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Hassibi, Babak (8)

Halbawi, Wael (3)Khina, Anatoly (2)Kostina, Victoria (2)Thrampoulidis, Christos (2)View MoreJournal2016 IEEE 55th Conference on Decision and Control (CDC) (2)2016 54th Annual Allerton Conference on Communication, Control, and Computing (Allerton) (1)2016 IEEE Information Theory Workshop (ITW) (1)2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) (1)2016 IEEE International Symposium on Information Theory (ISIT) (1)View MorePublisherInstitute of Electrical and Electronics Engineers (IEEE) (6)IEEE (2)SubjectApproximation algorithms (1)BER Analysis (1)Blind equalizers (1)Box Relaxation (1)BPSK (1)View MoreType
Conference Paper (8)

Year (Issue Date)2017 (5)2016 (3)Item AvailabilityMetadata Only (8)

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Constrained blind deconvolution using Wirtinger flow methods

Walk, Philipp; Jung, Peter; Hassibi, Babak (2017 International Conference on Sampling Theory and Applications (SampTA), IEEE, 2017-09-04) [Conference Paper]

In this work we consider one-dimensional blind deconvolution with prior knowledge of signal autocorrelations in the classical framework of polynomial factorization. In particular this univariate case highly suffers from several non-trivial ambiguities and therefore blind deconvolution is known to be ill-posed in general. However, if additional autocorrelation information is available and the corresponding polynomials are co-prime, blind deconvolution is uniquely solvable up to global phase. Using lifting, the outer product of the unknown vectors is the solution to a (convex) semi-definite program (SDP) demonstrating that -theoretically- recovery is computationally tractable. However, for practical applications efficient algorithms are required which should operate in the original signal space. To this end we also discuss a gradient descent algorithm (Wirtinger flow) for the original non-convex problem. We demonstrate numerically that such an approach has performance comparable to the semidefinite program in the noisy case. Our work is motivated by applications in blind communication scenarios and we will discuss a specific signaling scheme where information is encoded into polynomial roots.

Balanced and sparse Tamo-Barg codes

Halbawi, Wael; Duursma, Iwan; Dau, Hoang; Hassibi, Babak (2017 IEEE International Symposium on Information Theory (ISIT), IEEE, 2017-08-29) [Conference Paper]

We construct balanced and sparse generator matrices for Tamo and Barg's Locally Recoverable Codes (LRCs). More specifically, for a cyclic Tamo-Barg code of length n, dimension k and locality r, we show how to deterministically construct a generator matrix where the number of nonzeros in any two columns differs by at most one, and where the weight of every row is d + r - 1, where d is the minimum distance of the code. Since LRCs are designed mainly for distributed storage systems, the results presented in this work provide a computationally balanced and efficient encoding scheme for these codes. The balanced property ensures that the computational effort exerted by any storage node is essentially the same, whilst the sparse property ensures that this effort is minimal. The work presented in this paper extends a similar result previously established for Reed-Solomon (RS) codes, where it is now known that any cyclic RS code possesses a generator matrix that is balanced as described, but is sparsest, meaning that each row has d nonzeros.

Rate-cost tradeoffs in control

Kostina, Victoria; Hassibi, Babak (2016 54th Annual Allerton Conference on Communication, Control, and Computing (Allerton), Institute of Electrical and Electronics Engineers (IEEE), 2017-02-13) [Conference Paper]

Consider a distributed control problem with a communication channel connecting the observer of a linear stochastic system to the controller. The goal of the controller is minimize a quadratic cost function. The most basic special case of that cost function is the mean-square deviation of the system state from the desired state. We study the fundamental tradeoff between the communication rate r bits/sec and the limsup of the expected cost b, and show a lower bound on the rate necessary to attain b. The bound applies as long as the system noise has a probability density function. If target cost b is not too large, that bound can be closely approached by a simple lattice quantization scheme that only quantizes the innovation, that is, the difference between the controller's belief about the current state and the true state.

Improved bounds on the epidemic threshold of exact SIS models on complex networks

Ruhi, Navid Azizan; Thrampoulidis, Christos; Hassibi, Babak (2016 IEEE 55th Conference on Decision and Control (CDC), Institute of Electrical and Electronics Engineers (IEEE), 2017-01-05) [Conference Paper]

The SIS (susceptible-infected-susceptible) epidemic model on an arbitrary network, without making approximations, is a 2n-state Markov chain with a unique absorbing state (the all-healthy state). This makes analysis of the SIS model and, in particular, determining the threshold of epidemic spread quite challenging. It has been shown that the exact marginal probabilities of infection can be upper bounded by an n-dimensional linear time-invariant system, a consequence of which is that the Markov chain is “fast-mixing” when the LTI system is stable, i.e. when equation (where β is the infection rate per link, δ is the recovery rate, and λmax(A) is the largest eigenvalue of the network's adjacency matrix). This well-known threshold has been recently shown not to be tight in several cases, such as in a star network. In this paper, we provide tighter upper bounds on the exact marginal probabilities of infection, by also taking pairwise infection probabilities into account. Based on this improved bound, we derive tighter eigenvalue conditions that guarantee fast mixing (i.e., logarithmic mixing time) of the chain. We demonstrate the improvement of the threshold condition by comparing the new bound with the known one on various networks with various epidemic parameters.

Multi-rate control over AWGN channels via analog joint source-channel coding

Khina, Anatoly; Pettersson, Gustav M.; Kostina, Victoria; Hassibi, Babak (2016 IEEE 55th Conference on Decision and Control (CDC), Institute of Electrical and Electronics Engineers (IEEE), 2017-01-05) [Conference Paper]

We consider the problem of controlling an unstable plant over an additive white Gaussian noise (AWGN) channel with a transmit power constraint, where the signaling rate of communication is larger than the sampling rate (for generating observations and applying control inputs) of the underlying plant. Such a situation is quite common since sampling is done at a rate that captures the dynamics of the plant and which is often much lower than the rate that can be communicated. This setting offers the opportunity of improving the system performance by employing multiple channel uses to convey a single message (output plant observation or control input). Common ways of doing so are through either repeating the message, or by quantizing it to a number of bits and then transmitting a channel coded version of the bits whose length is commensurate with the number of channel uses per sampled message. We argue that such “separated source and channel coding” can be suboptimal and propose to perform joint source-channel coding. Since the block length is short we obviate the need to go to the digital domain altogether and instead consider analog joint source-channel coding. For the case where the communication signaling rate is twice the sampling rate, we employ the Archimedean bi-spiral-based Shannon-Kotel'nikov analog maps to show significant improvement in stability margins and linear-quadratic Gaussian (LQG) costs over simple schemes that employ repetition.

Balanced Reed-Solomon codes for all parameters

Halbawi, Wael; Liu, Zihan; Hassibi, Babak (2016 IEEE Information Theory Workshop (ITW), Institute of Electrical and Electronics Engineers (IEEE), 2016-10-27) [Conference Paper]

We construct balanced and sparsest generator matrices for cyclic Reed-Solomon codes with any length n and dimension k. By sparsest, we mean that each row has the least possible number of nonzeros, while balanced means that the number of nonzeros in any two columns differs by at most one. Codes allowing such encoding schemes are useful in distributed settings where computational load-balancing is critical. The problem was first studied by Dau et al. who showed, using probabilistic arguments, that there always exists an MDS code over a sufficiently large field such that its generator matrix is both sparsest and balanced. Motivated by the need for an explicit construction with efficient decoding, the authors of the current paper showed that the generator matrix of a cyclic Reed-Solomon code of length n and dimension k can always be transformed to one that is both sparsest and balanced, when n and k are such that k/n (n-k+1) is an integer. In this paper, we lift this condition and construct balanced and sparsest generator matrices for cyclic Reed-Solomon codes for any set of parameters.

(Almost) practical tree codes

Khina, Anatoly; Halbawi, Wael; Hassibi, Babak (2016 IEEE International Symposium on Information Theory (ISIT), Institute of Electrical and Electronics Engineers (IEEE), 2016-08-15) [Conference Paper]

We consider the problem of stabilizing an unstable plant driven by bounded noise over a digital noisy communication link, a scenario at the heart of networked control. To stabilize such a plant, one needs real-time encoding and decoding with an error probability profile that decays exponentially with the decoding delay. The works of Schulman and Sahai over the past two decades have developed the notions of tree codes and anytime capacity, and provided the theoretical framework for studying such problems. Nonetheless, there has been little practical progress in this area due to the absence of explicit constructions of tree codes with efficient encoding and decoding algorithms. Recently, linear time-invariant tree codes were proposed to achieve the desired result under maximum-likelihood decoding. In this work, we take one more step towards practicality, by showing that these codes can be efficiently decoded using sequential decoding algorithms, up to some loss in performance (and with some practical complexity caveats). We supplement our theoretical results with numerical simulations that demonstrate the effectiveness of the decoder in a control system setting.

Ber analysis of the box relaxation for BPSK signal recovery

Thrampoulidis, Christos; Abbasi, Ehsan; Xu, Weiyu; Hassibi, Babak (2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Institute of Electrical and Electronics Engineers (IEEE), 2016-06-24) [Conference Paper]

We study the problem of recovering an n-dimensional BPSK signal from m linear noise-corrupted measurements using the box relaxation method which relaxes the discrete set {±1}n to the convex set [-1,1]n to obtain a convex optimization algorithm followed by hard thresholding. When the noise and measurement matrix have iid standard normal entries, we obtain an exact expression for the bit-wise probability of error Pe in the limit of n and m growing and m/n fixed. At high SNR our result shows that the Pe of box relaxation is within 3dB of the matched filter bound (MFB) for square systems, and that it approaches the (MFB) as m grows large compared to n. Our results also indicate that as m, n → ∞, for any fixed set of size k, the error events of the corresponding k bits in the box relaxation method are independent.

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