10,277 research outputs found
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
Error-Correcting Codes for Automatic Control
Systems with automatic feedback control may consist of several remote devices, connected only by unreliable communication channels. It is necessary in these conditions to have a method for accurate, real-time state estimation in the presence of channel noise. This problem is addressed, for the case of polynomial-growth-rate state spaces, through a new type of error-correcting code that is online and computationally efficient. This solution establishes a constructive analog, for some applications in estimation and control, of the Shannon coding theorem
New Free Distance Bounds and Design Techniques for Joint Source-Channel Variable-Length Codes
International audienceThis paper proposes branch-and-prune algorithms for searching prefix-free joint source-channel codebooks with maximal free distance for given codeword lengths. For that purpose, it introduces improved techniques to bound the free distance of variable-length codes
Decoding Across the Quantum LDPC Code Landscape
We show that belief propagation combined with ordered statistics
post-processing is a general decoder for quantum low density parity check codes
constructed from the hypergraph product. To this end, we run numerical
simulations of the decoder applied to three families of hypergraph product
code: topological codes, fixed-rate random codes and a new class of codes that
we call semi-topological codes. Our new code families share properties of both
topological and random hypergraph product codes, with a construction that
allows for a finely-controlled trade-off between code threshold and stabilizer
locality. Our results indicate thresholds across all three families of
hypergraph product code, and provide evidence of exponential suppression in the
low error regime. For the Toric code, we observe a threshold in the range
. This result improves upon previous quantum decoders based on
belief propagation, and approaches the performance of the minimum weight
perfect matching algorithm. We expect semi-topological codes to have the same
threshold as Toric codes, as they are identical in the bulk, and we present
numerical evidence supporting this observation.Comment: The code for the BP+OSD decoder used in this work can be found on
Github: https://github.com/quantumgizmos/bp_os
EvoL: The new Padova T-SPH parallel code for cosmological simulations - I. Basic code: gravity and hydrodynamics
We present EvoL, the new release of the Padova N-body code for cosmological
simulations of galaxy formation and evolution. In this paper, the basic Tree +
SPH code is presented and analysed, together with an overview on the software
architectures. EvoL is a flexible parallel Fortran95 code, specifically
designed for simulations of cosmological structure formation on cluster,
galactic and sub-galactic scales. EvoL is a fully Lagrangian self-adaptive
code, based on the classical Oct-tree and on the Smoothed Particle
Hydrodynamics algorithm. It includes special features such as adaptive
softening lengths with correcting extra-terms, and modern formulations of SPH
and artificial viscosity. It is designed to be run in parallel on multiple CPUs
to optimize the performance and save computational time. We describe the code
in detail, and present the results of a number of standard hydrodynamical
tests.Comment: 33 pages, 49 figures, accepted on A&
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