Network Code Design for Orthogonal Two-hop Network with Broadcasting Relay: A Joint Source-Channel-Network Coding Approach

This paper addresses network code design for robust transmission of sources over an orthogonal two-hop wireless network with a broadcasting relay. The network consists of multiple sources and destinations in which each destination, benefiting the relay signal, intends to decode a subset of the sources. Two special instances of this network are orthogonal broadcast relay channel and the orthogonal multiple access relay channel. The focus is on complexity constrained scenarios, e.g., for wireless sensor networks, where channel coding is practically imperfect. Taking a source-channel and network coding approach, we design the network code (mapping) at the relay such that the average reconstruction distortion at the destinations is minimized. To this end, by decomposing the distortion into its components, an efficient design algorithm is proposed. The resulting network code is nonlinear and substantially outperforms the best performing linear network code. A motivating formulation of a family of structured nonlinear network codes is also presented. Numerical results and comparison with linear network coding at the relay and the corresponding distortion-power bound demonstrate the effectiveness of the proposed schemes and a promising research direction.Comment: 27 pages, 9 figures, Submited to IEEE Transaction on Communicatio

On bounds and algorithms for frequency synchronization for collaborative communication systems

Cooperative diversity systems are wireless communication systems designed to exploit cooperation among users to mitigate the effects of multipath fading. In fairly general conditions, it has been shown that these systems can achieve the diversity order of an equivalent MISO channel and, if the node geometry permits, virtually the same outage probability can be achieved as that of the equivalent MISO channel for a wide range of applicable SNR. However, much of the prior analysis has been performed under the assumption of perfect timing and frequency offset synchronization. In this paper, we derive the estimation bounds and associated maximum likelihood estimators for frequency offset estimation in a cooperative communication system. We show the benefit of adaptively tuning the frequency of the relay node in order to reduce estimation error at the destination. We also derive an efficient estimation algorithm, based on the correlation sequence of the data, which has mean squared error close to the Cramer-Rao Bound.Comment: Submitted to IEEE Transaction on Signal Processin

Memoryless relay strategies for two-way relay channels

We propose relaying strategies for uncoded two-way relay channels, where two terminals transmit simultaneously to each other with the help of a relay. In particular, we consider a memoryless system, where the signal transmitted by the relay is obtained by applying an instantaneous relay function to the previously received signal. For binary antipodal signaling, a class of so called absolute (abs)-based schemes is proposed in which the processing at the relay is solely based on the absolute value of the received signal. We analyze and optimize the symbol-error performance of existing and new abs-based and non-abs-based strategies under an average power constraint, including abs-based and non-abs-based versions of amplify and forward (AF), detect and forward (DF), and estimate and forward (EF). Additionally, we optimize the relay function via functional analysis such that the average probability of error is minimized at the high signal-to-noise ratio (SNR) regime. The optimized relay function is shown to be a Lambert W function parameterized on the noise power and the transmission energy. The optimized function behaves like abs-AF at low SNR and like abs-DF at high SNR, respectively; EF behaves similarly to the optimized function over the whole SNR range. We find the conditions under which each class of strategies is preferred. Finally, we show that all these results can also be generalized to higher order constellations

Lecture Notes on Network Information Theory

These lecture notes have been converted to a book titled Network Information Theory published recently by Cambridge University Press. This book provides a significantly expanded exposition of the material in the lecture notes as well as problems and bibliographic notes at the end of each chapter. The authors are currently preparing a set of slides based on the book that will be posted in the second half of 2012. More information about the book can be found at http://www.cambridge.org/9781107008731/. The previous (and obsolete) version of the lecture notes can be found at http://arxiv.org/abs/1001.3404v4/

Lattice Coding for the Two-way Two-relay Channel

Lattice coding techniques may be used to derive achievable rate regions which outperform known independent, identically distributed (i.i.d.) random codes in multi-source relay networks and in particular the two-way relay channel. Gains stem from the ability to decode the sum of codewords (or messages) using lattice codes at higher rates than possible with i.i.d. random codes. Here we develop a novel lattice coding scheme for the Two-way Two-relay Channel: 1 2 3 4, where Node 1 and 4 simultaneously communicate with each other through two relay nodes 2 and 3. Each node only communicates with its neighboring nodes. The key technical contribution is the lattice-based achievability strategy, where each relay is able to remove the noise while decoding the sum of several signals in a Block Markov strategy and then re-encode the signal into another lattice codeword using the so-called "Re-distribution Transform". This allows nodes further down the line to again decode sums of lattice codewords. This transform is central to improving the achievable rates, and ensures that the messages traveling in each of the two directions fully utilize the relay's power, even under asymmetric channel conditions. All decoders are lattice decoders and only a single nested lattice codebook pair is needed. The symmetric rate achieved by the proposed lattice coding scheme is within 0.5 log 3 bit/Hz/s of the symmetric rate capacity.Comment: submitted to IEEE Transactions on Information Theory on December 3, 201