Quantized Network Coding for Correlated Sources

Non-adaptive joint source network coding of correlated sources is discussed in this paper. By studying the information flow in the network, we propose quantized network coding as an alternative for packet forwarding. This technique has both network coding and distributed source coding advantages, simultaneously. Quantized network coding is a combination of random linear network coding in the (infinite) field of real numbers and quantization to cope with the limited capacity of links. With the aid of the results in the literature of compressed sensing, we discuss theoretical and practical feasibility of quantized network coding in lossless networks. We show that, due to the nature of the field it operates on, quantized network coding can provide good quality decoding at a sink node with the reception of a reduced number of packets. Specifically, we discuss the required conditions on local network coding coefficients, by using restricted isometry property and suggest a design, which yields in appropriate linear measurements. Finally, our simulation results show the achieved gain in terms of delivery delay, compared to conventional routing based packet forwarding.Comment: Submitted for IEEE Transactions on Signal Processin

On the Capacity Improvement of Multicast Traffic with Network Coding

In this paper, we study the contribution of network coding (NC) in improving the multicast capacity of random wireless ad hoc networks when nodes are endowed with multi-packet transmission (MPT) and multi-packet reception (MPR) capabilities. We show that a per session throughput capacity of $\Theta(nT^{3}(n))$, where $n$ is the total number of nodes and T(n) is the communication range, can be achieved as a tight bound when each session contains a constant number of sinks. Surprisingly, an identical order capacity can be achieved when nodes have only MPR and MPT capabilities. This result proves that NC does not contribute to the order capacity of multicast traffic in wireless ad hoc networks when MPR and MPT are used in the network. The result is in sharp contrast to the general belief (conjecture) that NC improves the order capacity of multicast. Furthermore, if the communication range is selected to guarantee the connectivity in the network, i.e., $T(n)\ge \Theta(\sqrt{\log n/n})$, then the combination of MPR and MPT achieves a throughput capacity of $\Theta(\frac{\log^{{3/2}} n}{\sqrt{n}})$ which provides an order capacity gain of $\Theta(\log^2 n)$ compared to the point-to-point multicast capacity with the same number of destinations

Combination Networks with or without Secrecy Constraints: The Impact of Caching Relays

This paper considers a two-hop network architecture known as a combination network, where a layer of relay nodes connects a server to a set of end users. In particular, a new model is investigated where the intermediate relays employ caches in addition to the end users. First, a new centralized coded caching scheme is developed that utilizes maximum distance separable (MDS) coding, jointly optimizes cache placement and delivery phase, and enables decomposing the combination network into a set virtual multicast sub-networks. It is shown that if the sum of the memory of an end user and its connected relay nodes is sufficient to store the database, then the server can disengage in the delivery phase and all the end users' requests can be satisfied by the caches in the network. Lower bounds on the normalized delivery load using genie-aided cut-set arguments are presented along with second hop optimality. Next recognizing the information security concerns of coded caching, this new model is studied under three different secrecy settings: 1) secure delivery where we require an external entity must not gain any information about the database files by observing the transmitted signals over the network links, 2) secure caching, where we impose the constraint that end users must not be able to obtain any information about files that they did not request, and 3) both secure delivery and secure caching, simultaneously. We demonstrate how network topology affects the system performance under these secrecy requirements. Finally, we provide numerical results demonstrating the system performance in each of the settings considered.Comment: 30 pages, 5 figures, submitted for publicatio

Structured Lattice Codes for Some Two-User Gaussian Networks with Cognition, Coordination and Two Hops

We study a number of two-user interference networks with multiple-antenna transmitters/receivers, transmitter side information in the form of linear combinations (over finite-field) of the information messages, and two-hop relaying. We start with a Cognitive Interference Channel (CIC) where one of the transmitters (non-cognitive) has knowledge of a rank-1 linear combination of the two information messages, while the other transmitter (cognitive) has access to a rank-2 linear combination of the same messages. This is referred to as the Network-Coded CIC, since such linear combination may be the result of some random linear network coding scheme implemented in the backbone wired network. For such channel we develop an achievable region based on a few novel concepts: Precoded Compute and Forward (PCoF) with Channel Integer Alignment (CIA), combined with standard Dirty-Paper Coding. We also develop a capacity region outer bound and find the sum symmetric GDoF of the Network-Coded CIC. Through the GDoF characterization, we show that knowing "mixed data" (linear combinations of the information messages) provides an unbounded spectral efficiency gain over the classical CIC counterpart, if the ratio of SNR to INR is larger than certain threshold. Then, we consider a Gaussian relay network having the two-user MIMO IC as the main building block. We use PCoF with CIA to convert the MIMO IC into a deterministic finite-field IC. Then, we use a linear precoding scheme over the finite-field to eliminate interference in the finite-field domain. Using this unified approach, we characterize the symmetric sum rate of the two-user MIMO IC with coordination, cognition, and two-hops. We also provide finite-SNR results which show that the proposed coding schemes are competitive against state of the art interference avoidance based on orthogonal access, for Rayleigh fading channels.Comment: revision for IEEE Transactions on Information Theor

Delay Reduction in Multi-Hop Device-to-Device Communication using Network Coding

This paper considers the problem of reducing the broadcast decoding delay of wireless networks using instantly decodable network coding (IDNC) based device-to-device (D2D) communications. In contrast with previous works that assume a fully connected network, this paper investigates a partially connected configuration in which multiple devices are allowed to transmit simultaneously. To that end, the different events occurring at each device are identified so as to derive an expression for the probability distribution of the decoding delay. Afterward, the joint optimization problem over the set of transmitting devices and packet combination of each is formulated. The optimal solution of the joint optimization problem is derived using a graph theoretic approach by introducing the cooperation graph in which each vertex represents a transmitting device with a weight translating its contribution to the network. The paper solves the problem by reformulating it as a maximum weight clique problem which can efficiently be solved. Numerical results suggest that the proposed solution outperforms state-of-the-art schemes and provides significant gain, especially for poorly connected networks

Performance of wireless network coding: motivating small encoding numbers

This paper focuses on a particular transmission scheme called local network coding, which has been reported to provide significant performance gains in practical wireless networks. The performance of this scheme strongly depends on the network topology and thus on the locations of the wireless nodes. Also, it has been shown previously that finding the encoding strategy, which achieves maximum performance, requires complex calculations to be undertaken by the wireless node in real-time. Both deterministic and random point pattern are explored and using the Boolean connectivity model we provide upper bounds for the maximum coding number, i.e., the number of packets that can be combined such that the corresponding receivers are able to decode. For the models studied, this upper bound is of order of $\sqrt{N}$, where $N$ denotes the (mean) number of neighbors. Moreover, achievable coding numbers are provided for grid-like networks. We also calculate the multiplicative constants that determine the gain in case of a small network. Building on the above results, we provide an analytic expression for the upper bound of the efficiency of local network coding. The conveyed message is that it is favorable to reduce computational complexity by relying only on small encoding numbers since the resulting expected throughput loss is negligible.Comment: 8 pages, 10 figure

Joint Inter-flow Network Coding and Opportunistic Routing in Multi-hop Wireless Mesh Networks: A Comprehensive Survey

Network coding and opportunistic routing are two recognized innovative ideas to improve the performance of wireless networks by utilizing the broadcast nature of the wireless medium. In the last decade, there has been considerable research on how to synergize inter-flow network coding and opportunistic routing in a single joint protocol outperforming each in any scenario. This paper explains the motivation behind the integration of these two techniques, and highlights certain scenarios in which the joint approach may even degrade the performance, emphasizing the fact that their synergistic effect cannot be accomplished with a naive and perfunctory combination. This survey paper also provides a comprehensive taxonomy of the joint protocols in terms of their fundamental components and associated challenges, and compares existing joint protocols. We also present concluding remarks along with an outline of future research directions.Comment: 51 pages, 17 figure

Efficient Probabilistic Inference in Generic Neural Networks Trained with Non-Probabilistic Feedback

Animals perform near-optimal probabilistic inference in a wide range of psychophysical tasks. Probabilistic inference requires trial-to-trial representation of the uncertainties associated with task variables and subsequent use of this representation. Previous work has implemented such computations using neural networks with hand-crafted and task-dependent operations. We show that generic neural networks trained with a simple error-based learning rule perform near-optimal probabilistic inference in nine common psychophysical tasks. In a probabilistic categorization task, error-based learning in a generic network simultaneously explains a monkey's learning curve and the evolution of qualitative aspects of its choice behavior. In all tasks, the number of neurons required for a given level of performance grows sub-linearly with the input population size, a substantial improvement on previous implementations of probabilistic inference. The trained networks develop a novel sparsity-based probabilistic population code. Our results suggest that probabilistic inference emerges naturally in generic neural networks trained with error-based learning rules.Comment: 30 pages, 10 figures, 6 supplementary figure

FlexONC: Joint Cooperative Forwarding and Network Coding with Precise Encoding Conditions

In recent years, network coding has emerged as an innovative method that helps a wireless network approach its maximum capacity, by combining multiple unicasts in one broadcast. However, the majority of research conducted in this area is yet to fully utilize the broadcasting nature of wireless networks, and still assumes fixed route between the source and destination that every packet should travel through. This assumption not only limits coding opportunities, but can also cause buffer overflow in some specific intermediate nodes. Although some studies considered scattering of the flows dynamically in the network, they still face some limitations. This paper explains pros and cons of some prominent research in network coding and proposes a Flexible and Opportunistic Network Coding scheme (FlexONC) as a solution to such issues. Furthermore, this research discovers that the conditions used in previous studies to combine packets of different flows are overly optimistic and would affect the network performance adversarially. Therefore, we provide a more accurate set of rules for packet encoding. The experimental results show that FlexONC outperforms previous methods especially in networks with high bit error rate, by better utilizing redundant packets spread in the network.Comment: 15 pages, 27 figure

NCRAWL: Network Coding for Rate Adaptive Wireless Links

Intersession network coding (NC) can provide significant performance benefits via mixing packets at wireless routers; these benefits are especially pronounced when NC is applied in conjunction with intelligent link scheduling. NC however imposes certain processing operations, such as encoding, decoding, copying and storage. When not utilized carefully, all these operations can induce tremendous processing overheads in practical, wireless, multi-rate settings. Our measurements with prior NC implementations suggest that such processing operations severely degrade the router throughput, especially at high bit rates. Motivated by this, we design {\bf NCRAWL}, a Network Coding framework for Rate Adaptive Wireless Links. The design of NCRAWL facilitates low overhead NC functionalities, thereby effectively approaching the theoretically expected capacity benefits of joint NC and scheduling. We implement and evaluate NCRAWL on a wireless testbed. Our experiments demonstrate that NCRAWL meets the theoretical predicted throughput gain while requiring much less CPU processing, compared to related frameworks