard has been extended to eliminate inter-sensor statistical redundancy for a multi-camera setup. For the formulation of results from all aspects, two strategies have been designed for inter-sensor communication. Moreover system is designed to work under two working modes (named as Scenario-A and Scenario-B). Results formulated in graphical formats show the system performance for both communication strategies under both working modes. Overall system performnace higher compression gains are obtained at lower bitrates.

We consider the distributed source coding problem in which correlated data picked up by scattered sensors has to be encoded separately and transmitted to a common receiver, subject to a rate-distortion constraint. Although near-to-optimal solutions based on Turbo and LDPC codes exist for this problem, in most cases the proposed techniques do not scale to networks of hundreds of sensors. We present a scalable solution based on the following key elements: (a) distortion-optimized index assignments for low-complexity distributed quantization, (b) source-optimized hierarchical clustering based on the Kullback-Leibler distance and (c) sum-product decoding on specific factor graphs exploiting the correlation of the data.

This paper presents a distributed coding scheme for the representation of 3D scenes captured by stereo omnidirectional cameras. We consider a scenario where images captured from two different viewpoints are encoded independently, with a balanced rate distribution among the different cameras. The distributed coding is built on multiresolution representation and partitioning of the visual information in each camera. The encoder transmits one partition after entropy coding, as well as the syndrome bits resulting from the channel encoding of the other partition. The decoder exploits the intra-view correlation and attempts to reconstruct the source image by combination of the entropy-coded partition and the syndrome information. At the same time, it exploits the interview correlation using motion estimation between images from different cameras. Experiments demonstrate that the distributed coding solution performs better than a scheme where images are handled independently, and that the coding rate stays balanced between encoders.

Multiview video refers to the simultaneous capturing of multiple video views with an array of closely spaced cameras. In an interactive multiview video streaming (IMVS) system, a client can play back the content in time in a single view, and may observe a scene of interest by switching to different viewpoints. Users independently choose their own view navigation paths through the high-dimensional multiview data. Distributed servers are deployed to collaboratively replicate video content in order to support user scalability. Such a system typically presents challenges in both coding and content replication. In coding, the multiview video must be encoded in order to support efficient viewswitching and distributed replication. In content replication, it is important to decide which data blocks to store at each server to facilitate view-switches at any time. In this paper, we co-design a coding structure and a distributed content replication strategy. First, we propose a coding structure based on redundant P-frames and distributed source coding (DSC) frames to achieve efficiency in coding, view switches and content replication. We then propose a heuristic-based distributed and cooperative replication strategy to take advantage of the correlation between the multiple views for resource-effective content delivery. Simulation results show that our coding and replication codesign is cost-effective in supporting IMVS services.

7
th International Conference on Signal Processing and Pattern Recognition (SIPR 2021) is a
forum for presenting new advances and research results in the fields of Digital Processing and
Pattern Recognition. The conference will bring together leading researchers, engineers and
scientists in the domain of interest from around the world.
Authors are solicited to contribute to the conference by submitting articles that illustrate research
results, projects, surveying works and industrial experiences.

This paper investigates the optimality of the binning approach in distributed source coding for both uniform and nonuniform sources. While the algebraic binning scheme is optimal for uniform sources both asymptotically and at finite lengths, it is shown that the optimality holds only asymptotically for nonuniform sources. Highperformance turbo codes are used with the binning scheme on several source distributions to quantify how close they can get to the theoretical limit with relatively large block sizes. For nonuniform sources, optimal code design and variable-length bin-indexes are exploited as a useful extension to the conventional binning scheme. It is shown that the two strategies combined can improve the compression rate by as much as 0.22 bit/symbol for highly biased sources.

In contrast to traditional predictive coding, Wyner-Ziv video coding enables low-cost encoding architectures, in which the computationally expensive tasks for performing motion estimation are shifted to the decoder-side. In Wyner-Ziv video coding, side-information generation is a key aspect profoundly affecting the compression capacity of the system. This paper presents a novel technique which enables side-information refinement after DC coefficient band decoding in a transform-domain Wyner-Ziv video codec. The proposed side-information refinement approach performs overlapped block motion estimation and compensation, utilizing multi-hypothesis pixel-based prediction. The experimental results show that the presented Wyner-Ziv video codec incorporating the proposed technique yields significant and systematic compression gains of up to 23.22% with respect to the state-of-the-art DISCOVER codec.

We address the problem of compressing correlated distributed sources, i.e., correlated sources which are not co-located or which cannot cooperate to directly exploit their correlation. We consider the related problem of compressing a source which is correlated with another source that is available only at the decoder. This problem has been studied in the information theory literature under the name of the Slepian-Wolf (1973) source coding problem for the lossless coding case, and as "rate-distortion with side information" for the lossy coding case. We provide a constructive practical framework based on algebraic trellis codes dubbed as DIstributed Source Coding Using Syndromes (DISCUS), that can be applicable in a variety of settings. Simulation results are presented for source coding of independent and identically distributed (i.i.d.) Gaussian sources with side information available at the decoder in the form of a noisy version of the source to be coded. Our results reveal the promise of this approach: using trellis-based quantization and coset construction, the performance of the proposed approach is 2-5 dB from the Wyner-Ziv (1976) bound.

In this two-part paper, we present a new achievable rate region for the general n-channel symmetric multiple descriptions problem. In part I, inspired by the concept of maximum-distance separable (MDS) erasure channel codes, we consider a special case of this rate region, where the source is encoded into n descriptions each with rate R. These descriptions are transmitted over n bandwidth constrained and errorless channels. During transmission, a subset of these channels can break down, thus erasing the corresponding descriptions. The decoder is interested in recovering the source with the reception of at least k descriptions. Thus, the encoder is allowed to sample only one realization of this breakdown process during the entire transmission. For Gaussian sources, we have the following interesting result: when any k descriptions arrive, the achievable distortion exactly matches the optimal distortion-rate performance corresponding to a source rate of kR bits; with the reception of any m > k descriptions, the source reconstruction quality is strictly better, the improvement being nearly linear in the number of descriptions received.

This paper considers the use of punctured quasi-arithmetic (QA) codes for the Slepian-Wolf problem. These entropy codes are defined by finite state machines for memory-less and first-order memory sources. Puncturing an entropy coded bit-stream leads to an ambiguity at the decoder side. The decoder makes use of a correlated version of the original in order to remove this ambiguity. A complete DSC scheme based on QA encoding with side information at the decoder is presented. The proposed scheme is adapted to memoryless and first-order memory sources. Simulation results reveal that the proposed scheme is efficient in terms of decoding performance for short sequences compared to well-known DSC using channel codes.

A variable rate Slepian-Wolf (SW) code is constructed which is vital for wireless sensor network applications. A practical scheme to construct SW codes is to use the syndrome of a channel code as a compressed representation of a codeword in presence of a side information [3]. The proposed solution is based on an efficient and practical algorithm to compute the syndrome of rate-compatible convolutional codes (RCPC). By using this algorithm, there is no need to compute the syndrome of punctured version of the mother code for each puncturing matrix which is complex. Instead, the the syndrome of the punctured code is designed to be the punctured version of the syndrome of the mother code using the same pattern of puncturing. The algorithm is general for all convolutional codes in Z q . The strategy is also generalized for parallel and serial concatenated convolutional codes.

A flexible rate Slepian-Wolf (SW) code is constructed, which is vital for wireless sensor network applications. The proposed solution is based on an efficient and practical algorithm to compute the syndrome of the rate-compatible convolutional codes (RCPC). Using this algorithm, there is no need to compute the syndrome of punctured version of the mother code for each puncturing matrix, which is complex. Instead, the syndrome of the punctured code is the punctured version of the syndrome of the mother code using the same pattern of puncturing. The algorithm is general for all convolutional codes in Zq. The strategy is also generalized for parallel and serial concatenated convolutional codes. For the cases, where the dependencies among sources are modeled as a virtual discrete channel, a simplified decoding scheme is suggested. This method is generalized to achieve all points on the SW boundary using a simple code design technique. Simulation results demonstrate the performance and effectiveness of the proposed methods.

The problem of sampling a discrete-time sequence of spatially bandlimited fields with a bounded dynamic range, in a distributed, communication-constrained, processing environment is addressed. A central unit, having access to the data gathered by a dense network of fixed-precision sensors, operating under stringent inter-node communication constraints, is required to reconstruct the field snapshots to maximum accuracy. Both deterministic and stochastic field models are considered. For stochastic fields, results are established in the almost-sure sense. The feasibility of having a flexible tradeoff between the oversampling rate (sensor density) and the analog-to-digital converter (ADC) precision, while achieving an exponential accuracy in the number of bits per Nyquist-interval per snapshot is demonstrated. This exposes an underlying ``conservation of bits'' principle: the bit-budget per Nyquist-interval per snapshot (the rate) can be distributed along the amplitude axis (sensor-precision) and space (sensor density) in an almost arbitrary discrete-valued manner, while retaining the same (exponential) distortion-rate characteristics. Achievable information scaling laws for field reconstruction over a bounded region are also derived: With N one-bit sensors per Nyquist-interval, $\Theta(\log N)$ Nyquist-intervals, and total network bitrate $R_{net} = \Theta((\log N)^2)$ (per-sensor bitrate $\Theta((\log N)/N)$), the maximum pointwise distortion goes to zero as $D = O((\log N)^2/N)$ or $D = O(R_{net} 2^{-\beta \sqrt{R_{net}}})$. This is shown to be possible with only nearest-neighbor communication, distributed coding, and appropriate interpolation algorithms. For a fixed, nonzero target distortion, the number of fixed-precision sensors and the network rate needed is always finite.

Communication of quantized information is frequently followed by a computation. We consider situations of distributed functional scalar quantization: distributed scalar quantization of (possibly correlated) sources followed by centralized computation of a function. Under smoothness conditions on the sources and function, companding scalar quantizer designs are developed to minimize mean-squared error (MSE) of the computed function as the quantizer resolution is allowed to grow. Striking improvements over quantizers designed without consideration of the function are possible and are larger in the entropy-constrained setting than in the fixed-rate setting. As extensions to the basic analysis, we characterize a large class of functions for which regular quantization suffices, consider certain functions for which asymptotic optimality is achieved without arbitrarily fine quantization, and allow limited collaboration between source encoders. In the entropy-constrained setting, a single bit per sample communicated between encoders can have an arbitrarily-large effect on functional distortion. In contrast, such communication has very little effect in the fixed-rate setting.

Suppose a function of N real source variables X N 1 = (X 1 , X 2 , . . . , X N ) is desired at a destination constrained to receive a limited number of bits. If the result of evaluating the function, Y = G(X N 1 ), can be itself encoded, this is the optimal strategy-the origin of Y becomes irrelevant to the communication problem. We consider two alternative scenarios: distributed quantization, in which each X i must be separately encoded; and linear transform coding of X N 1 . Optimal fixed-and variable-rate scalar quantizers are derived under the conventional assumptions of high-resolution quantization theory, and we find optimal transforms for transform coding. For certain classes of functions, examples demonstrate large improvements over using quantizers designed to minimize distortion of the X i s.

A Slepian-Wolf coding scheme for compressing two uniform memoryless binary sources using a single channel code that can achieve arbitrary rate allocation among encoders was outlined in the work of Pradhan and Ramchandran. Inspired by this work, we address the problem of practical code design for general multiterminal lossless networks where multiple memoryless correlated binary sources are separately compressed and sent; each decoder receives a set of compressed sources and attempts to jointly reconstruct them. First, we propose a near-lossless practical code design for the Slepian-Wolf system with multiple sources. For two uniform sources, if the code approaches the capacity of the channel that models the correlation between the sources, then the system will approach the theoretical limit. Thus, the great advantage of this design method is its possibility to approach the theoretical limits with a single channel code for any rate allocation among the encoders. Based on Slepian-Wolf code constructions, we continue with providing practical designs for the general lossless multiterminal network which consists of arbitrary number of encoders and decoders. Using irregular repeat-accumulate and turbo codes in our designs, we obtain the best results reported so far and almost reach the theoretical bounds.

Distributed source coding (DSC) has recently been considered as an efficient approach to data compression in wireless sensor networks (WSN). Using this coding method multiple sensor nodes compress their correlated observations without inter-node communications. Therefore energy and bandwidth can be efficiently saved. In this paper, we investigate a random-binning based DSC scheme for remote source estimation in WSN and its

Abstract-We consider the problem of reconstructing a de-terministic data field from binary quantized noisy observations of sensors randomly deployed over the field domain. Our focus is on the extremes of lack of control in the sensor deployment, arbitrariness and lack of knowledge of the ...

ó In a typical sensor network scenario a goal is to monitor a spatio-temporal process through a number of inexpensive sensing nodes, the key parameter being the delity at which the process has to be estimated at distant locations. We study such a scenario in which multiple encoders transmit their correlated data at nite rates to a distant and common decoder. In particular, we derive inner and outer bounds on the rate region for the random eld to be estimated with a given mean distortion.

The lifetime calculation of large dense sensor networks with fixed energy resources and the remaining residual energy have shown that for a constant energy resource in a sensor network the fault rate at the cluster head is network size invariant when using the network layer with no MAC losses. Even after increasing the battery capacities in the nodes the total lifetime does not increase after a max limit of 8 times. As this is a serious limitation lots of research has been done at the MAC layer which allows to adapt to the specific connectivity, traffic and channel polling needs for sensor networks. There have been lots of MAC protocols which allow to control the channel polling of new radios which are available to sensor nodes to communicate. This further reduces the communication overhead by idling and sleep scheduling thus extending the lifetime of the monitoring application. We address the two issues which effects