This work studies point-to-point, multiple access, and random access lossless source coding in the finite-blocklength regime. In each scenario, a random coding technique is developed and used to analyze third-order coding performance. Asymptotic results include a third-order characterization of the Slepian-Wolf rate region with an improved converse that relies on a connection to composite hypothesis testing. For dependent sources, the result implies that the independent encoders used by Slepian-Wolf codes can achieve the same third-order-optimal performance as a single joint encoder. The concept of random access source coding is introduced to generalize multiple access (Slepian-Wolf) source coding to the case where encoders decide independently whether or not to participate and the set of participating encoders is unknown {\em a priori} to both the encoders and the decoder. The proposed random access source coding strategy employs rateless coding with scheduled feedback. A random coding argument proves the existence of a single deterministic code of this structure that simultaneously achieves the third-order-optimal Slepian-Wolf performance for each possible active encoder set.
We address the recently suggested problem of causal lossless coding of a randomly arriving source samples. We construct variable-to-fixed coding schemes and show that they outperform the previously considered fixed-to-variable schemes when traffic is high both in terms of delay and Age of Information by appealing to tools from queueing theory. We supplement our theoretical bounds with numerical simulations.
A general lossless joint source-channel coding scheme based on linear codes is proposed and then analyzed in this paper. It is shown that a linear code with good joint spectrum can be used to establish limit-approaching joint source-channel coding schemes for arbitrary sources and channels, where the joint spectrum of the code is a generalization of the input-output weight distribution.
This paper deals with a coding problem called complementary delivery, where messages from two correlated sources are jointly encoded and each decoder reproduces one of two messages using the other message as the side information. Both lossless and lossy universal complementary delivery coding schemes are investigated. In the lossless case, it is demonstrated that a universal complementary delivery code can be constructed by only combining two Slepian-Wolf codes. Especially, it is shown that a universal lossless complementary delivery code, for which error probability is exponentially tight, ca…
Motivated from the fact that universal source coding on countably infinite alphabets is not feasible, this work introduces the notion of almost lossless source coding. Analog to the weak variable-length source coding problem studied by Han (IEEE TIT, 2000, 46, 1217-1226), almost lossless source coding aims at relaxing the lossless block-wise assumption to allow an average per-letter distortion that vanishes asymptotically as the block-length tends to infinity. In this setup, we show on one hand that Shannon entropy characterizes the minimum achievable rate (similarly to the case of finite alph…
The order of letters is not always relevant in a communication task. This paper discusses the implications of order irrelevance on source coding, presenting results in several major branches of source coding theory: lossless coding, universal lossless coding, rate-distortion, high-rate quantization, and universal lossy coding. The main conclusions demonstrate that there is a significant rate savings when order is irrelevant. In particular, lossless coding of n letters from a finite alphabet requires Theta(log n) bits and universal lossless coding requires n + o(n) bits for many countable alpha…
This paper presents prefix codes which minimize various criteria constructed as a convex combination of maximum codeword length and average codeword length or maximum redundancy and average redundancy, including a convex combination of the average of an exponential function of the codeword length and the average redundancy. This framework encompasses as a special case several criteria previously investigated in the literature, while relations to universal coding is discussed. The coding algorithm derived is parametric resulting in re-adjusting the initial source probabilities via a weighted pr…
The problem of lossless fixed-rate streaming coding of discrete memoryless sources with side information at the decoder is studied. A random time-varying tree-code is used to sequentially bin strings and a Stack Algorithm with a variable bias uses the side information to give a delay-universal coding system for lossless source coding with side information. The scheme is shown to give exponentially decaying probability of error with delay, with exponent equal to Gallager's random coding exponent for sources with side information. The mean of the random variable of computation for the stack deco…
Given a private source of information, $X^n$ and a public correlated source, $Y^n$, we study the problem of encoding the two-dimensional source $(X^n, Y^n)$ into an index $J$ such that a remote party, knowing $J$ and some external side information $Z^n$, can losslessly recover $Y^n$ while any eavesdropper knowing $J$ and possibly a correlated side information $E^n$ can retrieve very little information about $X^n$. We give general converse results for the amount of information about $X^n$ that might be leaked in such systems and and also achievability results that are optimal in some special ca…
Motivated by the question of whether the recently introduced Reduced Cutset Coding (RCC) offers rate-complexity performance benefits over conventional context-based conditional coding for sources with two-dimensional Markov structure, this paper compares several row-centric coding strategies that vary in the amount of conditioning as well as whether a model or an empirical table is used in the encoding of blocks of rows. The conclusion is that, at least for sources exhibiting low-order correlations, 1-sided model-based conditional coding is superior to the method of RCC for a given constraint …
The penalty incurred by imposing a finite delay constraint in lossless source coding of a memoryless source is investigated. It is well known that for the so-called block-to-variable and variable-to-variable codes, the redundancy decays at best polynomially with the delay, where in this case the delay is identified with the source block length or maximal source phrase length, respectively. In stark contrast, it is shown that for sequential codes (e.g., a delay-limited arithmetic code) the redundancy can be made to decay exponentially with the delay constraint. The corresponding redundancy-dela…
Distributed source coding is traditionally viewed in the block coding context -- all the source symbols are known in advance at the encoders. This paper instead considers a streaming setting in which iid source symbol pairs are revealed to the separate encoders in real time and need to be reconstructed at the decoder with some tolerable end-to-end delay using finite rate noiseless channels. A sequential random binning argument is used to derive a lower bound on the error exponent with delay and show that both ML decoding and universal decoding achieve the same positive error exponents inside t…
We consider a real-time streaming source coding system in which an encoder observes a sequence of randomly arriving symbols from an i.i.d. source, and feeds binary codewords to a FIFO buffer that outputs one bit per time unit to a decoder. Each source symbol represents a status update by the source, and the timeliness of the system is quantified by the age of information (AoI), defined as the time difference between the present time and the generation time of the most up-to-date symbol at the output of the decoder. When the FIFO buffer is allowed to be empty, we propose an optimal prefix-free …
A general lossless joint source-channel coding (JSCC) scheme based on linear codes and random interleavers for multiple-access channels (MACs) is presented and then analyzed in this paper. By the information-spectrum approach and the code-spectrum approach, it is shown that a linear code with a good joint spectrum can be used to establish limit-approaching lossless JSCC schemes for correlated general sources and general MACs, where the joint spectrum is a generalization of the input-output weight distribution. Some properties of linear codes with good joint spectra are investigated. A formula …
Tight bounds for several symmetric divergence measures are derived in terms of the total variation distance. It is shown that each of these bounds is attained by a pair of 2 or 3-element probability distributions. An application of these bounds for lossless source coding is provided, refining and improving a certain bound by Csiszár. Another application of these bounds has been recently introduced by Yardi. et al. for channel-code detection.
Depth coding in 3D-HEVC for the multiview video plus depth (MVD) architecture (i) deforms object shapes due to block-level edge-approximation; (ii) misses an opportunity for high compressibility at near-lossless quality by failing to exploit strong homogeneity (clustering tendency) in depth syntax, motion vector components, and residuals at frame-level; and (iii) restricts interactivity and limits responsiveness of independent use of depth information for "non-viewing" applications due to texture-depth coding dependency. This paper presents a standalone depth sequence coder, which operates in …
In this paper we consider lossless source coding for a class of sources specified by the total variational distance ball centred at a fixed nominal probability distribution. The objective is to find a minimax average length source code, where the minimizers are the codeword lengths -- real numbers for arithmetic or Shannon codes -- while the maximizers are the source distributions from the total variational distance ball. Firstly, we examine the maximization of the average codeword length by converting it into an equivalent optimization problem, and we give the optimal codeword lenghts via a w…
We examine lossless data compression from an average delay perspective. An encoder receives input symbols one per unit time from an i.i.d. source and submits binary codewords to a FIFO buffer that transmits bits at a fixed rate to a receiver/decoder. Each input symbol at the encoder is viewed as a status update by the source and the system performance is characterized by the status update age, defined as the number of time units (symbols) the decoder output lags behind the encoder input. An upper bound on the average status age is derived from the exponential bound on the probability of error …
Predictive coding is attractive for compression onboard of spacecrafts thanks to its low computational complexity, modest memory requirements and the ability to accurately control quality on a pixel-by-pixel basis. Traditionally, predictive compression focused on the lossless and near-lossless modes of operation where the maximum error can be bounded but the rate of the compressed image is variable. Rate control is considered a challenging problem for predictive encoders due to the dependencies between quantization and prediction in the feedback loop, and the lack of a signal representation th…
Data compression is an efficient technique to save data storage and transmission costs. However, traditional data compression methods always ignore the impact of user preferences on the statistical distributions of symbols transmitted over the links. Notice that the development of big data technologies and popularization of smart devices enable analyses on user preferences based on data collected from personal handsets. This paper presents a user preference aware lossless data compression method, termed edge source coding, to compress data at the network edge. An optimization problem is formul…
Inspired by the context of compressing encrypted sources, this paper considers the general tradeoff between rate, end-to-end delay, and probability of error for lossless source coding with side-information. The notion of end-to-end delay is made precise by considering a sequential setting in which source symbols are revealed in real time and need to be reconstructed at the decoder within a certain fixed latency requirement. Upper bounds are derived on the reliability functions with delay when side-information is known only to the decoder as well as when it is also known at the encoder. When th…
In this paper, we consider a class of multiterminal source coding problems, each subject to distortion constraints computed using a specific, entropy-based, distortion measure. We provide the achievable rate distortion region for two cases and, in so doing, we demonstrate a relationship between the lossy multiterminal source coding problems with our specific distortion measure and (1) the canonical Slepian-Wolf lossless distributed source coding network, and (2) the Ahlswede-Körner-Wyner source coding with side information problem in which only one of the sources is recovered losslessly.
This paper provides upper and lower bounds on the optimal guessing moments of a random variable taking values on a finite set when side information may be available. These moments quantify the number of guesses required for correctly identifying the unknown object and, similarly to Arikan's bounds, they are expressed in terms of the Arimoto-Rényi conditional entropy. Although Arikan's bounds are asymptotically tight, the improvement of the bounds in this paper is significant in the non-asymptotic regime. Relationships between moments of the optimal guessing function and the MAP error probabili…
In this paper we prove the separation of source-network coding and channel coding in wireline networks. For the purposes of this work, a wireline network is any network of independent, memoryless, point-to-point, finite-alphabet channels used to transmit dependent sources either losslessly or subject to a distortion constraint. In deriving this result, we also prove that in a general memoryless network with dependent sources, lossless and zero-distortion reconstruction are equivalent provided that the conditional entropy of each source given the other sources is non-zero. Furthermore, we exten…
This paper presents lossless prefix codes optimized with respect to a pay-off criterion consisting of a convex combination of maximum codeword length and average codeword length. The optimal codeword lengths obtained are based on a new coding algorithm which transforms the initial source probability vector into a new probability vector according to a merging rule. The coding algorithm is equivalent to a partition of the source alphabet into disjoint sets on which a new transformed probability vector is defined as a function of the initial source probability vector and a scalar parameter. The p…
University College London（伦敦大学学院）；University of Edinburgh（爱丁堡大学）
We generalize the 'bits back with ANS' method to time-series models with a latent Markov structure. This family of models includes hidden Markov models (HMMs), linear Gaussian state space models (LGSSMs) and many more. We provide experimental evidence that our method is effective for small scale models, and discuss its applicability to larger scale settings such as video compression.
The bits-back argument suggests that latent variable models can be turned into lossless compression schemes. Translating the bits-back argument into efficient and practical lossless compression schemes for general latent variable models, however, is still an open problem. Bits-Back with Asymmetric Numeral Systems (BB-ANS), recently proposed by Townsend et al. (2019), makes bits-back coding practically feasible for latent variable models with one latent layer, but it is inefficient for hierarchical latent variable models. In this paper we propose Bit-Swap, a new compression scheme that generali…
We consider multi-terminal source coding with a single encoder and multiple decoders where either the encoder or the decoders can take cost constrained actions which affect the quality of the side information present at the decoders. For the scenario where decoders take actions, we characterize the rate-cost trade-off region for lossless source coding, and give an achievability scheme for lossy source coding for two decoders which is optimum for a variety of special cases of interest. For the case where the encoder takes actions, we characterize the rate-cost trade-off for a class of lossless …
This work studies the problem of distributed compression of correlated sources with an action-dependent joint distribution. This class of problems is, in fact, an extension of the Slepian-Wolf model, but where cost-constrained actions taken by the encoder or the decoder affect the generation of one of the sources. The purpose of this work is to study the implications of actions on the achievable rates. In particular, two cases where transmission occurs over a rate-limited link are studied; case A for actions taken at the decoder and case B where actions are taken at the encoder. A complete sin…
University of Toronto（多伦多大学）；Vector Institute（向量研究所）；Facebook AI Research（脸书人工智能研究院）；University College London（伦敦大学学院）；University of Oxford（牛津大学）
Latent variable models have been successfully applied in lossless compression with the bits-back coding algorithm. However, bits-back suffers from an increase in the bitrate equal to the KL divergence between the approximate posterior and the true posterior. In this paper, we show how to remove this gap asymptotically by deriving bits-back coding algorithms from tighter variational bounds. The key idea is to exploit extended space representations of Monte Carlo estimators of the marginal likelihood. Naively applied, our schemes would require more initial bits than the standard bits-back coder,…
Beijing National Research Center for Information Science and Technology（北京信息科学与技术国家研究中心）；Tsinghua University（清华大学）
Soft compression is a lossless image compression method, which is committed to eliminating coding redundancy and spatial redundancy at the same time by adopting locations and shapes of codebook to encode an image from the perspective of information theory and statistical distribution. In this paper, we propose a new concept, compressible indicator function with regard to image, which gives a threshold about the average number of bits required to represent a location and can be used for revealing the performance of soft compression. We investigate and analyze soft compression for binary image, …
Adapting Diffusion Language Models for Lossless Pixel-Level Image Transmission
College of Information Science and Electronic Engineering, Zhejiang University（浙江大学信息科学与电子工程学院）；Shenzhen CyberAray Network Technology Co., Ltd（深圳CyberAray网络技术有限公司）；School of Mechanical Engineering and Electronic Information, China University of Geosciences（中国地质大学（武汉）机械与电子信息学院）；Zhejiang Lab（浙江实验室）
Deep latent variable models have seen recent success in many data domains. Lossless compression is an application of these models which, despite having the potential to be highly useful, has yet to be implemented in a practical manner. We present `Bits Back with ANS' (BB-ANS), a scheme to perform lossless compression with latent variable models at a near optimal rate. We demonstrate this scheme by using it to compress the MNIST dataset with a variational auto-encoder model (VAE), achieving compression rates superior to standard methods with only a simple VAE. Given that the scheme is highly am…
This paper asks a basic question: how much training is required to beat a universal source coder? Traditionally, there have been two types of source coders: fixed, optimum coders such as Huffman coders; and universal source coders, such as Lempel-Ziv The paper considers a third type of source coders: learned coders. These are coders that are trained on data of a particular type, and then used to encode new data of that type. This is a type of coder that has recently become very popular for (lossy) image and video coding. The paper consider two criteria for performance of learned coders: the av…
We apply so-called tree straight-line programs to the problem of lossless compression of binary trees. We derive upper bound on the maximal pointwise redundancy (or worst-case redundancy) that improve previous bounds obtained by Zhang, Yang, and Kieffer using directed acyclic graphs. Using this, we obtain universal codes for new classes of structered tree sources.
Consider a sequence $X^n$ of length $n$ emitted by a Discrete Memoryless Source (DMS) with unknown distribution $p_X$. The objective is to construct a lossless source code that maps $X^n$ to a sequence $\widehat{Y}^m$ of length $m$ that is indistinguishable, in terms of Kullback-Leibler divergence, from a sequence emitted by another DMS with known distribution $p_Y$. The main result is the existence of a coding scheme that performs this task with an optimal ratio $m/n$ equal to $H(X)/H(Y)$, the ratio of the Shannon entropies of the two distributions, as $n$ goes to infinity. The coding scheme …
Slepian-Wolf theorem is a well-known framework that targets almost lossless compression of (two) data streams with symbol-by-symbol correlation between the outputs of (two) distributed sources. However, this paper considers a different scenario which does not fit in the Slepian-Wolf framework. We consider two identical but spatially separated sources. We wish to study the universal compression of a sequence of length $n$ from one of the sources provided that the decoder has access to (i.e., memorized) a sequence of length $m$ from the other source. Such a scenario occurs, for example, in the u…
We consider a system in which two nodes take correlated measurements of a random source with time-varying and unknown statistics. The observations of the source at the first node are to be losslessly replicated with a given probability of outage at the second node, which receives data from the first node over a constant-rate errorless channel. We develop a system and associated strategies for joint distributed source coding (encoding and decoding) and transmission control in order to achieve low end-to-end delay. Slepian-Wolf coding in its traditional form cannot be applied in our scenario, si…
In this paper, we propose {\em distributed network compression via memory}. We consider two spatially separated sources with correlated unknown source parameters. We wish to study the universal compression of a sequence of length $n$ from one of the sources provided that the decoder has access to (i.e., memorized) a sequence of length $m$ from the other source. In this setup, the correlation does not arise from symbol-by-symbol dependency of two outputs from the two sources (as in Slepian-Wolf setup). Instead, the two sequences are correlated because they are originated from the two sources wi…
In 2009, a lossless compression algorithm based on 1D chaotic maps known as Generalized Luröth Series (or GLS) has been proposed. This algorithm (GLS-coding) encodes the input message as a symbolic sequence on an appropriate 1D chaotic map (GLS) and the compressed file is obtained as the initial value by iterating backwards on the map. For ergodic sources, it was shown that GLS-coding achieves the best possible lossless compression (in the noiseless setting) bounded by Shannon entropy. However, in the presence of noise, even small errors in the compressed file leads to catastrophic decoding er…
We consider the problem of zero error source coding with limited feedback when side information is present at the receiver. First, we derive an achievable rate region for arbitrary joint distributions on the source and the side information. When all source pairs of source and side information symbols are observable with non-zero probability, we show that this characterization gives the entire rate region. Next, we demonstrate a class of sources for which asymptotically zero feedback suffices to achieve zero-error coding at the rate promised by the Slepian-Wolf bound for asymptotically lossless…
Linear encoders with good joint spectra are suitable candidates for optimal lossless joint source-channel coding (JSCC), where the joint spectrum is a variant of the input-output complete weight distribution and is considered good if it is close to the average joint spectrum of all linear encoders (of the same coding rate). In spite of their existence, little is known on how to construct such encoders in practice. This paper is devoted to their construction. In particular, two families of linear encoders are presented and proved to have good joint spectra. The first family is derived from Gabi…
A technique of lossless compression via substring enumeration (CSE) attains compression ratios as well as popular lossless compressors for one-dimensional (1D) sources. The CSE utilizes a probabilistic model built from the circular string of an input source for encoding the source.The CSE is applicable to two-dimensional (2D) sources such as images by dealing with a line of pixels of 2D source as a symbol of an extended alphabet. At the initial step of the CSE encoding process, we need to output the number of occurrences of all symbols of the extended alphabet, so that the time complexity incr…
This paper proves the separation between source-network coding and channel coding in networks of noisy, discrete, memoryless channels. We show that the set of achievable distortion matrices in delivering a family of dependent sources across such a network equals the set of achievable distortion matrices for delivering the same sources across a distinct network which is built by replacing each channel by a noiseless, point-to-point bit-pipe of the corresponding capacity. Thus a code that applies source-network coding across links that are made almost lossless through the application of independ…
This paper studies an almost-lossless source-channel coding scheme in which source messages are assigned to different classes and encoded with a channel code that depends on the class index. The code performance is analyzed by means of random-coding error exponents and validated by simulation of a low-complexity implementation using existing source and channel codes. While each class code can be seen as a concatenation of a source code and a channel code, the overall performance improves on that of separate source-channel coding and approaches that of joint source-channel coding when the numbe…
Locally decodable channel codes form a special class of error-correcting codes with the property that the decoder is able to reconstruct any bit of the input message from querying only a few bits of a noisy codeword. It is well known that such codes require significantly more redundancy (in particular have vanishing rate) compared to their non-local counterparts. In this paper, we define a dual problem, i.e. locally decodable source codes (LDSC). We consider both almost lossless (block error) and lossy (bit error) cases. In almost lossless case, we show that optimal compression (to entropy) is…
Polar codes, introduced recently by Arıkan, are the first family of codes known to achieve capacity of symmetric channels using a low complexity successive cancellation decoder. Although these codes, combined with successive cancellation, are optimal in this respect, their finite-length performance is not record breaking. We discuss several techniques through which their finite-length performance can be improved. We also study the performance of these codes in the context of source coding, both lossless and lossy, in the single-user context as well as for distributed applications.
We determine the rate region of the vector Gaussian one-helper source-coding problem under a covariance matrix distortion constraint. The rate region is achieved by a simple scheme that separates the lossy vector quantization from the lossless spatial compression. The converse is established by extending and combining three analysis techniques that have been employed in the past to obtain partial results for the problem.
We consider multiple description coding for the Gaussian source with K descriptions under the symmetric mean squared error distortion constraints, and provide an approximate characterization of the rate region. We show that the rate region can be sandwiched between two polytopes, between which the gap can be upper bounded by constants dependent on the number of descriptions, but independent of the exact distortion constraints. Underlying this result is an exact characterization of the lossless multi-level diversity source coding problem: a lossless counterpart of the MD problem. This connectio…
This paper deals with a universal coding problem for a certain kind of multiterminal source coding network called a generalized complementary delivery network. In this network, messages from multiple correlated sources are jointly encoded, and each decoder has access to some of the messages to enable it to reproduce the other messages. Both fixed-to-fixed length and fixed-to-variable length lossless coding schemes are considered. Explicit constructions of universal codes and the bounds of the error probabilities are clarified by using methods of types and graph-theoretical analysis.
This paper deals with a universal coding problem for a certain kind of multiterminal source coding system that we call the complementary delivery coding system. In this system, messages from two correlated sources are jointly encoded, and each decoder has access to one of the two messages to enable it to reproduce the other message. Both fixed-to-fixed length and fixed-to-variable length lossless coding schemes are considered. Explicit constructions of universal codes and bounds of the error probabilities are clarified via type-theoretical and graph-theoretical analyses. [[Keywords]] multiterm…
Universal fixed-to-variable lossless source coding for memoryless sources is studied in the finite blocklength and higher-order asymptotics regimes. Optimal third-order coding rates are derived for general fixed-to-variable codes and for prefix codes. It is shown that the non-prefix Type Size code, in which codeword lengths are chosen in ascending order of type class size, achieves the optimal third-order rate and outperforms classical Two-Stage codes. Converse results are proved making use of a result on the distribution of the empirical entropy and Laplace's approximation. Finally, the fixed…
A new approach to data compression is developed and applied to multimedia content. This method separates messages into components suitable for both lossless coding and 'lossy' or statistical coding techniques, compressing complex objects by separately encoding signals and noise. This is demonstrated by compressing the most significant bits of data exactly, since they are typically redundant and compressible, and either fitting a maximally likely noise function to the residual bits or compressing them using lossy methods. Upon decompression, the significant bits are decoded and added to a noise…
A joint source-channel coding (JSCC) scheme based on hybrid digital/analog coding is proposed for the transmission of correlated sources over discrete-memoryless two-way channels (DM-TWCs). The scheme utilizes the correlation between the sources in generating channel inputs, thus enabling the users to coordinate their transmission to combat channel noise. The hybrid scheme also subsumes prior coding methods such as rate-one separate source-channel coding and uncoded schemes for two-way lossy transmission, as well as the correlation-preserving coding scheme for (almost) lossless transmission. M…
