392 research outputs found
Adaptive Cut Generation Algorithm for Improved Linear Programming Decoding of Binary Linear Codes
Linear programming (LP) decoding approximates maximum-likelihood (ML)
decoding of a linear block code by relaxing the equivalent ML integer
programming (IP) problem into a more easily solved LP problem. The LP problem
is defined by a set of box constraints together with a set of linear
inequalities called "parity inequalities" that are derived from the constraints
represented by the rows of a parity-check matrix of the code and can be added
iteratively and adaptively. In this paper, we first derive a new necessary
condition and a new sufficient condition for a violated parity inequality
constraint, or "cut," at a point in the unit hypercube. Then, we propose a new
and effective algorithm to generate parity inequalities derived from certain
additional redundant parity check (RPC) constraints that can eliminate
pseudocodewords produced by the LP decoder, often significantly improving the
decoder error-rate performance. The cut-generating algorithm is based upon a
specific transformation of an initial parity-check matrix of the linear block
code. We also design two variations of the proposed decoder to make it more
efficient when it is combined with the new cut-generating algorithm. Simulation
results for several low-density parity-check (LDPC) codes demonstrate that the
proposed decoding algorithms significantly narrow the performance gap between
LP decoding and ML decoding
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
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
Tevatron-for-LHC Report: Preparations for Discoveries
This is the "TeV4LHC" report of the "Physics Landscapes" Working Group,
focused on facilitating the start-up of physics explorations at the LHC by
using the experience gained at the Tevatron. We present experimental and
theoretical results that can be employed to probe various scenarios for physics
beyond the Standard Model.Comment: 222 pp., additional contribution added, typos/layout correcte
PYTHIA 6.4 Physics and Manual
The PYTHIA program can be used to generate high-energy-physics `events', i.e.
sets of outgoing particles produced in the interactions between two incoming
particles. The objective is to provide as accurate as possible a representation
of event properties in a wide range of reactions, within and beyond the
Standard Model, with emphasis on those where strong interactions play a role,
directly or indirectly, and therefore multihadronic final states are produced.
The physics is then not understood well enough to give an exact description;
instead the program has to be based on a combination of analytical results and
various QCD-based models. This physics input is summarized here, for areas such
as hard subprocesses, initial- and final-state parton showers, underlying
events and beam remnants, fragmentation and decays, and much more. Furthermore,
extensive information is provided on all program elements: subroutines and
functions, switches and parameters, and particle and process data. This should
allow the user to tailor the generation task to the topics of interest.Comment: 576 pages, no figures, uses JHEP3.cls. The code and further
information may be found on the PYTHIA web page:
http://www.thep.lu.se/~torbjorn/Pythia.html Changes in version 2: Mistakenly
deleted section heading for "Physics Processes" reinserted, affecting section
numbering. Minor updates to take into account referee comments and new colour
reconnection option
PYTHIA 6.3 Physics and Manual
The PYTHIA program can be used to generate high-energy-physics `events', i.e.
sets of outgoing particles produced in the interactions between two incoming
particles. The objective is to provide as accurate as possible a representation
of event properties in a wide range of reactions, with emphasis on those where
strong interactions play a role, directly or indirectly, and therefore
multihadronic final states are produced. The physics is then not understood
well enough to give an exact description; instead the program has to be based
on a combination of analytical results and various QCD-based models. This
physics input is summarized here, for areas such as hard subprocesses, initial-
and final-state parton showers, beam remnants and underlying events,
fragmentation and decays, and much more. Furthermore, extensive information is
provided on all program elements: subroutines and functions, switches and
parameters, and particle and process data. This should allow the user to tailor
the generation task to the topics of interest.Comment: 8 + 454 page
Black Hole Binary Dynamics from the Double Copy and Effective Theory
We describe a systematic framework for computing the conservative potential of a compact binary system using modern tools from scattering amplitudes and effective field theory. Our approach combines methods for integration and matching adapted from effective field theory, generalized unitarity, and the double-copy construction, which relates gravity integrands to simpler gauge-theory expressions. With these methods we derive the third post-Minkowskian correction to the conservative two-body Hamiltonian for spinless black holes. We describe in some detail various checks of our integration methods and the resulting Hamiltonian
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