arXiv subjects

Michael Gastpar

Publications and source records attributed to Michael Gastpar.

At least 91 records · Page 5Linked to original sources

arXiv2016

Information-Theoretic Caching: Sequential Coding for Computing

Under the paradigm of caching, partial data is delivered before the actual requests of users are known. In this paper, this problem is modeled as a canonical distributed source coding problem with side information, where the side information represents the users' requests. For the single-user case, a single-letter characterization of the optimal rate region is established, and for several important special cases, closed-form solutions are given, including the scenario of uniformly distributed user requests. In this case, it is shown that the optimal caching strategy is closely related to total correlation and Wyner's common information. Using the insight gained from the single-user case, three two-user scenarios admitting single-letter characterization are considered, which draw connections to existing source coding problems in the literature: the Gray--Wyner system and distributed successive refinement. Finally, the model studied by Maddah-Ali and Niesen is rephrased to make a comparison with the considered information-theoretic model. Although the two caching models have a similar behavior for the single-user case, it is shown through a two-user example that the two caching models behave differently in general.

cs.IT↗

arXiv2016

Computation in Multicast Networks: Function Alignment and Converse Theorems

The classical problem in network coding theory considers communication over multicast networks. Multiple transmitters send independent messages to multiple receivers which decode the same set of messages. In this work, computation over multicast networks is considered: each receiver decodes an identical function of the original messages. For a countably infinite class of two-transmitter two-receiver single-hop linear deterministic networks, the computing capacity is characterized for a linear function (modulo-2 sum) of Bernoulli sources. Inspired by the geometric concept of interference alignment in networks, a new achievable coding scheme called function alignment is introduced. A new converse theorem is established that is tighter than cut-set based and genie-aided bounds. Computation (vs. communication) over multicast networks requires additional analysis to account for multiple receivers sharing a network's computational resources. We also develop a network decomposition theorem which identifies elementary parallel subnetworks that can constitute an original network without loss of optimality. The decomposition theorem provides a conceptually-simpler algebraic proof of achievability that generalizes to $L$-transmitter $L$-receiver networks.

cs.IT↗

arXiv2016

Multi-Library Coded Caching

We study the problem of coded caching when the server has access to several libraries and each user makes independent requests from every library. The single-library scenario has been well studied and it has been proved that coded caching can significantly improve the delivery rate compared to uncoded caching. In this work we show that when all the libraries have the same number of files, memory-sharing is optimal and the delivery rate cannot be improved via coding across files from different libraries. In this setting, the optimal memory-sharing strategy is one that divides the cache of each user proportional to the size of the files in different libraries. As for the general case, when the number of files in different libraries are arbitrary, we propose an inner-bound based on memory-sharing and an outer-bound based on concatenation of files from different libraries.

cs.IT↗

arXiv2016

A New Converse Bound for Coded Caching

An information-theoretic lower bound is developed for the caching system studied by Maddah-Ali and Niesen. By comparing the proposed lower bound with the decentralized coded caching scheme of Maddah-Ali and Niesen, the optimal memory--rate tradeoff is characterized to within a multiplicative gap of $4.7$ for the worst case, improving the previous analytical gap of $12$. Furthermore, for the case when users' requests follow the uniform distribution, the multiplicative gap is tightened to $4.7$, improving the previous analytical gap of $72$. As an independent result of interest, for the single-user average case in which the user requests multiple files, it is proved that caching the most requested files is optimal.

cs.IT↗

arXiv2015

$K$ Users Caching Two Files: An Improved Achievable Rate

Caching is an approach to smoothen the variability of traffic over time. Recently it has been proved that the local memories at the users can be exploited for reducing the peak traffic in a much more efficient way than previously believed. In this work we improve upon the existing results and introduce a novel caching strategy that takes advantage of simultaneous coded placement and coded delivery in order to decrease the worst case achievable rate with $2$ files and $K$ users. We will show that for any cache size $\frac{1}{K}<M<1$ our scheme outperforms the state of the art.

cs.IT↗

arXiv2015

Secure Transmission on the Two-hop Relay Channel with Scaled Compute-and-Forward

In this paper, we consider communication on a two-hop channel, in which a source wants to send information reliably and securely to the destination via a relay. We consider both the untrusted relay case and the external eavesdropper case. In the untrusted relay case, the relay behaves as an eavesdropper and there is a cooperative node which sends a jamming signal to confuse the relay when the it is receiving from the source. We propose two secure transmission schemes using the scaled compute-and-forward technique. One of the schemes is based on a random binning code and the other one is based on a lattice chain code. It is proved that in either the high Signal-to-Noise-Ratio (SNR) scenario and/or the restricted relay power scenario, if the destination is used as the jammer, both schemes outperform all existing schemes and achieve the upper bound. In particular, if the SNR is large and the source, the relay, and the cooperative jammer have identical power and channels, both schemes achieve the upper bound for secrecy rate, which is merely $1/2$ bit per channel use lower than the channel capacity without secrecy constraints. We also prove that one of our schemes achieves a positive secrecy rate in the external eavesdropper case in which the relay is trusted and there exists an external eavesdropper.

cs.IT↗

arXiv2015

Efficient Algorithms for the Data Exchange Problem

In this paper we study the data exchange problem where a set of users is interested in gaining access to a common file, but where each has only partial knowledge about it as side-information. Assuming that the file is broken into packets, the side-information considered is in the form of linear combinations of the file packets. Given that the collective information of all the users is sufficient to allow recovery of the entire file, the goal is for each user to gain access to the file while minimizing some communication cost. We assume that users can communicate over a noiseless broadcast channel, and that the communication cost is a sum of each user's cost function over the number of bits it transmits. For instance, the communication cost could simply be the total number of bits that needs to be transmitted. In the most general case studied in this paper, each user can have any arbitrary convex cost function. We provide deterministic, polynomial-time algorithms (in the number of users and packets) which find an optimal communication scheme that minimizes the communication cost. To further lower the complexity, we also propose a simple randomized algorithm inspired by our deterministic algorithm which is based on a random linear network coding scheme.

cs.IT↗

arXiv2015

Asymmetric Compute-and-Forward with CSIT

We present a modified compute-and-forward scheme which utilizes Channel State Information at the Transmitters (CSIT) in a natural way. The modified scheme allows different users to have different coding rates, and use CSIT to achieve larger rate region. This idea is applicable to all systems which use the compute-and-forward technique and can be arbitrarily better than the regular scheme in some settings.

cs.IT↗

arXiv2015

Lattice Codes for Many-to-One Interference Channels With and Without Cognitive Messages

A new achievable rate region is given for the Gaussian cognitive many-to-one interference channel. The proposed novel coding scheme is based on the compute-and-forward approach with lattice codes. Using the idea of decoding sums of codewords, our scheme improves considerably upon the conventional coding schemes which treat interference as noise or decode messages simultaneously. Our strategy also extends directly to the usual many-to-one interference channels without cognitive messages. Comparing to the usual compute-and-forward scheme where a fixed lattice is used for the code construction, the novel scheme employs scaled lattices and also encompasses key ingredients of the existing schemes for the cognitive interference channel. With this new component, our scheme achieves a larger rate region in general. For some symmetric channel settings, new constant gap or capacity results are established, which are independent of the number of users in the system.

cs.IT↗

arXiv2014

Compute-and-Forward: Finding the Best Equation

Compute-and-Forward is an emerging technique to deal with interference. It allows the receiver to decode a suitably chosen integer linear combination of the transmitted messages. The integer coefficients should be adapted to the channel fading state. Optimizing these coefficients is a Shortest Lattice Vector (SLV) problem. In general, the SLV problem is known to be prohibitively complex. In this paper, we show that the particular SLV instance resulting from the Compute-and-Forward problem can be solved in low polynomial complexity and give an explicit deterministic algorithm that is guaranteed to find the optimal solution.

cs.IT↗

arXiv2014

Integer-Forcing Linear Receivers

Linear receivers are often used to reduce the implementation complexity of multiple-antenna systems. In a traditional linear receiver architecture, the receive antennas are used to separate out the codewords sent by each transmit antenna, which can then be decoded individually. Although easy to implement, this approach can be highly suboptimal when the channel matrix is near singular. This paper develops a new linear receiver architecture that uses the receive antennas to create an effective channel matrix with integer-valued entries. Rather than attempting to recover transmitted codewords directly, the decoder recovers integer combinations of the codewords according to the entries of the effective channel matrix. The codewords are all generated using the same linear code which guarantees that these integer combinations are themselves codewords. Provided that the effective channel is full rank, these integer combinations can then be digitally solved for the original codewords. This paper focuses on the special case where there is no coding across transmit antennas and no channel state information at the transmitter(s), which corresponds either to a multi-user uplink scenario or to single-user V-BLAST encoding. In this setting, the proposed integer-forcing linear receiver significantly outperforms conventional linear architectures such as the zero-forcing and linear MMSE receiver. In the high SNR regime, the proposed receiver attains the optimal diversity-multiplexing tradeoff for the standard MIMO channel with no coding across transmit antennas. It is further shown that in an extended MIMO model with interference, the integer-forcing linear receiver achieves the optimal generalized degrees-of-freedom.

cs.IT↗

arXiv2013

Computation Over Gaussian Networks With Orthogonal Components

Function computation of arbitrarily correlated discrete sources over Gaussian networks with orthogonal components is studied. Two classes of functions are considered: the arithmetic sum function and the type function. The arithmetic sum function in this paper is defined as a set of multiple weighted arithmetic sums, which includes averaging of the sources and estimating each of the sources as special cases. The type or frequency histogram function counts the number of occurrences of each argument, which yields many important statistics such as mean, variance, maximum, minimum, median, and so on. The proposed computation coding first abstracts Gaussian networks into the corresponding modulo sum multiple-access channels via nested lattice codes and linear network coding and then computes the desired function by using linear Slepian-Wolf source coding. For orthogonal Gaussian networks (with no broadcast and multiple-access components), the computation capacity is characterized for a class of networks. For Gaussian networks with multiple-access components (but no broadcast), an approximate computation capacity is characterized for a class of networks.

cs.IT↗

arXiv2013

Coding Schemes and Asymptotic Capacity of the Gaussian Broadcast and Interference Channels with Feedback

A coding scheme is proposed for the memoryless Gaussian broadcast channel with correlated noises and feedback. For all noise correlations other than -1, the gap between the sum-rate the scheme achieves and the full-cooperation bound vanishes as the signal-to-noise ratio tends to infinity. When the correlation coefficient is -1, the gains afforded by feedback are unbounded and the prelog is doubled. When the correlation coefficient is +1 we demonstrate a dichotomy: If the noise variances are equal, then feedback is useless, and otherwise, feedback affords unbounded rate gains and doubles the prelog. The unbounded feedback gains, however, require perfect (noiseless) feedback. When the feedback links are noisy the feedback gains are bounded, unless the feedback noise decays to zero sufficiently fast with the signal-to-noise ratio. Extensions to more receivers are also discussed as is the memoryless Gaussian interference channel with feedback.

cs.IT↗

arXiv2013

Interactive Computation of Type-Threshold Functions in Collocated Broadcast-Superposition Networks

In wireless sensor networks, various applications involve learning one or multiple functions of the measurements observed by sensors, rather than the measurements themselves. This paper focuses on type-threshold functions, e.g., the maximum and indicator functions. Previous work studied this problem under the collocated collision network model and showed that under many probabilistic models for the measurements, the achievable computation rates converge to zero as the number of sensors increases. This paper considers two network models reflecting both the broadcast and superposition properties of wireless channels: the collocated linear finite field network and the collocated Gaussian network. A general multi-round coding scheme exploiting not only the broadcast property but particularly also the superposition property of the networks is developed. Through careful scheduling of concurrent transmissions to reduce redundancy, it is shown that given any independent measurement distribution, all type-threshold functions can be computed reliably with a non-vanishing rate in the collocated Gaussian network, even if the number of sensors tends to infinity.

cs.IT↗

arXiv2013

Approximate Sparsity Pattern Recovery: Information-Theoretic Lower Bounds

Recovery of the sparsity pattern (or support) of an unknown sparse vector from a small number of noisy linear measurements is an important problem in compressed sensing. In this paper, the high-dimensional setting is considered. It is shown that if the measurement rate and per-sample signal-to-noise ratio (SNR) are finite constants independent of the length of the vector, then the optimal sparsity pattern estimate will have a constant fraction of errors. Lower bounds on the measurement rate needed to attain a desired fraction of errors are given in terms of the SNR and various key parameters of the unknown vector. The tightness of the bounds in a scaling sense, as a function of the SNR and the fraction of errors, is established by comparison with existing achievable bounds. Near optimality is shown for a wide variety of practically motivated signal models.

cs.IT↗

arXiv2013

Polar Codes For Broadcast Channels

Polar codes are introduced for discrete memoryless broadcast channels. For $m$-user deterministic broadcast channels, polarization is applied to map uniformly random message bits from $m$ independent messages to one codeword while satisfying broadcast constraints. The polarization-based codes achieve rates on the boundary of the private-message capacity region. For two-user noisy broadcast channels, polar implementations are presented for two information-theoretic schemes: i) Cover's superposition codes; ii) Marton's codes. Due to the structure of polarization, constraints on the auxiliary and channel-input distributions are identified to ensure proper alignment of polarization indices in the multi-user setting. The codes achieve rates on the capacity boundary of a few classes of broadcast channels (e.g., binary-input stochastically degraded). The complexity of encoding and decoding is $O(n*log n)$ where $n$ is the block length. In addition, polar code sequences obtain a stretched-exponential decay of $O(2^{-n^β})$ of the average block error probability where $0 < β< 0.5$.

cs.IT↗

arXiv2012

Random Access with Physical-layer Network Coding

Leveraging recent progress in physical-layer network coding we propose a new approach to random access: When packets collide, it is possible to recover a linear combination of the packets at the receiver. Over many rounds of transmission, the receiver can thus obtain many linear combinations and eventually recover all original packets. This is by contrast to slotted ALOHA where packet collisions lead to complete erasures. The throughput of the proposed strategy is derived and shown to be significantly superior to the best known strategies, including multipacket reception.

cs.IT↗

arXiv2012

Approximate Ergodic Capacity of a Class of Fading 2-user 2-hop Networks

We consider a fading AWGN 2-user 2-hop network where the channel coefficients are independent and identically distributed (i.i.d.) drawn from a continuous distribution and vary over time. For a broad class of channel distributions, we characterize the ergodic sum capacity to within a constant number of bits/sec/Hz, independent of signal-to-noise ratio. The achievability follows from the analysis of an interference neutralization scheme where the relays are partitioned into $M$ pairs, and interference is neutralized separately by each pair of relays. When $M=1$, the proposed ergodic interference neutralization characterizes the ergodic sum capacity to within $4$ bits/sec/Hz for i.i.d. uniform phase fading and approximately $4.7$ bits/sec/Hz for i.i.d. Rayleigh fading. We further show that this gap can be tightened to $4\log π-4$ bits/sec/Hz (approximately $2.6$) for i.i.d. uniform phase fading and $4-4\log( \frac{3π}{8})$ bits/sec/Hz (approximately $3.1$) for i.i.d. Rayleigh fading in the limit of large $M$.

cs.IT↗