The problem of the universal compression of a sequence from a library of several small to moderate length sequences from similar context arises in many practical scenarios, such as the compression of the storage data and the Internet traffic. In such scenarios, it is often required to compress and decompress every sequence individually. However, the universal compression of the individual sequences suffers from significant redundancy overhead. In this paper, we aim at answering whether or not having a memory unit in the middle can result in a fundamental gain in the universal compression. We present the problem setup in the most basic scenario consisting of a server node $S$, a relay node $R$ (i.e., the memory unit), and a client node $C$. We assume that server $S$ wishes to send the sequence $x^n$ to the client $C$ who has never had any prior communication with the server, and hence, is not capable of memorization of the source context. However, $R$ has previously communicated with $S$ to forward previous sequences from $S$ to the clients other than $C$, and thus, $R$ has memorized a context $y^m$ shared with $S$. Note that if the relay node was absent the source could possibly apply universal compression to $x^n$ and transmit to $C$ whereas the presence of memorized context at $R$ can possibly reduce the communication overhead in $S$-$R$ link. In this paper, we investigate the fundamental gain of the context memorization in the memory-assisted universal compression of the sequence $x^n$ over conventional universal source coding by providing a lower bound on the gain of memory-assisted source coding.
This paper investigates a source coding problem in which two terminals communicating through a relay wish to estimate one another's source within some distortion constraint. The relay has access to side information that is correlated with the sources. Two different schemes based on the order of communication, \emph{distributed source coding/delivery} and \emph{two cascaded rounds}, are proposed and inner and outer bounds for the resulting rate-distortion regions are provided. Examples are provided to show that neither rate-distortion region includes the other one.
We present nonasymptotic bounds on the maximum coding rate achievable over a Rician block-fading channel for a fixed packet size and a fixed packet error probability. Our bounds, which apply to the scenario where no a priori channel state information is available at the receiver, allow one to quantify the tradeoff between the rate gains resulting from the exploitation of time-frequency diversity and the rate loss resulting from fast channel variations and pilot-symbol overhead.
We show how to protect a stream of quantum information from decoherence induced by a noisy quantum communication channel. We exploit preshared entanglement and a convolutional coding structure to develop a theory of entanglement-assisted quantum convolutional coding. Our construction produces a Calderbank-Shor-Steane (CSS) entanglement-assisted quantum convolutional code from two arbitrary classical binary convolutional codes. The rate and error-correcting properties of the classical convolutional codes directly determine the corresponding properties of the resulting entanglement-assisted quan…
The recent increase in number of wireless devices has been driven by the growing markets of smart homes and the Internet of Things (IoT). As a result, expanding and/or efficient utilization of the radio frequency (RF) spectrum is critical to accommodate such an increase in wireless bandwidth. Alternatively, recent free-space optical (FSO) communication technologies have demonstrated the feasibility of building WiFO, a high capacity indoor wireless network using the femtocell architecture. Since FSO transmission does not interfere with the RF signals, such a system can be integrated with the cu…
A novel Rateless-coding-assisted Multi-Packet Relaying (RMPR) protocol is proposed for large-size data spreading in mobile wireless networks. With this lightweight and robust protocol, the packet redundancy is reduced by a factor of $\sqrt n$, while the spreading time is reduced at least by a factor of $\ln (n)$. Closed-form bounds and explicit non-asymptotic results are presented, which are further validated through simulations. Besides, the packet duplication phenomenon in the network setting is analyzed for the first time.
Many applications require data processing to be performed on individual pieces of data which are of finite sizes, e.g., files in cloud storage units and packets in data networks. However, traditional universal compression solutions would not perform well over the finite-length sequences. Recently, we proposed a framework called memory-assisted universal compression that holds a significant promise for reducing the amount of redundant data from the finite-length sequences. The proposed compression scheme is based on the observation that it is possible to learn source statistics (by memorizing p…
Several studies have identified a significant amount of redundancy in the network traffic. For example, it is demonstrated that there is a great amount of redundancy within the content of a server over time. This redundancy can be leveraged to reduce the network flow by the deployment of memory units in the network. The question that arises is whether or not the deployment of memory can result in a fundamental improvement in the performance of the network. In this paper, we answer this question affirmatively by first establishing the fundamental gains of memory-assisted source compression and …
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…
The aim of this paper is to prove the achievability of fixed-rate universal coding problems by using our previously introduced notion of hash property. These problems are the fixed-rate lossless universal source coding problem and the fixed-rate universal channel coding problem. Since an ensemble of sparse matrices satisfies the hash property requirement, it is proved that we can construct universal codes by using sparse matrices.
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…
Consider a wireless broadcast device-to-device (D2D) network wherein users' devices are interested in receiving some popular files. Each user's device possesses part of the content which is acquired in previous transmissions and cooperates with others to recover the missing packets by exchanging Instantly Decodable Network Coding (IDNC) packets. Recently, a distributed solution, relying on a non-cooperative game-theoretic formulation, has been proposed to reduce the communication time for fully connected D2D networks, i.e., single-hop D2D networks. In this paper, we develop a distributed game-…
This work contains two main contributions concerning the asymmetric broadcast channel. The first is an analysis of the exact random coding error exponents for both users, and the second is the derivation of universal decoders for both users. These universal decoders are certain variants of the maximum mutual information (MMI) universal decoder, which achieve the corresponding random coding exponents of optimal decoding. In addition, we introduce some lower bounds, which involve optimization over very few parameters, unlike the original, exact exponents, which involve minimizations over auxilia…
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…
Recently, network coding technique has emerged as a promising approach that supports reliable transmission over wireless loss channels. In existing protocols where users have no interest in considering the encoded packets they had in coding or decoding operations, this rule is expensive and inefficient. This paper studies the impact of encoded packets in the reliable unicast network coding via some theoretical analysis. Using our approach, receivers do not only store the encoded packets they overheard, but also report these information to their neighbors, such that users enable to take account…
A multiterminal lossy coding problem, which includes various problems such as the Wyner-Ziv problem and the complementary delivery problem as special cases, is considered. It is shown that any point in the achievable rate-distortion region can be attained even if the source statistics are not known.
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.
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.
We consider a setting of Slepian--Wolf coding, where the random bin of the source vector undergoes channel coding, and then decoded at the receiver, based on additional side information, correlated to the source. For a given distribution of the randomly selected channel codewords, we propose a universal decoder that depends on the statistics of neither the correlated sources nor the channel, assuming first that they are both memoryless. Exact analysis of the random-binning/random-coding error exponent of this universal decoder shows that it is the same as the one achieved by the optimal maximu…
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…
This paper deals with the problem of universal lossless coding on a countable infinite alphabet. It focuses on some classes of sources defined by an envelope condition on the marginal distribution, namely exponentially decreasing envelope classes with exponent $α$. The minimax redundancy of exponentially decreasing envelope classes is proved to be equivalent to $\frac{1}{4 α\log e} \log^2 n$. Then a coding strategy is proposed, with a Bayes redundancy equivalent to the maximin redundancy. At last, an adaptive algorithm is provided, whose redundancy is equivalent to the minimax redundancy
In this paper, we consider the design of a new secrecy transmission scheme for a four-node relay-eavesdropper channel. The key idea of the proposed scheme is to combine noisy network coding with the interference assisted strategy for wiretap channel with a helping interferer. A new achievable secrecy rate is characterized for both discrete memoryless and Gaussian channels. Such a new rate can be viewed as a general framework, where the existing interference assisted schemes such as noisy-forwarding and cooperative jamming approaches can be shown as special cases of the proposed scheme. In addi…
We derive universal classical-quantum superposition coding and universal classical-quantum multiple access channel code by using generalized packing lemmas for the type method. Using our classical-quantum universal superposition code, we establish the capacity region of a classical-quantum compound broadcast channel with degraded message sets. Our universal classical-quantum multiple access channel codes have two types of codes. One is a code with joint decoding and the other is a code with separate decoding. The former universally achieves corner points of the capacity region and the latter u…
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…
We define an algorithm that parses multidimensional arrays sequentially into mainly unrepeated but nested multidimensional sub-arrays of increasing size, and show that the resulting sub-block pointer encoder compresses almost every realization of any finite-alphabet ergodic process on $\mathbb{Z}_{\geq0}^d$ to the entropy, in the limit.
Universal variable-to-fixed (V-F) length coding of $d$-dimensional exponential family of distributions is considered. We propose an achievable scheme consisting of a dictionary, used to parse the source output stream, making use of the previously-introduced notion of quantized types. The quantized type class of a sequence is based on partitioning the space of minimal sufficient statistics into cuboids. Our proposed dictionary consists of sequences in the boundaries of transition from low to high quantized type class size. We derive the asymptotics of the $ε$-coding rate of our coding scheme fo…
In this work, a new upper bound for average error probability of a two-user discrete memoryless (DM) multiple-access channel (MAC) is derived. This bound can be universally obtained for all discrete memoryless MACs with given input and output alphabets. This is the first bound of this type that explicitly uses the method of expurgation. It is shown that the exponent of this bound is greater than or equal to those of previously known bounds.
Recently, a coding technique called position-based coding has been used to establish achievability statements for various kinds of classical communication protocols that use quantum channels. In the present paper, we apply this technique in the entanglement-assisted setting in order to establish lower bounds for error exponents, lower bounds on the second-order coding rate, and one-shot lower bounds. We also demonstrate that position-based coding can be a powerful tool for analyzing other communication settings. In particular, we reduce the quantum simultaneous decoding conjecture for entangle…
We present a novel lossless universal source coding algorithm that uses parallel computational units to increase the throughput. The length-$N$ input sequence is partitioned into $B$ blocks. Processing each block independently of the other blocks can accelerate the computation by a factor of $B$, but degrades the compression quality. Instead, our approach is to first estimate the minimum description length (MDL) source underlying the entire input, and then encode each of the $B$ blocks in parallel based on the MDL source. With this two-pass approach, the compression loss incurred by using more…
In this paper, we first propose an universal polar coding scheme for parallel Gaussian channels with non-binary inputs. It is assumed that the encoder knows only the sum capacity of M parallel channels instead of the capacity of any single channel. By decomposing each parallel channel into T = [log2r] sub channels, we therefore obtain MT binary sub-channels. A super polar coding scheme that across all sub-channels is then proposed. This scheme can achieve the sum capacity when the block length is sufficiently large. We have also discussed the applications of parallel polar coding design for bo…
We consider a space communication network consisting of Geosynchronous Earth Orbit satellites (GEOSs) and Low Earth Orbit satellites (LEOSs). In case of no direct communication link between two GEOSs, the data exchange between them is through relay by the LEOSs. In particular, the source GEOS sends coded data to multiple LEOSs based on the distributed storage framework. The destination GEOS then retrieves certain amount of data from each LEOS for data reconstruction. For the GEOS-LEOS downlink, a regenerating-code-based transmission scheme is optimized to guarantee data reconstructability, whe…
We study the problem of universal decoding for unknown discrete memoryless channels in the presence of erasure/list option at the decoder, in the random coding regime. Specifically, we harness a universal version of Forney's classical erasure/list decoder developed in earlier studies, which is based on the competitive minimax methodology, and guarantees universal achievability of a certain fraction of the optimum random coding error exponents. In this paper, we derive an exact single-letter expression for the maximum achievable fraction. Examples are given in which the maximal achievable fract…
We consider wiretap channels with uncertainty on the eavesdropper channel under (i) noisy blockwise type II, (ii) compound, or (iii) arbitrarily varying models. We present explicit wiretap codes that can handle these models in a unified manner and only rely on three primitives, namely source coding with side information, universal hashing, and distribution approximation. Our explicit wiretap codes achieve the best known single-letter achievable rates, previously obtained non-constructively, for the models considered. Our results are obtained for strong secrecy, do not require a pre-shared secr…
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…
Beckman Institute（贝克曼研究所）；University of Illinois（伊利诺伊大学）
The problem of joint universal source coding and modeling, treated in the context of lossless codes by Rissanen, was recently generalized to fixed-rate lossy coding of finitely parametrized continuous-alphabet i.i.d. sources. We extend these results to variable-rate lossy block coding of stationary ergodic sources and show that, for bounded metric distortion measures, any finitely parametrized family of stationary sources satisfying suitable mixing, smoothness and Vapnik-Chervonenkis learnability conditions admits universal schemes for joint lossy source coding and identification. We also give…
This paper investigates universal polar coding schemes. In particular, a notion of ordering (called convolutional path) is introduced between probability distributions to determine when a polar compression (or communication) scheme designed for one distribution can also succeed for another one. The original polar decoding algorithm is also generalized to an algorithm allowing to learn information about the source distribution using the idea of checkers. These tools are used to construct a universal compression algorithm for binary sources, operating at the lowest achievable rate (entropy), wit…
Silva et al. proposed a universal secure network coding scheme based on MRD codes, which can be applied to any underlying network code. This paper considers a stronger eavesdropping model where the eavesdroppers possess the ability to re-select the tapping links during the transmission. We give a proof for the impossibility of attaining universal security against such adversaries using Silva et al.'s code for all choices of code parameters, even with restricted number of tapped links. We also consider the cases with restricted tapping duration and derive some conditions for this code to be sec…
Universal coding of integers~(UCI) is a class of variable-length code, such that the ratio of the expected codeword length to $\max\{1,H(P)\}$ is within a constant factor, where $H(P)$ is the Shannon entropy of the decreasing probability distribution $P$. However, if we consider the ratio of the expected codeword length to $H(P)$, the ratio tends to infinity by using UCI, when $H(P)$ tends to zero. To solve this issue, this paper introduces a class of codes, termed generalized universal coding of integers~(GUCI), such that the ratio of the expected codeword length to $H(P)$ is within a constan…
We study the problem of reducing the communication overhead from a noisy wire-tap channel or storage system where data is encoded as a matrix, when more columns (or their linear combinations) are available. We present its applications to reducing communication overheads in universal secure linear network coding and secure distributed storage with crisscross errors and erasures and in the presence of a wire-tapper. Our main contribution is a method to transform coding schemes based on linear rank-metric codes, with certain properties, to schemes with lower communication overheads. By applying t…
We prove a one-shot "minimax" converse bound for quantum channel coding assisted by positive partial transpose channels between sender and receiver. The bound is similar in spirit to the converse by Polyanskiy, Poor, and Verdu [IEEE Trans. Info. Theory 56, 2307-2359 (2010)] for classical channel coding, and also enjoys the saddle point property enabling the order of optimizations to be interchanged. Equivalently, the bound can be formulated as a semidefinite program satisfying strong duality. The convex nature of the bound implies channel symmetries can substantially simplify the optimization,…
This paper considers structure learning from data with $n$ samples of $p$ variables, assuming that the structure is a forest, using the Chow-Liu algorithm. Specifically, for incomplete data, we construct two model selection algorithms that complete in $O(p^2)$ steps: one obtains a forest with the maximum posterior probability given the data, and the other obtains a forest that converges to the true one as $n$ increases. We show that the two forests are generally different when some values are missing. Additionally, we present estimations for benchmark data sets to demonstrate that both algorit…
A solution to the problem of asymptotically optimum perfect universal steganography of finite memoryless sources with a passive warden is provided, which is then extended to contemplate a distortion constraint. The solution rests on the fact that Slepian's Variant I permutation coding implements first-order perfect universal steganography of finite host signals with optimum embedding rate. The duality between perfect universal steganography with asymptotically optimum embedding rate and lossless universal source coding with asymptotically optimum compression rate is evinced in practice by show…
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 $…
We consider nonparametric or universal sequential hypothesis testing problem when the distribution under the null hypothesis is fully known but the alternate hypothesis corresponds to some other unknown distribution. These algorithms are primarily motivated from spectrum sensing in Cognitive Radios and intruder detection in wireless sensor networks. We use easily implementable universal lossless source codes to propose simple algorithms for such a setup. The algorithms are first proposed for discrete alphabet. Their performance and asymptotic properties are studied theoretically. Later these a…
We consider a setup in which Alice selects a pdf $f$ from a set of prescribed pdfs $\mathscr{P}$ and sends a prefix-free codeword $W$ to Bob in order to allow him to generate a single instance of the random variable $X\sim f$. We describe a universal coding scheme for this setup and establish an upper bound on the expected codeword length when the pdf $f$ is bounded, orthogonally concave (which includes quasiconcave pdf), and has a finite first absolute moment. A dyadic decomposition scheme is used to express the pdf as a mixture of uniform pdfs over hypercubes. Alice randomly selects a hyperc…
The problem of joint universal source coding and modeling, addressed by Rissanen in the context of lossless codes, is generalized to fixed-rate lossy coding of continuous-alphabet memoryless sources. We show that, for bounded distortion measures, any compactly parametrized family of i.i.d. real vector sources with absolutely continuous marginals (satisfying appropriate smoothness and Vapnik--Chervonenkis learnability conditions) admits a joint scheme for universal lossy block coding and parameter estimation, and give nonasymptotic estimates of convergence rates for distortion redundancies and …
In entropy coding, universal coding of integers~(UCI) is a binary universal prefix code, such that the ratio of the expected codeword length to $\max\{1, H(P)\}$ is less than or equal to a constant expansion factor $K_{\mathcal{C}}$ for any probability distribution $P$, where $H(P)$ is the Shannon entropy of $P$. $K_{\mathcal{C}}^{*}$ is the infimum of the set of expansion factors. The optimal UCI is defined as a class of UCI possessing the smallest $K_{\mathcal{C}}^{*}$. Based on prior research, the range of $K_{\mathcal{C}}^{*}$ for the optimal UCI is $2\leq K_{\mathcal{C}}^{*}\leq 2.75$. Cu…
We investigate the Wyner-Ziv coding in which the statistics of the principal source is known but the statistics of the channel generating the side-information is unknown except that it is in a certain class. The class consists of channels such that the distortion between the principal source and the side-information is smaller than a threshold, but channels may be neither stationary nor ergodic. In this situation, we define a new rate-distortion function as the minimum rate such that there exists a Wyner-Ziv code that is universal for every channel in the class. Then, we show an upper bound an…
We consider a novel variant of $d$-semifaithful lossy coding in which the distortion measure is revealed only to the encoder and only at run-time, as well as an extension of it in which the distortion constraint $d$ is also revealed at run-time. Two forms of rate redundancy are used to analyze the performance, and achievability results of both a pointwise and minimax nature are demonstrated. The first coding scheme uses ideas from VC dimension and growth functions, the second uses appropriate quantization of the space of distortion measures, and the third relies on a random coding argument.
