Publications (118)73.77 Total impact
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ABSTRACT: A framework is developed for decodeandforward based relaying using standard coding and decoding that are good for the singleinput singleoutput (SISO) additive white Gaussian noise channel. The framework is applicable to various scenarios and demonstrated for several important cases. Each of these scenarios is transformed into an equivalent Gaussian multipleinput multipleoutput (MIMO) commonmessage broadcast problem, which proves useful even when all links are SISO ones. Over the effective MIMO broadcast channel, a recently developed Gaussian MIMO commonmessage broadcast scheme is applied. This scheme transforms the MIMO links into a set of parallel SISO channels with no loss of mutual information, using linear pre and postprocessing combined with successive decoding. Over these resulting SISO channels, “offtheshelf” scalar codes may be used.  [Show abstract] [Hide abstract]
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.  [Show abstract] [Hide abstract]
ABSTRACT: The Gaussian multipleinput multipleoutput twoway relay channel is considered. By applying linear pre and postprocessing, the channel matrices are transformed into triangular form having equal diagonals. Over the obtained triangular channels, dirtypaper coding is applied, yielding parallel symmetric scalar twoway relay channels; thus, reducing the coding task to that of coding over the scalar symmetric twoway relay channel. Any existing coding technique can then be readily applied over these resulting channels. This technique allows to obtain new achievable rates in the symmetric case.  [Show abstract] [Hide abstract]
ABSTRACT: The integerforcing receiver architecture has recently been proposed as a highperformance, yet lowcomplexity, equalization scheme, that is applicable when all data streams are encoded with the same linear code. It was further shown in [1], that this receiver architecture, when coupled with spacetime linear precoding is able to achieve the capacity of the openloop multipleinput multipleoutput channel, up to a constant gap that depends only on the number of transmit antennas. The gap, however, is quite large and thus provides performance guarantees that are useful only for high values of capacity. In this work, we consider the problem of multicast over multipleinput multipleoutput channels to a modest number of users, and with spaceonly linear precoding. It is assumed that channel state information is available to the transmitter, allowing it to optimize the precoding matrix so as to maximize the achievable transmission rate. It is numerically demonstrated that this architecture allows to very closely approach the multicast capacity at all transmission rates regimes. 
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.  [Show abstract] [Hide abstract]
ABSTRACT: We consider the finiteblocklength performance of singular channels (e.g., the binary erasure channel). At least for symmetric singular channels, it is known that the next correction term after the channel dispersion is the "constant" term. We show that for such channels, the asymptotic significance of tie breaking (i.e., making a fair decision in the case of multiple codewords of equal likelihood) is greater than for nonsingular channels. Specifically, for an ensemble of codebooks, where the codewords are independent with the same marginal distribution, the constant correction term is increased by exactly one nat. 
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. 
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.  [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.  [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.  [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.  [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. 
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.  [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.
Publication Stats
3k  Citations  
73.77  Total Impact Points  
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Institutions

19982013

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


20042005

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