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.Comment: IEEE Transactions on Information Theory, accepte

Compute-and-Forward: Harnessing Interference through Structured Codes

Interference is usually viewed as an obstacle to communication in wireless networks. This paper proposes a new strategy, compute-and-forward, that exploits interference to obtain significantly higher rates between users in a network. The key idea is that relays should decode linear functions of transmitted messages according to their observed channel coefficients rather than ignoring the interference as noise. After decoding these linear equations, the relays simply send them towards the destinations, which given enough equations, can recover their desired messages. The underlying codes are based on nested lattices whose algebraic structure ensures that integer combinations of codewords can be decoded reliably. Encoders map messages from a finite field to a lattice and decoders recover equations of lattice points which are then mapped back to equations over the finite field. This scheme is applicable even if the transmitters lack channel state information.Comment: IEEE Trans. Info Theory, to appear. 23 pages, 13 figure

Network coding for transport protocols

With the proliferation of smart devices that require Internet connectivity anytime, anywhere, and the recent technological advances that make it possible, current networked systems will have to provide a various range of services, such as content distribution, in a wide range of settings, including wireless environments. Wireless links may experience temporary losses, however, TCP, the de facto protocol for robust unicast communications, reacts by reducing the congestion window drastically and injecting less traffic in the network. Consequently the wireless links are underutilized and the overall performance of the TCP protocol in wireless environments is poor. As content delivery (i.e. multicasting) services, such as BBC iPlayer, become popular, the network needs to support the reliable transport of the data at high rates, and with specific delay constraints. A typical approach to deliver content in a scalable way is to rely on peer-to-peer technology (used by BitTorrent, Spotify and PPLive), where users share their resources, including bandwidth, storage space, and processing power. Still, these systems suffer from the lack of incentives for resource sharing and cooperation, and this problem is exacerbated in the presence of heterogenous users, where a tit-for-tat scheme is difficult to implement. Due to the issues highlighted above, current network architectures need to be changed in order to accommodate the users¿ demands for reliable and quality communications. In other words, the emergent need for advanced modes of information transport requires revisiting and improving network components at various levels of the network stack. The innovative paradigm of network coding has been shown as a promising technique to change the design of networked systems, by providing a shift from how data flows traditionally move through the network. This shift implies that data flows are no longer kept separate, according to the ¿store-and-forward¿ model, but they are also processed and mixed in the network. By appropriately combining data by means of network coding, it is expected to obtain significant benefits in several areas of network design and architecture. In this thesis, we set out to show the benefits of including network coding into three communication paradigms, namely point-topoint communications (e.g. unicast), point-to-multipoint communications (e.g. multicast), and multipoint-to-multipoint communications (e.g. peer-to-peer networks). For the first direction, we propose a network coding-based multipath scheme and show that TCP unicast sessions are feasible in highly volatile wireless environments. For point-to-multipoint communications, we give an algorithm to optimally achieve all the rate pairs from the rate region in the case of degraded multicast over the combination network. We also propose a system for live streaming that ensures reliability and quality of service to heterogenous users, even if data transmissions occur over lossy wireless links. Finally, for multipoint-to-multipoint communications, we design a system to provide incentives for live streaming in a peer-to-peer setting, where users have subscribed to different levels of quality. Our work shows that network coding enables a reliable transport of data, even in highly volatile environments, or in delay sensitive scenarios such as live streaming, and facilitates the implementation of an efficient incentive system, even in the presence of heterogenous users. Thus, network coding can solve the challenges faced by next generation networks in order to support advanced information transport.Postprint (published version

Multiple Multicasts with the Help of a Relay

The problem of simultaneous multicasting of multiple messages with the help of a relay terminal is considered. In particular, a model is studied in which a relay station simultaneously assists two transmitters in multicasting their independent messages to two receivers. The relay may also have an independent message of its own to multicast. As a first step to address this general model, referred to as the compound multiple access channel with a relay (cMACr), the capacity region of the multiple access channel with a "cognitive" relay is characterized, including the cases of partial and rate-limited cognition. Then, achievable rate regions for the cMACr model are presented based on decode-and-forward (DF) and compress-and-forward (CF) relaying strategies. Moreover, an outer bound is derived for the special case, called the cMACr without cross-reception, in which each transmitter has a direct link to one of the receivers while the connection to the other receiver is enabled only through the relay terminal. The capacity region is characterized for a binary modulo additive cMACr without cross-reception, showing the optimality of binary linear block codes, thus highlighting the benefits of physical layer network coding and structured codes. Results are extended to the Gaussian channel model as well, providing achievable rate regions for DF and CF, as well as for a structured code design based on lattice codes. It is shown that the performance with lattice codes approaches the upper bound for increasing power, surpassing the rates achieved by the considered random coding-based techniques.Comment: Submitted to Transactions on Information Theor

On multicasting nested message sets over combination networks

In this paper, we study delivery of two nested message sets over combination networks with an arbitrary number of receivers, where a subset of receivers (public receivers) demand only the lower priority message and a subset of receivers (private receivers) demand both the lower and the higher priority messages. We give a complete rate region characterization over combination networks with three public and many private receivers, where achievability is through linear coding. Our encoding scheme is general and characterizes an achievable region for arbitrary number of public and private receivers

On Multicasting Nested Message Sets Over Combination Networks

In this paper, we study delivery of two nested message sets over combination networks with an arbitrary number of receivers, where a subset of receivers (public receivers) demand only the lower priority message and a subset of receivers (private receivers) demand both the lower and the higher priority messages. We give a complete rate region characterization over combination networks with three public and many private receivers, where achievability is through linear coding. Our encoding scheme is general and characterizes an achievable region for arbitrary number of public and private receivers