Slepian-Wolf Region Research Articles

Performance analysis of one‐source‐with‐one‐helper transmission over shadowed κ$\kappa$‐μ$\mu$ fading multiple access channels

The performance of correlated sources transmission over multiple access shadowed κ $\kappa$ - μ $\mu$ fading channels is investigated, in which one of the correlated sources needs to be recovered at the destination, whereas the other serves as a helper. The sufficient condition for lossless coding is determined by the intersection of the modified Slepian–Wolf region and the multiple access channel region. The outage probability upper bounds are derived based on the sufficient condition, with the Gaussian codebook capacity and the constellation constrained capacity, respectively. The difference between the outage probabilities derived with the two kinds of capacities is found to be very minor, when the spectrum efficiency or source rate is low; however, with high spectrum efficiency or high source rate, such difference becomes significant. A closed-form outage approximation is also obtained at the high signal-to-noise ratio region. The accuracy of the analytical results is verified by the Monte-Carlo simulations. It is found that shadowing significantly affects the outage performance, however, it has no effect on the diversity gain. Furthermore, the power allocation between the source and the helper is studied to minimize the outage probability and it is found that generally more power should be allocated to the helper in the case with higher source-helper correlation.

Outage Probability of One-Source-With-One- Helper Sensor Systems in Block Rayleigh Fading Multiple Access Channels

Two correlated sources are transmitted over a block Rayleigh fading multiple access channel (MAC), where information recovery from only one of the sources is aimed at, and the other is used as a helper which helps recover the source sequences at the destination. In this article, the successful transmission is defined as in the case the transmission rates satisfy the intersection of both the MAC region and the Slepian-Wolf (SW) region with a helper, referred to as h-SW region, even though it is a sufficient condition. Then, the outage is defined as the average probability that the two regions do not have an intersection. The explicit expressions of the outage probability of the system are derived, in the form of multiple integrals with respect to the probability density function of instantaneous signal-to-noise ratios of each link. To have an in-depth insight regarding the contributions of some special cases to the successful transmission probability, the occurrence probabilities of these cases are also evaluated. The results indicate that outage probabilities decrease as the correlation between the source and helper information increases. The impacts of geometric gains of each link and the correlation of each link's fading variation are also considered. The most significant finding of this article is that h-SW over a MAC improves the throughput efficiency compared to the orthogonal transmission both in independent and correlated block Rayleigh fading channels without sacrificing the outage probability.

Generalized Compute-Compress-and-Forward

Compute-and-forward (CF) harnesses interference in wireless communications by exploiting structured coding. The key idea of CF is to compute integer combinations of code words from multiple source nodes, rather than to decode individual code words by treating others as noise. Compute-compress-and-forward (CCF) can further enhance the network performance by introducing compression operations at receivers. In this paper, we develop a more general compression framework, termed generalized CCF (GCCF), where the compression function involves the selection of message segments over finite fields. We show that GCCF achieves a broader compression rate region than CCF. We also compare our compression rate region with the fundamental Slepian–Wolf (SW) region. We show that GCCF is optimal in the sense of achieving the minimum total compression rate. We also establish the criteria under which GCCF achieves the SW region. In addition, we consider a two-hop relay network employing the GCCF scheme. We formulate a sum-rate maximization problem and develop an approximate algorithm to solve the problem. Numerical results are presented to demonstrate the performance superiority of GCCF over CCF and other schemes.

Achievable Moderate Deviations Asymptotics for Streaming Compression of Correlated Sources

Motivated by streaming multi-view video coding and wireless sensor networks, we consider the problem of blockwise streaming compression of a pair of correlated sources, which we term streaming Slepian-Wolf coding. We study the moderate deviations regime in which the rate pairs of a sequence of codes converge, along a straight line, to various points on the boundary of the Slepian-Wolf region at a speed slower than the inverse square root of the blocklength $n$, while the error probability decays subexponentially fast in $n$. Our main result focuses on directions of approaches to corner points of the Slepian-Wolf region. It states that for each correlated source and all corner points, there exists a non-empty subset of directions of approaches such that the moderate deviations constant (the constant of proportionality for the subexponential decay of the error probability) is enhanced (over the non-streaming case) by at least a factor of $T$, the block delay of decoding source block pairs. We specialize our main result to the setting of streaming lossless source coding and generalize this result to the setting where we have different delay requirements for each of the two source blocks. The proof of our main result involves the use of various analytical tools and amalgamates several ideas from the recent information-theoretic streaming literature. We adapt the so-called truncated memory encoding idea from Draper and Khisti (2011) and Lee, Tan, and Khisti (2016) to ensure that the effect of error accumulation is nullified in the limit of large blocklengths. We also adapt the use of the so-called minimum weighted empirical suffix entropy decoder which was used by Draper, Chang, and Sahai (2014) to derive achievable error exponents for symbolwise streaming Slepian-Wolf coding.

On Linear Coding over Finite Rings and Applications to Computing

This paper presents a coding theorem for linear coding over finite rings, in the setting of the Slepian–Wolf source coding problem. This theorem covers corresponding achievability theorems of Elias (IRE Conv. Rec. 1955, 3, 37–46) and Csiszár (IEEE Trans. Inf. Theory 1982, 28, 585–592) for linear coding over finite fields as special cases. In addition, it is shown that, for any set of finite correlated discrete memoryless sources, there always exists a sequence of linear encoders over some finite non-field rings which achieves the data compression limit, the Slepian–Wolf region. Hence, the optimality problem regarding linear coding over finite non-field rings for data compression is closed with positive confirmation with respect to existence. For application, we address the problem of source coding for computing, where the decoder is interested in recovering a discrete function of the data generated and independently encoded by several correlated i.i.d. random sources. We propose linear coding over finite rings as an alternative solution to this problem. Results in Körner–Marton (IEEE Trans. Inf. Theory 1979, 25, 219–221) and Ahlswede–Han (IEEE Trans. Inf. Theory 1983, 29, 396–411, Theorem 10) are generalized to cases for encoding (pseudo) nomographic functions (over rings). Since a discrete function with a finite domain always admits a nomographic presentation, we conclude that both generalizations universally apply for encoding all discrete functions of finite domains. Based on these, we demonstrate that linear coding over finite rings strictly outperforms its field counterpart in terms of achieving better coding rates and reducing the required alphabet sizes of the encoders for encoding infinitely many discrete functions.

On Rate Requirements for Achieving the Centralized Performance in Distributed Estimation

We consider a distributed parameter estimation problem, in which multiple terminals send messages related to their local observations using limited rates to a fusion center which obtains an estimate of a parameter related to the observations of all terminals. It is well known that if the transmission rates are in the Slepian–Wolf region, the fusion center can fully recover all observations and hence can construct an estimator having the same performance as that of the centralized case. One natural question is whether Slepian–Wolf rates are necessary to achieve the same estimation performance as that of the centralized case. In this paper, we show that the answer to this question is negative. We establish our result by explicitly constructing an asymptotically minimum variance unbiased estimator that has the same performance as that of the optimal estimator in the centralized case while using information rates less than the conditions required in the Slepian–Wolf rate region. The key idea is that, instead of aiming to recover the observations at the fusion center, we design universal schemes enabling the fusion center to compute a sufficient statistic using rates outside of the Selpian–Wolf region.

A Dichotomy of Functions in Distributed Coding: An Information Spectral Approach

The problem of distributed data compression for function computation is considered, where: 1) the function to be computed is not necessarily symbolwise function and 2) the information source has memory and may not be stationary nor ergodic. We introduce the class of smooth sources and give a sufficient condition on functions so that the achievable rate region for computing coincides with the Slepian-Wolf region (i.e., the rate region for reproducing the entire source) for any smooth sources. Moreover, for symbolwise functions, the necessary and sufficient condition for the coincidence is established. Our result for the full side-information case is a generalization of the result by Ahlswede and Csiszár to sources with memory; our dichotomy theorem is different from Han and Kobayashi's dichotomy theorem, which reveals an effect of memory in distributed function computation. All results are given not only for fixed-length coding but also for variable-length coding in a unified manner. Furthermore, for the full side-information case, the error probability in the moderate deviation regime is also investigated.

Slepian–Wolf Coding Over Cooperative Relay Networks

This paper deals with the problem of multicasting a set of discrete memoryless correlated sources (DMCS) over a cooperative relay network. Necessary conditions with cut-set interpretation are presented. A \emph{Joint source-Wyner-Ziv encoding/sliding window decoding} scheme is proposed, in which decoding at each receiver is done with respect to an ordered partition of other nodes. For each ordered partition a set of feasibility constraints is derived. Then, utilizing the sub-modular property of the entropy function and a novel geometrical approach, the results of different ordered partitions are consolidated, which lead to sufficient conditions for our problem. The proposed scheme achieves operational separation between source coding and channel coding. It is shown that sufficient conditions are indeed necessary conditions in two special cooperative networks, namely, Aref network and finite-field deterministic network. Also, in Gaussian cooperative networks, it is shown that reliable transmission of all DMCS whose Slepian-Wolf region intersects the cut-set bound region within a constant number of bits, is feasible. In particular, all results of the paper are specialized to obtain an achievable rate region for cooperative relay networks which includes relay networks and two-way relay networks.

Universal coding for the Slepian-Wolf data compression system and the strong converse theorem

Universal coding for the Slepian-Wolf (1973) data compression system is considered. We shall demonstrate based on a simple observation that the error exponent given by Csiszar and Korner (1980) for the universal coding system can strictly be sharpened in general for a region of relatively higher rates. This kind of observation can be carried over also to the case of lower rates outside the Slepian-Wolf region, which establishes the strong converse along with the optimal exponent.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A dichotomy of functions&amp;lt;tex&amp;gt;F(X, Y)&amp;lt;/tex&amp;gt;of correlated sources&amp;lt;tex&amp;gt;(X, Y)&amp;lt;/tex&amp;gt;

Consider separate encoding of correlated sources X^{n}=(X_{l}, \cdots ,X_{n}), Y^{n} = (Y_{l}, \cdots ,Y_{n}) for the decoder to reliably reproduce a function \{F(X_{i}, Y_{i})\}^{n}_{i=1} . We establish the necessary and sufficient condition for the set of all achievable rates to coincide with the Slepian-Wolf region whenever the probability density p(x,y) is positive for all (x,y) .