42,870 research outputs found
Aspects of local linear complexity
The concept of linear complexity is important in cryptography, and in particular in the study of stream ciphers. There are two varieties of linear complexity; global linear complexity, which applies to infinite periodic binary sequences, and local linear complexity, which applies to binary sequences of finite length.This thesis is concerned primarily with the latter.The local linear complexity of a finite binary sequence can be computed using the Berlekamp-Massey algorithm. Chapter 2 deals with a number of aspects of this algorithm.The Berlekamp-Massey algorithm also yields the linear complexity profile of a binary sequence. Linear complexity profiles are discussed in Chapter 3, and a number of associated enumeration results are obtained.In Chapter 4 it is shown that if the bits of a binary sequence satisfy certain conditions, expressible as a set of linear equations, then the linear complexity profile of the sequence will be restricted in some way. These restrictions take the form of conditions on the heights of the jumps in the profile.The final chapter deals with the randomness testing of binary sequences. Statistical tests for randomness based on linear complexity profiles are derived, and it is demonstrated how these tests can identify the non-randomness in the sequences discussed in the preceding chapter.<p
Summary Based Structures with Improved Sublinear Recovery for Compressed Sensing
We introduce a new class of measurement matrices for compressed sensing,
using low order summaries over binary sequences of a given length. We prove
recovery guarantees for three reconstruction algorithms using the proposed
measurements, including minimization and two combinatorial methods. In
particular, one of the algorithms recovers -sparse vectors of length in
sublinear time , and requires at most
measurements. The empirical oversampling constant
of the algorithm is significantly better than existing sublinear recovery
algorithms such as Chaining Pursuit and Sudocodes. In particular, for and , the oversampling factor is between 3 to 8. We provide
preliminary insight into how the proposed constructions, and the fast recovery
scheme can be used in a number of practical applications such as market basket
analysis, and real time compressed sensing implementation
Two computational primitives for algorithmic self-assembly: Copying and counting
Copying and counting are useful primitive operations for computation and construction. We have made DNA crystals that copy and crystals that count as they grow. For counting, 16 oligonucleotides assemble into four DNA Wang tiles that subsequently crystallize on a polymeric nucleating scaffold strand, arranging themselves in a binary counting pattern that could serve as a template for a molecular electronic demultiplexing circuit. Although the yield of counting crystals is low, and per-tile error rates in such crystals is roughly 10%, this work demonstrates the potential of algorithmic self-assembly to create complex nanoscale patterns of technological interest. A subset of the tiles for counting form information-bearing DNA tubes that copy bit strings from layer to layer along their length
Two-Variable Logic with Two Order Relations
It is shown that the finite satisfiability problem for two-variable logic
over structures with one total preorder relation, its induced successor
relation, one linear order relation and some further unary relations is
EXPSPACE-complete. Actually, EXPSPACE-completeness already holds for structures
that do not include the induced successor relation. As a special case, the
EXPSPACE upper bound applies to two-variable logic over structures with two
linear orders. A further consequence is that satisfiability of two-variable
logic over data words with a linear order on positions and a linear order and
successor relation on the data is decidable in EXPSPACE. As a complementing
result, it is shown that over structures with two total preorder relations as
well as over structures with one total preorder and two linear order relations,
the finite satisfiability problem for two-variable logic is undecidable
Coded Adaptive Linear Precoded Discrete Multitone Over PLC Channel
Discrete multitone modulation (DMT) systems exploit the capabilities of
orthogonal subcarriers to cope efficiently with narrowband interference, high
frequency attenuations and multipath fadings with the help of simple
equalization filters. Adaptive linear precoded discrete multitone (LP-DMT)
system is based on classical DMT, combined with a linear precoding component.
In this paper, we investigate the bit and energy allocation algorithm of an
adaptive LP-DMT system taking into account the channel coding scheme. A coded
adaptive LPDMT system is presented in the power line communication (PLC)
context with a loading algorithm which accommodates the channel coding gains in
bit and energy calculations. The performance of a concatenated channel coding
scheme, consisting of an inner Wei's 4-dimensional 16-states trellis code and
an outer Reed-Solomon code, in combination with the proposed algorithm is
analyzed. Theoretical coding gains are derived and simulation results are
presented for a fixed target bit error rate in a multicarrier scenario under
power spectral density constraint. Using a multipath model of PLC channel, it
is shown that the proposed coded adaptive LP-DMT system performs better than
coded DMT and can achieve higher throughput for PLC applications
Quantifying hidden order out of equilibrium
While the equilibrium properties, states, and phase transitions of
interacting systems are well described by statistical mechanics, the lack of
suitable state parameters has hindered the understanding of non-equilibrium
phenomena in diverse settings, from glasses to driven systems to biology. The
length of a losslessly compressed data file is a direct measure of its
information content: The more ordered the data is, the lower its information
content and the shorter the length of its encoding can be made. Here, we
describe how data compression enables the quantification of order in
non-equilibrium and equilibrium many-body systems, both discrete and
continuous, even when the underlying form of order is unknown. We consider
absorbing state models on and off-lattice, as well as a system of active
Brownian particles undergoing motility-induced phase separation. The technique
reliably identifies non-equilibrium phase transitions, determines their
character, quantitatively predicts certain critical exponents without prior
knowledge of the order parameters, and reveals previously unknown ordering
phenomena. This technique should provide a quantitative measure of organization
in condensed matter and other systems exhibiting collective phase transitions
in and out of equilibrium
Learning Convex Partitions and Computing Game-theoretic Equilibria from Best Response Queries
Suppose that an -simplex is partitioned into convex regions having
disjoint interiors and distinct labels, and we may learn the label of any point
by querying it. The learning objective is to know, for any point in the
simplex, a label that occurs within some distance from that point.
We present two algorithms for this task: Constant-Dimension Generalised Binary
Search (CD-GBS), which for constant uses queries, and Constant-Region Generalised Binary
Search (CR-GBS), which uses CD-GBS as a subroutine and for constant uses
queries.
We show via Kakutani's fixed-point theorem that these algorithms provide
bounds on the best-response query complexity of computing approximate
well-supported equilibria of bimatrix games in which one of the players has a
constant number of pure strategies. We also partially extend our results to
games with multiple players, establishing further query complexity bounds for
computing approximate well-supported equilibria in this setting.Comment: 38 pages, 7 figures, second version strengthens lower bound in
Theorem 6, adds footnotes with additional comments and fixes typo
Trellis decoding complexity of linear block codes
In this partially tutorial paper, we examine minimal trellis representations of linear block codes and analyze several measures of trellis complexity: maximum state and edge dimensions, total span length, and total vertices, edges and mergers. We obtain bounds on these complexities as extensions of well-known dimension/length profile (DLP) bounds. Codes meeting these bounds minimize all the complexity measures simultaneously; conversely, a code attaining the bound for total span length, vertices, or edges, must likewise attain it for all the others. We define a notion of “uniform” optimality that embraces different domains of optimization, such as different permutations of a code or different codes with the same parameters, and we give examples of uniformly optimal codes and permutations. We also give some conditions that identify certain cases when no code or permutation can meet the bounds. In addition to DLP-based bounds, we derive new inequalities relating one complexity measure to another, which can be used in conjunction with known bounds on one measure to imply bounds on the others. As an application, we infer new bounds on maximum state and edge complexity and on total vertices and edges from bounds on span lengths
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