arXiv subjects

Uri Erez

Publications and source records attributed to Uri Erez.

45 records · Page 3Linked to original sources

arXiv2011

Rateless Coding for Gaussian Channels

A rateless code-i.e., a rate-compatible family of codes-has the property that codewords of the higher rate codes are prefixes of those of the lower rate ones. A perfect family of such codes is one in which each of the codes in the family is capacity-achieving. We show by construction that perfect rateless codes with low-complexity decoding algorithms exist for additive white Gaussian noise channels. Our construction involves the use of layered encoding and successive decoding, together with repetition using time-varying layer weights. As an illustration of our framework, we design a practical three-rate code family. We further construct rich sets of near-perfect rateless codes within our architecture that require either significantly fewer layers or lower complexity than their perfect counterparts. Variations of the basic construction are also developed, including one for time-varying channels in which there is no a priori stochastic model.

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arXiv2011

Modulation for MIMO Networks with Several Users

In a recent work, a capacity-achieving scheme for the common-message two-user MIMO broadcast channel, based on single-stream coding and decoding, was described. This was obtained via a novel joint unitary triangularization which is applied to the corresponding channel matrices. In this work, the triangularization is generalized, to any (finite) number of matrices, allowing multi-user applications. To that end, multiple channel uses are jointly treated, in a manner reminiscent of space-time coding. As opposed to the two-user case, in the general case there does not always exist a perfect (capacity-achieving) solution. However, a nearly optimal scheme (with vanishing loss in the limit of large blocks) always exists. Common-message broadcasting is but one example of communication networks with MIMO links which can be solved using an approach coined "Network Modulation"; the extension beyond two links carries over to these problems.

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arXiv2011

Joint Unitary Triangularization for MIMO Networks

This work considers communication networks where individual links can be described as MIMO channels. Unlike orthogonal modulation methods (such as the singular-value decomposition), we allow interference between sub-channels, which can be removed by the receivers via successive cancellation. The degrees of freedom earned by this relaxation are used for obtaining a basis which is simultaneously good for more than one link. Specifically, we derive necessary and sufficient conditions for shaping the ratio vector of sub-channel gains of two broadcast-channel receivers. We then apply this to two scenarios: First, in digital multicasting we present a practical capacity-achieving scheme which only uses scalar codes and linear processing. Then, we consider the joint source-channel problem of transmitting a Gaussian source over a two-user MIMO channel, where we show the existence of non-trivial cases, where the optimal distortion pair (which for high signal-to-noise ratios equals the optimal point-to-point distortions of the individual users) may be achieved by employing a hybrid digital-analog scheme over the induced equivalent channel. These scenarios demonstrate the advantage of choosing a modulation basis based upon multiple links in the network, thus we coin the approach "network modulation".

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arXiv2009

Lattice Strategies for the Dirty Multiple Access Channel

A generalization of the Gaussian dirty-paper problem to a multiple access setup is considered. There are two additive interference signals, one known to each transmitter but none to the receiver. The rates achievable using Costa's strategies (i.e. by a random binning scheme induced by Costa's auxiliary random variables) vanish in the limit when the interference signals are strong. In contrast, it is shown that lattice strategies ("lattice precoding") can achieve positive rates independent of the interferences, and in fact in some cases - which depend on the noise variance and power constraints - they are optimal. In particular, lattice strategies are optimal in the limit of high SNR. It is also shown that the gap between the achievable rate region and the capacity region is at most 0.167 bit. Thus, the dirty MAC is another instance of a network setup, like the Korner-Marton modulo-two sum problem, where linear coding is potentially better than random binning. Lattice transmission schemes and conditions for optimality for the asymmetric case, where there is only one interference which is known to one of the users (who serves as a "helper" to the other user), and for the "common interference" case are also derived. In the former case the gap between the helper achievable rate and its capacity is at most 0.085 bit.

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arXiv2008

Technical Report: Achievable Rates for the MAC with Correlated Channel-State Information

In this paper we provide an achievable rate region for the discrete memoryless multiple access channel with correlated state information known non-causally at the encoders using a random binning technique. This result is a generalization of the random binning technique used by Gel'fand and Pinsker for the problem with non-causal channel state information at the encoder in point to point communication.

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arXiv2008

A Simple Extension of the $\modulo$-$Λ$ Transformation

A simple lemma is derived that allows to transform a general scalar (non-Gaussian, non-additive) continuous-alphabet channel as well as a general multiple-access channel into a modulo-additive noise channel. While in general the transformation is information lossy, it allows to leverage linear coding techniques and capacity results derived for networks comprised of additive Gaussian nodes to more general networks.

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arXiv2008

Achieving the Gaussian Rate-Distortion Function by Prediction

The "water-filling" solution for the quadratic rate-distortion function of a stationary Gaussian source is given in terms of its power spectrum. This formula naturally lends itself to a frequency domain "test-channel" realization. We provide an alternative time-domain realization for the rate-distortion function, based on linear prediction. This solution has some interesting implications, including the optimality at all distortion levels of pre/post filtered vector-quantized differential pulse code modulation (DPCM), and a duality relationship with decision-feedback equalization (DFE) for inter-symbol interference (ISI) channels.

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arXiv2006

Carbon Copying Onto Dirty Paper

A generalization of the problem of writing on dirty paper is considered in which one transmitter sends a common message to multiple receivers. Each receiver experiences on its link an additive interference (in addition to the additive noise), which is known noncausally to the transmitter but not to any of the receivers. Applications range from wireless multi-antenna multicasting to robust dirty paper coding. We develop results for memoryless channels in Gaussian and binary special cases. In most cases, we observe that the availability of side information at the transmitter increases capacity relative to systems without such side information, and that the lack of side information at the receivers decreases capacity relative to systems with such side information. For the noiseless binary case, we establish the capacity when there are two receivers. When there are many receivers, we show that the transmitter side information provides a vanishingly small benefit. When the interference is large and independent across the users, we show that time sharing is optimal. For the Gaussian case we present a coding scheme and establish its optimality in the high signal-to-interference-plus-noise limit when there are two receivers. When the interference is large and independent across users we show that time-sharing is again optimal. Connections to the problem of robust dirty paper coding are also discussed.

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arXiv2006

Fundamental Limits and Scaling Behavior of Cooperative Multicasting in Wireless Networks

A framework is developed for analyzing capacity gains from user cooperation in slow fading wireless networks when the number of nodes (network size) is large. The framework is illustrated for the case of a simple multipath-rich Rayleigh fading channel model. Both unicasting (one source and one destination) and multicasting (one source and several destinations) scenarios are considered. We introduce a meaningful notion of Shannon capacity for such systems, evaluate this capacity as a function of signal-to-noise ratio (SNR), and develop a simple two-phase cooperative network protocol that achieves it. We observe that the resulting capacity is the same for both unicasting and multicasting, but show that the network size required to achieve any target error probability is smaller for unicasting than for multicasting. Finally, we introduce the notion of a network ``scaling exponent'' to quantify the rate of decay of error probability with network size as a function of the targeted fraction of the capacity. This exponent provides additional insights to system designers by enabling a finer grain comparison of candidate cooperative transmission protocols in even moderately sized networks.

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