Integer-Forcing Source Coding

Integer-Forcing (IF) is a new framework, based on compute-and-forward, for decoding multiple integer linear combinations from the output of a Gaussian multiple-input multiple-output channel. This work applies the IF approach to arrive at a new low-complexity scheme, IF source coding, for distributed lossy compression of correlated Gaussian sources under a minimum mean squared error distortion measure. All encoders use the same nested lattice codebook. Each encoder quantizes its observation using the fine lattice as a quantizer and reduces the result modulo the coarse lattice, which plays the role of binning. Rather than directly recovering the individual quantized signals, the decoder first recovers a full-rank set of judiciously chosen integer linear combinations of the quantized signals, and then inverts it. In general, the linear combinations have smaller average powers than the original signals. This allows to increase the density of the coarse lattice, which in turn translates to smaller compression rates. We also propose and analyze a one-shot version of IF source coding, that is simple enough to potentially lead to a new design principle for analog-to-digital converters that can exploit spatial correlations between the sampled signals.Comment: Submitted to IEEE Transactions on Information Theor

Achievable Rate Regions for Two-Way Relay Channel using Nested Lattice Coding

This paper studies Gaussian Two-Way Relay Channel where two communication nodes exchange messages with each other via a relay. It is assumed that all nodes operate in half duplex mode without any direct link between the communication nodes. A compress-and-forward relaying strategy using nested lattice codes is first proposed. Then, the proposed scheme is improved by performing a layered coding : a common layer is decoded by both receivers and a refinement layer is recovered only by the receiver which has the best channel conditions. The achievable rates of the new scheme are characterized and are shown to be higher than those provided by the decode-and-forward strategy in some regions.Comment: 27 pages, 13 figures, Submitted to IEEE Transactions on Wireless Communications (October 2013

Reliable Physical Layer Network Coding

When two or more users in a wireless network transmit simultaneously, their electromagnetic signals are linearly superimposed on the channel. As a result, a receiver that is interested in one of these signals sees the others as unwanted interference. This property of the wireless medium is typically viewed as a hindrance to reliable communication over a network. However, using a recently developed coding strategy, interference can in fact be harnessed for network coding. In a wired network, (linear) network coding refers to each intermediate node taking its received packets, computing a linear combination over a finite field, and forwarding the outcome towards the destinations. Then, given an appropriate set of linear combinations, a destination can solve for its desired packets. For certain topologies, this strategy can attain significantly higher throughputs over routing-based strategies. Reliable physical layer network coding takes this idea one step further: using judiciously chosen linear error-correcting codes, intermediate nodes in a wireless network can directly recover linear combinations of the packets from the observed noisy superpositions of transmitted signals. Starting with some simple examples, this survey explores the core ideas behind this new technique and the possibilities it offers for communication over interference-limited wireless networks.Comment: 19 pages, 14 figures, survey paper to appear in Proceedings of the IEE

Source-Channel Diversity for Parallel Channels

We consider transmitting a source across a pair of independent, non-ergodic channels with random states (e.g., slow fading channels) so as to minimize the average distortion. The general problem is unsolved. Hence, we focus on comparing two commonly used source and channel encoding systems which correspond to exploiting diversity either at the physical layer through parallel channel coding or at the application layer through multiple description source coding. For on-off channel models, source coding diversity offers better performance. For channels with a continuous range of reception quality, we show the reverse is true. Specifically, we introduce a new figure of merit called the distortion exponent which measures how fast the average distortion decays with SNR. For continuous-state models such as additive white Gaussian noise channels with multiplicative Rayleigh fading, optimal channel coding diversity at the physical layer is more efficient than source coding diversity at the application layer in that the former achieves a better distortion exponent. Finally, we consider a third decoding architecture: multiple description encoding with a joint source-channel decoding. We show that this architecture achieves the same distortion exponent as systems with optimal channel coding diversity for continuous-state channels, and maintains the the advantages of multiple description systems for on-off channels. Thus, the multiple description system with joint decoding achieves the best performance, from among the three architectures considered, on both continuous-state and on-off channels.Comment: 48 pages, 14 figure

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

A Simple Cooperative Diversity Method Based on Network Path Selection

Cooperative diversity has been recently proposed as a way to form virtual antenna arrays that provide dramatic gains in slow fading wireless environments. However most of the proposed solutions require distributed space-time coding algorithms, the careful design of which is left for future investigation if there is more than one cooperative relay. We propose a novel scheme, that alleviates these problems and provides diversity gains on the order of the number of relays in the network. Our scheme first selects the best relay from a set of M available relays and then uses this best relay for cooperation between the source and the destination. We develop and analyze a distributed method to select the best relay that requires no topology information and is based on local measurements of the instantaneous channel conditions. This method also requires no explicit communication among the relays. The success (or failure) to select the best available path depends on the statistics of the wireless channel, and a methodology to evaluate performance for any kind of wireless channel statistics, is provided. Information theoretic analysis of outage probability shows that our scheme achieves the same diversity-multiplexing tradeoff as achieved by more complex protocols, where coordination and distributed space-time coding for M nodes is required, such as those proposed in [7]. The simplicity of the technique, allows for immediate implementation in existing radio hardware and its adoption could provide for improved flexibility, reliability and efficiency in future 4G wireless systems.Comment: To appear, IEEE JSAC, special issue on 4