Efficient Maximum-Likelihood Decoding of Linear Block Codes on Binary Memoryless Channels

In this work, we consider efficient maximum-likelihood decoding of linear block codes for small-to-moderate block lengths. The presented approach is a branch-and-bound algorithm using the cutting-plane approach of Zhang and Siegel (IEEE Trans. Inf. Theory, 2012) for obtaining lower bounds. We have compared our proposed algorithm to the state-of-the-art commercial integer program solver CPLEX, and for all considered codes our approach is faster for both low and high signal-to-noise ratios. For instance, for the benchmark (155,64) Tanner code our algorithm is more than 11 times as fast as CPLEX for an SNR of 1.0 dB on the additive white Gaussian noise channel. By a small modification, our algorithm can be used to calculate the minimum distance, which we have again verified to be much faster than using the CPLEX solver.Comment: Submitted to 2014 International Symposium on Information Theory. 5 Pages. Accepte

Minimum Pseudoweight Analysis of 3-Dimensional Turbo Codes

In this work, we consider pseudocodewords of (relaxed) linear programming (LP) decoding of 3-dimensional turbo codes (3D-TCs). We present a relaxed LP decoder for 3D-TCs, adapting the relaxed LP decoder for conventional turbo codes proposed by Feldman in his thesis. We show that the 3D-TC polytope is proper and $C$-symmetric, and make a connection to finite graph covers of the 3D-TC factor graph. This connection is used to show that the support set of any pseudocodeword is a stopping set of iterative decoding of 3D-TCs using maximum a posteriori constituent decoders on the binary erasure channel. Furthermore, we compute ensemble-average pseudoweight enumerators of 3D-TCs and perform a finite-length minimum pseudoweight analysis for small cover degrees. Also, an explicit description of the fundamental cone of the 3D-TC polytope is given. Finally, we present an extensive numerical study of small-to-medium block length 3D-TCs, which shows that 1) typically (i.e., in most cases) when the minimum distance $d_{\rm min}$ and/or the stopping distance $h_{\rm min}$ is high, the minimum pseudoweight (on the additive white Gaussian noise channel) is strictly smaller than both the $d_{\rm min}$ and the $h_{\rm min}$, and 2) the minimum pseudoweight grows with the block length, at least for small-to-medium block lengths.Comment: To appear in IEEE Transactions on Communication

Mathematical Programming Decoding of Binary Linear Codes: Theory and Algorithms

Mathematical programming is a branch of applied mathematics and has recently been used to derive new decoding approaches, challenging established but often heuristic algorithms based on iterative message passing. Concepts from mathematical programming used in the context of decoding include linear, integer, and nonlinear programming, network flows, notions of duality as well as matroid and polyhedral theory. This survey article reviews and categorizes decoding methods based on mathematical programming approaches for binary linear codes over binary-input memoryless symmetric channels.Comment: 17 pages, submitted to the IEEE Transactions on Information Theory. Published July 201

Pseudocodewords of linear programming decoding of 3-dimensional turbo codes

In this work, we consider pseudocodewords of (relaxed) linear programming (LP) decoding of 3-dimensional turbo codes (3D-TCs), recently introduced by Berrou et al.. Here, we consider binary 3D-TCs while the original work of Berrou et al. considered double-binary codes. We present a relaxed LP decoder for 3D-TCs, which is an adaptation of the relaxed LP decoder for conventional turbo codes proposed by Feldman in his thesis. The vertices of this relaxed polytope are the pseudocodewords. We show that the support set of any pseudocodeword is a stopping set of iterative decoding of 3D-TCs using maximum a posteriori constituent decoders on the binary erasure channel. Furthermore, we present a numerical study of small block length 3D-TCs, which shows that typically the minimum pseudoweight (on the additive white Gaussian noise (AWGN) channel) is smaller than both the minimum distance and the stopping distance. In particular, we performed an exhaustive search over all interleaver pairs in the 3D-TC (with input block length K = 128) based on quadratic permutation polynomials over integer rings with a quadratic inverse. The search shows that the best minimum AWGN pseudoweight is strictly smaller than the best minimum/stopping distance

PANIC: the new panoramic NIR camera for Calar Alto

PANIC is a wide-field NIR camera, which is currently under development for the Calar Alto observatory (CAHA) in Spain. It uses a mosaic of four Hawaii-2RG detectors and covers the spectral range from 0.8-2.5 micron(z to K-band). The field-of-view is 30x30 arcmin. This instrument can be used at the 2.2m telescope (0.45arcsec/pixel, 0.5x0.5 degree FOV) and at the 3.5m telescope (0.23arcsec/pixel, 0.25x0.25 degree FOV). The operating temperature is about 77K, achieved by liquid Nitrogen cooling. The cryogenic optics has three flat folding mirrors with diameters up to 282 mm and nine lenses with diameters between 130 mm and 255 mm. A compact filter unit can carry up to 19 filters distributed over four filter wheels. Narrow band (1%) filters can be used. The instrument has a diameter of 1.1 m and it is about 1 m long. The weight limit of 400 kg at the 2.2m telescope requires a light-weight cryostat design. The aluminium vacuum vessel and radiation shield have wall thicknesses of only 6 mm and 3 mm respectively.Comment: This paper has been presented in the SPIE of Astronomical Telescopes and Instrumentation 2008 in Marseille (France

Introduction to Mathematical Programming-Based Error-Correction Decoding

Decoding error-correctiong codes by methods of mathematical optimization, most importantly linear programming, has become an important alternative approach to both algebraic and iterative decoding methods since its introduction by Feldman et al. At first celebrated mainly for its analytical powers, real-world applications of LP decoding are now within reach thanks to most recent research. This document gives an elaborate introduction into both mathematical optimization and coding theory as well as a review of the contributions by which these two areas have found common ground.Comment: LaTeX sources maintained here: https://github.com/supermihi/lpdintr

Automated Evaluation of Environmental Coupling for Advanced LIGO Gravitational Wave Detections

The extreme sensitivity required for direct observation of gravitational waves by the Advanced LIGO detectors means that environmental noise is increasingly likely to contaminate Advanced LIGO gravitational wave signals if left unaddressed. Consequently, environmental monitoring efforts have been undertaken and novel noise mitigation techniques have been developed which have reduced environmental coupling and made it possible to analyze environmental artifacts with potential to affect the 90 gravitational wave events detected from 2015-2020 by the Advanced LIGO detectors. So far, there is no evidence for environmental contamination in gravitational wave detections. However, automated, rapid ways to monitor and assess the degree of environmental coupling between gravitational wave detectors and their surroundings are needed as the rate of detections continues to increase. We introduce a computational tool, PEMcheck, for quantifying the degree of environmental coupling present in gravitational wave signals using data from the extant collection of environmental monitoring sensors at each detector. We find that PEMcheck's automated analysis identifies only a small number of gravitational waves that merit further study by environmental noise experts due to possible contamination, a substantial improvement over the manual vetting that occurred for every gravitational wave candidate in the first two observing runs. With the validation provided herein; PEMcheck will play a critical role in event validation during LIGO's fourth observing run as an integral part of the data quality report produced for each gravitational wave candidate.Comment: 26 pages, 9 figures. Copy of accepted manuscrip