2,347 research outputs found
A Closed-Form Shave from Occam's Quantum Razor: Exact Results for Quantum Compression
The causal structure of a stochastic process can be more efficiently
transmitted via a quantum channel than a classical one, an advantage that
increases with codeword length. While previously difficult to compute, we
express the quantum advantage in closed form using spectral decomposition,
leading to direct computation of the quantum communication cost at all encoding
lengths, including infinite. This makes clear how finite-codeword compression
is controlled by the classical process' cryptic order and allows us to analyze
structure within the length-asymptotic regime of infinite-cryptic order (and
infinite Markov order) processes.Comment: 21 pages, 13 figures;
http://csc.ucdavis.edu/~cmg/compmech/pubs/eqc.ht
Fast performance estimation of block codes
Importance sampling is used in this paper to address the classical yet important problem of performance estimation of block codes. Simulation distributions that comprise discreteand continuous-mixture probability densities are motivated and used for this application. These mixtures are employed in concert with the so-called g-method, which is a conditional importance sampling technique that more effectively exploits knowledge of underlying input distributions. For performance estimation, the emphasis is on bit by bit maximum a-posteriori probability decoding, but message passing algorithms for certain codes have also been investigated. Considered here are single parity check codes, multidimensional product codes, and briefly, low-density parity-check codes. Several error rate results are presented for these various codes, together with performances of the simulation techniques
Hybrid Coding Technique for Pulse Detection in an Optical Time Domain Reflectometer
The paper introduces a novel hybrid coding technique for improved pulse detection in an optical time domain reflectometer. The hybrid schemes combines Simplex codes with signal averaging to articulate a very sophisticated coding technique that considerably reduces the processing time to extract specified coding gains in comparison to the existing techniques. The paper quantifies the coding gain of the hybrid scheme mathematically and provide simulative results in direct agreement with the theoretical performance. Furthermore, the hybrid scheme has been tested on our self-developed OTDR
Design and Analysis of Nonbinary LDPC Codes for Arbitrary Discrete-Memoryless Channels
We present an analysis, under iterative decoding, of coset LDPC codes over
GF(q), designed for use over arbitrary discrete-memoryless channels
(particularly nonbinary and asymmetric channels). We use a random-coset
analysis to produce an effect that is similar to output-symmetry with binary
channels. We show that the random selection of the nonzero elements of the
GF(q) parity-check matrix induces a permutation-invariance property on the
densities of the decoder messages, which simplifies their analysis and
approximation. We generalize several properties, including symmetry and
stability from the analysis of binary LDPC codes. We show that under a Gaussian
approximation, the entire q-1 dimensional distribution of the vector messages
is described by a single scalar parameter (like the distributions of binary
LDPC messages). We apply this property to develop EXIT charts for our codes. We
use appropriately designed signal constellations to obtain substantial shaping
gains. Simulation results indicate that our codes outperform multilevel codes
at short block lengths. We also present simulation results for the AWGN
channel, including results within 0.56 dB of the unconstrained Shannon limit
(i.e. not restricted to any signal constellation) at a spectral efficiency of 6
bits/s/Hz.Comment: To appear, IEEE Transactions on Information Theory, (submitted
October 2004, revised and accepted for publication, November 2005). The
material in this paper was presented in part at the 41st Allerton Conference
on Communications, Control and Computing, October 2003 and at the 2005 IEEE
International Symposium on Information Theor
Tight Bounds on the R\'enyi Entropy via Majorization with Applications to Guessing and Compression
This paper provides tight bounds on the R\'enyi entropy of a function of a
discrete random variable with a finite number of possible values, where the
considered function is not one-to-one. To that end, a tight lower bound on the
R\'enyi entropy of a discrete random variable with a finite support is derived
as a function of the size of the support, and the ratio of the maximal to
minimal probability masses. This work was inspired by the recently published
paper by Cicalese et al., which is focused on the Shannon entropy, and it
strengthens and generalizes the results of that paper to R\'enyi entropies of
arbitrary positive orders. In view of these generalized bounds and the works by
Arikan and Campbell, non-asymptotic bounds are derived for guessing moments and
lossless data compression of discrete memoryless sources.Comment: The paper was published in the Entropy journal (special issue on
Probabilistic Methods in Information Theory, Hypothesis Testing, and Coding),
vol. 20, no. 12, paper no. 896, November 22, 2018. Online available at
https://www.mdpi.com/1099-4300/20/12/89
Authentication of Satellite Navigation Signals by Wiretap Coding and Artificial Noise
In order to combat the spoofing of global navigation satellite system (GNSS)
signals we propose a novel approach for satellite signal authentication based
on information-theoretic security. In particular we superimpose to the
navigation signal an authentication signal containing a secret message
corrupted by artificial noise (AN), still transmitted by the satellite. We
impose the following properties: a) the authentication signal is synchronous
with the navigation signal, b) the authentication signal is orthogonal to the
navigation signal and c) the secret message is undecodable by the attacker due
to the presence of the AN. The legitimate receiver synchronizes with the
navigation signal and stores the samples of the authentication signal with the
same synchronization. After the transmission of the authentication signal,
through a separate public asynchronous authenticated channel (e.g., a secure
Internet connection) additional information is made public allowing the
receiver to a) decode the secret message, thus overcoming the effects of AN,
and b) verify the secret message. We assess the performance of the proposed
scheme by the analysis of both the secrecy capacity of the authentication
message and the attack success probability, under various attack scenarios. A
comparison with existing approaches shows the effectiveness of the proposed
scheme
Tight and simple Web graph compression
Analysing Web graphs has applications in determining page ranks, fighting Web
spam, detecting communities and mirror sites, and more. This study is however
hampered by the necessity of storing a major part of huge graphs in the
external memory, which prevents efficient random access to edge (hyperlink)
lists. A number of algorithms involving compression techniques have thus been
presented, to represent Web graphs succinctly but also providing random access.
Those techniques are usually based on differential encodings of the adjacency
lists, finding repeating nodes or node regions in the successive lists, more
general grammar-based transformations or 2-dimensional representations of the
binary matrix of the graph. In this paper we present two Web graph compression
algorithms. The first can be seen as engineering of the Boldi and Vigna (2004)
method. We extend the notion of similarity between link lists, and use a more
compact encoding of residuals. The algorithm works on blocks of varying size
(in the number of input lines) and sacrifices access time for better
compression ratio, achieving more succinct graph representation than other
algorithms reported in the literature. The second algorithm works on blocks of
the same size, in the number of input lines, and its key mechanism is merging
the block into a single ordered list. This method achieves much more attractive
space-time tradeoffs.Comment: 15 page
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