arXiv subjects

David A. Karpuk

Publications and source records attributed to David A. Karpuk.

6 recordsLinked to original sources

arXiv2019

Private Polynomial Computation from Lagrange Encoding

Private computation is a generalization of private information retrieval, in which a user is able to compute a function on a distributed dataset without revealing the identity of that function to the servers. In this paper it is shown that Lagrange encoding, a powerful technique for encoding Reed-Solomon codes, enables private computation in many cases of interest. In particular, we present a scheme that enables private computation of polynomials of any degree on Lagrange encoded data, while being robust to Byzantine and straggling servers, and to servers colluding to attempt to deduce the identities of the functions to be evaluated. Moreover, incorporating ideas from the well-known Shamir secret sharing scheme allows the data itself to be concealed from the servers as well. Our results extend private computation to high degree polynomials and to data-privacy, and reveal a tight connection between private computation and coded computation.

cs.IT↗

arXiv2016

Channel Pre-Inversion and max-SINR Vector Perturbation for Large-Scale Broadcast Channels

We study channel pre-inversion and vector perturbation (VP) schemes for large-scale broadcast channels, wherein a transmitter has $M$ transmit antennas and is transmitting to $K$ single-antenna non-cooperating receivers. We provide results which predict the capacity of MMSE pre-inversion as $K\rightarrow\infty$. We construct a new VP strategy, max-SINR vector perturbation (MSVP), which maximizes a sharp estimate of the signal-to-interference-plus-noise ratio. We provide results which predict the performance of MSVP and demonstrate that MSVP outperforms other VP methods. Lastly, we combine MSVP with the low-complexity Sorted QR Precoding method to show that MSVP has the potential to efficiently deliver data to a very large number of users at close to channel capacity.

cs.IT↗

arXiv2016

Well-Rounded Lattices for Coset Coding in MIMO Wiretap Channels

The concept of well-rounded lattices has recently found important applications in the setting of a fading single-input single-output (SISO) wiretap channel. It has been shown that, under this setup, the property of being well-rounded is critical for minimizing the eavesdropper's probability of correct decoding in lower SNR regimes. The superior performance of coset codes constructed from well-rounded lattices has been illustrated in several simulations. In the present article, this work is extended to fading multiple-input multiple-output (MIMO) wiretap channels, and similar design criteria as in the SISO case are derived. Further, explicit coset codes for Rayleigh fading MIMO wiretap channels are designed. In particular, it is shown through extensive simulations that sublattices of the well-known Alamouti code and Golden code which meet our design criteria perform better than scalar multiples of the code lattice for the same parameters.

cs.IT↗

arXiv2016

Nested Lattice Codes for Vector Perturbation Systems

Vector perturbation is an encoding method for broadcast channels in which the transmitter solves a shortest vector problem in a lattice to create a perturbation vector, which is then added to the data before transmission. In this work, we introduce nested lattice codes into vector perturbation systems, resulting in a strategy which we deem matrix perturbation. We propose design criteria for the nested lattice codes, and show empirically that lattices satisfying these design criteria can improve the performance of vector perturbation systems. The resulting design criteria are the same as those recently proposed for the Compute-and-Forward protocol.

cs.IT↗

arXiv2013

Rotating Non-Uniform and High-Dimensional Constellations Using Geodesic Flow on Lie Groups

We use a numerical algorithm on the Lie group of rotation matrices to obtain rotated constellations for Rayleigh fading channels. Our approach minimizes the union bound for the pairwise error probability to produce rotations optimized for a given signal-to-noise ratio. This approach circumvents explicit parametrization of rotation matrices, which has previously prevented robust numerical methods from being applied to constellation rotation. Our algorithm is applicable to arbitrary finite constellations in arbitrary dimensions, and one can thus apply our method to non-uniform constellations, which are of interest for practical concerns due to their ability to increase BICM capacity. We show how our rotations can improve the codeword error performance of non-uniform constellations, and we also apply our method to reproduce and improve rotations given by ideal lattices in cyclotomic fields.

cs.IT↗

arXiv2012

Weil-étale Cohomology over $p$-adic Fields

We establish duality results for the cohomology of the Weil group of a $p$-adic field, analogous to, but more general than, results from Galois cohomology. We prove a duality theorem for discrete Weil modules, which implies Tate-Nakayama Duality. We define Weil-smooth cohomology for varieties over local fields, and prove a duality theorem for the cohomology of $\G_m$ on a smooth, proper curve with a rational point. This last theorem is analogous to, and implies, a classical duality theorem for such curves.

math.NT↗