Slepian-Wolf Rate Region Research Articles

Lossless Source Coding in the Point-to-Point, Multiple Access, and Random Access Scenarios

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.

Performance Analysis of Lossy Decode-and-Forward for Non-Orthogonal MARCs

Non-orthogonal transmission is considered to be one of the promising techniques for improving the throughput of the existing and future wireless communication networks. We concentrate on the transmission of both independent and correlated binary sources over a non-orthogonal multiple access relay channel (MARC), which consists of two sources, one relay, and one destination. The lossy decode-and-forward (DF), developed from the conventional DF, is adopted at the relay. Two time slots are required with non-orthogonal transmission over such network setup, while three time slots are required with the conventional orthogonal transmission. We analyze the outage probability of transmission of independent binary sources over the non-orthogonal MARC based on the theorem of multiple access channel (MAC) with a helper, which combines the Slepian-Wolf rate region and the MAC capacity region. For the performance verification, we implement a practical coding-decoding chain, which is applicable to the transmission of both independent and correlated binary sources. Exclusive-OR based multi-user complete decoding is introduced at the relay node, and iterative joint decoding is utilized at the destination by taking into consideration the estimated intra-link error probability and correlation information between the sources. The practical simulation results are well matched with the theoretical analyses.

Multiple Access Relay Channel With Relay-Sources Feedback

Feedback analysis on the rate region of multi-user channels is a problem of great importance in information and communication theory. In this paper, the Slepian-Wolf multiple access relay channel (SW-MARC) with relay-sources feedback is studied as a more general model of MARC where feedback outputs are taken into consideration. First, an inner bound on the capacity region of the discret alphabet and memoryless (DM) model of this channel (DM-SW-MARC) is obtained using partial decode and forward strategy. Second, an outer bound on the capacity region is derived by applying Fano’s inequality. Third, the DM results are extended to the continuous alphabet version, where an inner bound on the capacity region of the Gaussian MARC (GMARC) with relay-sources feedback is derived. Fourth, it is shown that our results include the important previous works on multiple-access channel with feedback (Cover-Leung rate region) and without feedback (Slepian-Wolf (SW) rate region, etc.) as special cases. Finally, we investigate the effect of feedback and show that the presence of feedback enables the sources to understand each other’s messages, which in turn allows the sources to cooperate to resolve the residual uncertainty at the receiver in an efficient way and at the same time, independent fresh information from the sources is superimposed upon the resolution information.

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.

Polar codes for distributed source coding

A polar coding method to construct a distributed source coding scheme which can achieve any point on the dominant face of the Slepian-Wolf rate region for sources with uniform marginals is proposed. Source encoding and decoding operations are performed using efficient algorithms which makes practical implementation feasible. Simulation results are given to exhibit the performance of the presented method.

Maximizing Gathered Samples in Wireless Sensor Networks with Slepian-Wolf Coding

We consider an energy constrained wireless sensor network, with arbitrary number of nodes, where source nodes utilize Slepian-Wolf (SW) coding before transmission to a joint decoder. We investigate optimal and near-optimal SW coding rates, transmit powers, and transmit durations that maximize the number of collected samples during the network lifetime, subject to channel capacity, SW rate region, and residual energy constraints. We find optimal (near-optimal) closed-form solutions in the absence (presence) of an energy constraint at the joint decoder. We take into account the energy consumption of SW encoding and decoding and communication circuitry. Numerical results demonstrate the effectiveness of the proposed optimization, especially when the joint decoder is not energy constrained.

LDPC code design for asynchronous Slepian-Wolf coding

We consider asynchronous Slepian-Wolf coding where the two encoders may not have completely accurate timing information to synchronize their individual block code boundaries, and propose LDPC code design in this scenario. A new information-theoretic coding scheme based on source splitting is provided, which can achieve the entire asynchronous Slepian-Wolf rate region. Unlike existing methods based on source splitting, the proposed scheme does not require common randomness at the encoder and the decoder, or the construction of super-letter from several individual symbols. We then design LDPC codes based on this new scheme, by applying the recently discovered source-channel code correspondence. Experimental results validate the effectiveness of the proposed method.

Distributed source coding using short to moderate length rate-compatible LDPC codes: the entire Slepian-Wolf rate region

In this paper, we propose a scheme for distributed source coding of correlated sources using a single systematic LDPC code. In particular, since we are interested in wireless sensor network applications, we consider LDPC codes with short to moderate lengths that achieve every arbitrary coding rate on the Slepian-Wolf rate region. We simplify the distributed source coding problem to the rate-compatible LDPC code design with an unequal error protection property. The decoders communicate to each other to exchange information bits prior to decoding. However, thereafter, each performs the decoding independently. Therefore, errors in one decoder do not affect the other one. The simulation results confirm that the gap from the theoretical limit remains almost the same for different rates on the Slepian-Wolf rate region. First, we consider two correlated sources. We show that our proposed scheme improves the performance of distributed source coding of two sources considerably. This benefit is more stressed for application with short to moderate length sequences. Then, we study distributed source coding of three sources. As a special case, we investigate three sources that are pairwise correlated with the same correlation probability. We show that the gap from the theoretical limit is smaller than that of previous work. We also investigate the distributed source coding of correlated sources when there is no prior knowledge of the correlation parameter at the time of code design. We note that although the proposed distributed source coding is well suited for sensor networks (where sequences with less than 10000 bits are used), the method can be generalized to other distributed source coding applications.

A general and optimal framework to achieve the entire rate region for Slepian–Wolf coding

This paper considers symmetric Slepian–Wolf (SW) coding of two memoryless binary symmetric sources. We propose a simple and general framework, termed the Symmetric SF–ISF Framework (SSIF), (i) which can be efficiently applied to any linear channel code, (ii) which incurs no rate loss when converting the channel code to the Slepian–Wolf code, and (iii) which can achieve an arbitrary point in the Slepian–Wolf rate region. The proposed SW encoder implements the binning approach through a syndrome former (SF). The proposed SW decoder performs optimal estimation by first recovering the difference pattern between the sources using a matching inverse syndrome former (ISF), and subsequently recovering individual source sequences through syndrome former partitioning. Through rigorous proof and discussion, we show that the proposed framework is capable of achieving any rate pair promised by the theory. Hamming codes, turbo product codes, turbo codes and LDPC codes are provided as examples to demonstrate the generality and efficiency of the framework.

Networked Slepian–Wolf: Theory, Algorithms, and Scaling Laws

Consider a set of correlated sources located at the nodes of a network, and a set of sinks that are the destinations for some of the sources. The minimization of cost functions which are the product of a function of the rate and a function of the path weight is considered, for both the data-gathering scenario, which is relevant in sensor networks, and general traffic matrices, relevant for general networks. The minimization is achieved by jointly optimizing a) the transmission structure, which is shown to consist in general of a superposition of trees, and b) the rate allocation across the source nodes, which is done by Slepian-Wolf coding. The overall minimization can be achieved in two concatenated steps. First, the optimal transmission structure is found, which in general amounts to finding a Steiner tree, and second, the optimal rate allocation is obtained by solving an optimization problem with cost weights determined by the given optimal transmission structure, and with linear constraints given by the Slepian-Wolf rate region. For the case of data gathering, the optimal transmission structure is fully characterized and a closed-form solution for the optimal rate allocation is provided. For the general case of an arbitrary traffic matrix, the problem of finding the optimal transmission structure is NP-complete. For large networks, in some simplified scenarios, the total costs associated with Slepian-Wolf coding and explicit communication (conditional encoding based on explicitly communicated side information) are compared. Finally, the design of decentralized algorithms for the optimal rate allocation is analyzed.