Publications (113)69.12 Total impact
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ABSTRACT: In the scalar dirty multipleaccess channel, in addition to Gaussian noise, two additive interference signals are present, each known noncausally to a single transmitter. It was shown by Philosof et al. that for strong interferences, an i.i.d. ensemble of codes does not achieve the capacity region. Rather, a structuredcodes approach was presented, which was shown to be optimal in the limit of high signaltonoise ratios, where the sumcapacity is dictated by the minimal ("bottleneck") channel gain. In the present work, we consider the multipleinput multipleoutput (MIMO) variant of this setting. In order to incorporate structured codes in this case, one can utilize matrix decompositions, which transform the channel into effective parallel scalar dirty multipleaccess channels. This approach however suffers from a "bottleneck" effect for each effective scalar channel and therefore the achievable rates strongly depend on the chosen decomposition. It is shown that a recently proposed decomposition, where the diagonals of the effective channel matrices are equal up to a scaling factor, is optimal at high signaltonoise ratios, under an equal rank assumption. This approach is then extended to any number of users. Finally, an application to physicallayer network coding for the MIMO twoway relay channel is presented. 
Article: On computeandforward with feedback
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ABSTRACT: We consider a Gaussian multipleaccess channel where each user's message is identified with a vector of elements from a finite field, and the receiver's goal is to decode a linear combination of these finite field vectors. It is further assumed that each transmitter can causally observe the channel's output through a clean feedback link. We propose a novel coding scheme for this setup, which can be seen as an extension of the CoverLeung scheme for the computation problem. This scheme is shown to achieve computation rates higher than the best known computation rates for the same scenario without feedback. In particular, for the symmetric twouser Gaussian multipleaccess channel, the proposed scheme attains a symmetric computation rate greater than 1/2 log(3/4 + SNR). 
Article: Performance Analysis and Optimal Filter Design for SigmaDelta Modulation via Duality with DPCM
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ABSTRACT: Sampling above the Nyquistrate is at the heart of sigmadelta modulation, where the increase in sampling rate is translated to a reduction in the overall (minimum meansquarederror) reconstruction distortion. This is attained by using a feedback filter at the encoder, in conjunction with a lowpass filter at the decoder. The goal of this work is to characterize the optimal tradeoff between the persample quantization rate and the resulting meansquarederror distortion, under various restrictions on the feedback filter. To this end, we establish a duality relation between the performance of sigmadelta modulation, and that of differential pulsecode modulation when applied to (discretetime) bandlimited inputs. As the optimal tradeoff for the latter scheme is fully understood, the full characterization for sigmadelta modulation, as well as the optimal feedback filters, immediately follow. 
Conference Paper: Performance of precoded integerforcing for parallel Gaussian channels
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ABSTRACT: Recently, an openloop transmission scheme for multipleinput multipleoutput Gaussian channels based on precoded integerforcing was proposed. The transmitter encodes the data into independent streams, all taken from the same linear code. The coded streams are then linearly precoded using a unitary matrix. At the receiver side, integerforcing equalization is applied, followed by singlestream decoding. It was shown that this communication architecture achieves capacity up to a finite gap. In the present work we consider precoded integerforcing for parallel Gaussian channels. We derive tighter bounds for this class of channels, which are related to the minimum product distance figure of merit. We further suggest a practical scheme that is applicable for all transmission rates, where the precoding matrix is capacitydependent, chosen so as to maximize the achievable rate for a given value of capacity. For example, it is shown that for the case of two and three parallel channels, the scheme universally (for any value of capacity) achieves 94% and 82% of capacity, respectively.2014 IEEE International Symposium on Information Theory (ISIT); 06/2014 
Article: RematchandForward: Joint Source–Channel Coding for Parallel Relaying With Spectral Mismatch
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ABSTRACT: The Gaussian parallel relay network, introduced by Schein and Gallager, consists of a concatenation of a Gaussian additive broadcast channel from a single encoder to a layer of relays followed by a Gaussian multipleaccess channel from the relays to the final destination (decoder), where all noises are independent. This setup exhibits an inherent conflict between digital and analog relaying; while analog relaying [known as amplifyandforward (A&F)] suffers from noise accumulation, digital relaying (known as decodeandforward) looses the potential coherence gain in combining the relay noises at the decoder. For a large number of relays, the coherence gain is large, and thus analog relaying has better performance; however, it is limited to white channels of equal bandwidth. In this paper, we present a generalization of the analog approach to the case of bandwidth mismatch. Our strategy, coined rematch and forward (R&F), is based upon applying joint sourcechannel coding techniques that belong to a certain class of maximally analog schemes. Using such techniques, R&F converts the bandwidth of the broadcast section to that of the multipleaccess section, creating an equivalent matchedbandwidth network over which A&F is applied. It is shown that this strategy exploits the full bandwidth of the individual channels, without sacrificing the coherence gain offered by A&F. Specifically, for given individuallink capacities, R&F remains within a constant gap from the network capacity for any number of relays and any bandwidth ratio between the sections. Finally, the approach is extended to the case of colored channels.IEEE Transactions on Information Theory 01/2014; 60(1):605622. DOI:10.1109/TIT.2013.2287722 · 2.33 Impact Factor 
Article: IntegerForcing Source Coding
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ABSTRACT: IntegerForcing (IF) is a new framework, based on computeandforward, for decoding multiple integer linear combinations from the output of a Gaussian multipleinput multipleoutput channel. This work applies the IF approach to arrive at a new lowcomplexity 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 fullrank 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 oneshot version of IF source coding, that is simple enough to potentially lead to a new design principle for analogtodigital converters that can exploit spatial correlations between the sampled signals.  [Show abstract] [Hide abstract]
ABSTRACT: Lattice coding and decoding have been shown to achieve the capacity of the additive white Gaussian noise (AWGN) channel. This was accomplished using a minimum meansquare error scaling and randomization to transform the AWGN channel into a modulolattice additive noise channel of the same capacity. It has been further shown that when operating at rates below capacity but above the critical rate of the channel, there exists a ratedependent scaling such that the associated modulolattice channel attains the error exponent of the AWGN channel. A geometric explanation for this result is developed. In particular, it is shown how the geometry of typical error events for the modulolattice channel coincides with that of a spherical code for the AWGN channel.  [Show abstract] [Hide abstract]
ABSTRACT: Integerforcing receivers generalize traditional linear receivers for the multipleinput multipleoutput channel by decoding integerlinear combinations of the transmitted streams, rather then the streams themselves. Previous works have shown that the additional degree of freedom in choosing the integer coefficients enables this receiver to approach the performance of maximumlikelihood decoding in various scenarios. Nonetheless, even for the optimal choice of integer coefficients, the additive noise at the equalizer's output is still correlated. In this work we study a variant of integerforcing, termed successive integerforcing, that exploits these noise correlations to improve performance. This scheme is the integerforcing counterpart of successive interference cancellation for traditional linear receivers. Similarly to the latter, we show that successive integerforcing is capacity achieving when it is possible to optimize the rate allocation to the different streams. In comparison to standard successive interference cancellation receivers, the successive integerforcing receiver offers more possibilities for capacity achieving rate tuples, and in particular, ones that are more balanced.  [Show abstract] [Hide abstract]
ABSTRACT: Multicast is the general method of conveying the same information to multiple users over a broadcast channel. In this work, the Gaussian multipleinput multipleoutput broadcast channel is considered, with multiple receive nodes, each equipped with an arbitrary number of antennas. A "closed loop" scenario is assumed, for which a practical multicast scheme is constructed which approaches capacity, by applying judiciously chosen unitary operations at the transmit and receives nodes that triangularize the channel matrices such that the resulting matrices have equal diagonals. This, along with the utilization of successive interference cancellation, reduces the coding and decoding tasks to those of coding and decoding over the singleantenna additive white Gaussian noise channel. Over the resulting effective channel, any "offtheshelf" code may be employed. For the twouser case, it was recently shown that such joint unitary triangularization is always possible. In this work it is shown that for more users, joint triangularization of the time extensions of the channel matrices is necessary in general, which corresponds to carrying out the unitary processing over multiple channel uses. It is further shown that exact triangularization, where all resulting diagonals are equal, is not always possible, and appropriate conditions for the existence of such are established for certain cases. When exact triangularization is not possible, an approximate construction is proposed, that achieves the desired equal diagonals up to constantlength prefix and suffix. By enlarging the number of channel uses processed together, the loss in rate due to the prefix and the suffix can be made arbitrarily small.IEEE Transactions on Information Theory 06/2013; 61(5). DOI:10.1109/TIT.2015.2409836 · 2.33 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: The performance limits of scalar coding for multipleinput singleoutput channels are revisited in this work. By employing randomized beamforming, Narula et al. demonstrated that the loss of scalar coding is universally bounded by ~ 2.51 dB (or 0.833 bits/symbol) for any number of antennas and channel gains. In this work, by using randomized beamforming in conjunction with spacetime codes, it is shown that the bound can be tightened to ~ 1.1 dB (or 0.39 bits/symbol).  [Show abstract] [Hide abstract]
ABSTRACT: A static (constant channel gains) real Kuser interference channel is considered, where all interference (cross) channel gains are integers. For such channels, previous results demonstrate that the number of degrees of freedom is very sensitive to slight variations in the direct channel gains. In this paper, we derive an achievable rate region for such channels that is valid for finite SNR. At moderate values of SNR, the derived rate region is robust to slight variations in the direct channel gains. At asymptotic high SNR conditions, known results on the degrees of freedom are recovered. The new rate region is based on lattice interference alignment. The result is established via a new coding theorem for the twouser Gaussian multipleaccess channel where both users use a single linear code.IEEE Transactions on Information Theory 05/2013; 59(5):27352759. DOI:10.1109/TIT.2012.2235523 · 2.33 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We consider upper bounds on the error probability in channel coding. We derive an improved maximumlikelihood union bound, which takes into account events where the likelihood of the correct codeword is tied with that of some competitors. We compare this bound to various previous results, both qualitatively and quantitatively. With respect to maximal error probability of linear codes, we observe that when the channel is additive, the derivation of bounds, as well as the assumptions on the admissible encoder and decoder, simplify considerably.02/2013; DOI:10.1109/ISIT.2013.6620522  [Show abstract] [Hide abstract]
ABSTRACT: An openloop singleuser multipleinput multipleoutput communication scheme is considered where a transmitter, equipped with multiple antennas, encodes the data into independent streams all taken from the same linear code. The coded streams are then linearly precoded using the encoding matrix of a perfect linear dispersion spacetime code. At the receiver side, integerforcing equalization is applied, followed by standard singlestream decoding. It is shown that this communication architecture achieves the capacity of any Gaussian multipleinput multipleoutput channel up to a gap that depends only on the number of transmit antennas.IEEE Transactions on Information Theory 01/2013; 61(1). DOI:10.1109/ITW.2013.6691273 · 2.33 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: This paper gives a simplified proof for the existence of nested lattice codebooks that allow to achieve the capacity of the additive white Gaussian noise channel. The proof is selfcontained and relies only on basic probabilistic and geometrical arguments. An ensemble of nested lattices which is different than the one used in previous proofs is introduced. This ensemble, in addition to giving rise to a simple proof, can be easily generalized to an ensemble of nested lattices chains. As a result, the proof technique given here easily extends to showing the existence of "good" chains of nested lattices.  [Show abstract] [Hide abstract]
ABSTRACT: In this work we show how an improved lower bound to the error exponent of the memoryless multipleaccess (MAC) channel is attained via the use of linear codes, thus demonstrating that structure can be beneficial even in cases where there is no capacity gain. We show that if the MAC channel is moduloadditive, then any error probability, and hence any error exponent, achievable by a linear code for the corresponding singleuser channel, is also achievable for the MAC channel. Specifically, for an alphabet of prime cardinality, where linear codes achieve the best known exponents in the singleuser setting and the optimal exponent above the critical rate, this performance carries over to the MAC setting. At least at low rates, where expurgation is needed, our approach strictly improves performance over previous results, where expurgation was used at most for one of the users. Even when the MAC channel is not additive, it may be transformed into such a channel. While the transformation is lossy, we show that the distributed structure gain in some "nearly additive" cases outweighs the loss, and thus the error exponent can improve upon the best known error exponent for these cases as well. Finally we apply a similar approach to the Gaussian MAC channel. We obtain an improvement over the best known achievable exponent, given by Gallager, for certain rate pairs, using lattice codes which satisfy a nesting condition. 
Conference Paper: Expurgation for discrete multipleaccess channels via linear codes
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ABSTRACT: We consider the error exponent of the memoryless multipleaccess (MAC) channel. We show that if the MAC channel is moduloadditive, then any error probability, and hence any error exponent, achievable by a linear code for the corresponding singleuser channel, is also achievable for the MAC channel. Specifically, for an alphabet of prime cardinality, where linear codes achieve the best known exponents in the singleuser setting (and the optimal exponent above the critical rate), this performance carries over to the MAC setting. At least at low rates, where expurgation is needed, our approach strictly improves performance over previous results, where expurgation was used at most for one of the users. Even when the MAC channel is not additive, it may be transformed into such a channel. While the transformation is lossy, we show that the distributed structure gain in some “nearly additive” cases outweighs the loss, and thus we can improve upon the best known exponent for these cases as well. This approach is related to that previously proposed for the Gaussian MAC channel, and is based on “distributed structure”.Information Theory Proceedings (ISIT), 2012 IEEE International Symposium on; 07/2012  [Show abstract] [Hide abstract]
ABSTRACT: Interference alignment has emerged as a powerful tool in the analysis of multiuser networks. Despite considerable recent progress, the capacity region of the Gaussian Kuser interference channel is still unknown in general, in part due to the challenges associated with alignment on the signal scale using lattice codes. This paper develops a new framework for lattice interference alignment, based on the computeandforward approach. Within this framework, each receiver decodes by first recovering two or more linear combinations of the transmitted codewords with integervalued coefficients and then solving these equations for its desired codeword. For the special case of symmetric channel gains, this framework is used to derive the approximate sum capacity of the Gaussian interference channel, up to an explicitly defined outage set of the channel gains. The key contributions are the capacity lower bounds for the weak through strong interference regimes, where each receiver should jointly decode its own codeword along with part of the interfering codewords. As part of the analysis, it is shown that decoding K linear combinations of the codewords can approach the sum capacity of the Kuser Gaussian multipleaccess channel up to a gap of no more than K log(K)/2 bits.06/2012; 60(6). DOI:10.1109/ISIT.2012.6283726 
Article: Spacetime MIMO multicasting
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ABSTRACT: Multicasting is the general method of conveying the same information to multiple users over a broadcast channel. In this work, the Gaussian MIMO broadcast channel is considered, with multiple users and any number of antennas at each node. A "closed loop" scenario is assumed, for which a practical capacityachieving multicast scheme is constructed. In the proposed scheme, linear modulation is carried over time and space together, which allows to transform the problem into that of transmission over parallel scalar subchannels, the gains of which are equal, except for a fraction of subchannels that vanishes with the number of time slots used. Over these subchannels, offtheshelf fixedrate AWGN codes can be used to approach capacity.04/2012; DOI:10.1109/ISIT.2012.6284041 
Conference Paper: Decodeandforward for the Gaussian 29d relay channel via standard AWGN coding and decoding
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ABSTRACT: This work considers practical implementation of the decodeandforward relaying protocol for the fullduplex Gaussian relay channel. Unlike previous works which developed coding techniques tailored to this protocol, it is shown that standard codes which are good for the Gaussian scalar channel of fixed signal 5a8 tonoise ratio suffice to approach the theoretical performance promised by this protocol. The proposed technique employs only linear operations and successive interference cancelation in conjunction with fixed signaltonoise ratio base codes, and the achievable rate is solely dictated by the performance of these base codes. The same approach and results carry over to the multipleantenna case as well.Information Theory Workshop (ITW), 2012 IEEE; 01/2012  [Show abstract] [Hide abstract]
ABSTRACT: This short note gives an overview of the concept of integerforcing architectures for MIMO systems. Such architectures employ a linear receiver structure, i.e., a static linear transform followed by separate singlestream decoders, thus enjoying a significant complexity advantage over joint decoding of all streams. In standard linear receivers, the component singlestream decoders each decode one of the original data streams. In the integerforcing architecture, each component decoder decodes an integer linear combination of several streams. Finally, these integer linear combinations are inverted to recover the original messages. Integerforcing architectures can significantly outperform other linear MIMO receivers, including receivers that employ successive interference cancellation.
Publication Stats
3k  Citations  
69.12  Total Impact Points  
Top Journals
Institutions

19982013

Tel Aviv University
 Department of Electrical Engineering  Systems
Tell Afif, Tel Aviv, Israel


20042007

Massachusetts Institute of Technology
 Department of Electrical Engineering and Computer Science
Cambridge, MA, United States
