17,213 research outputs found
Computational methods in codes and games
This dissertation discusses exhaustive search algorithms and heuristic search methods in combinatorial optimization, including combinatorial games.
In this work unidirectional covering codes are introduced and some theoretical foundations for them are laid. Exhaustive search is used to construct asymmetric covering codes, unidirectional covering codes and multiple coverings with given parametersâor to show that no such codes exist. Integer programming formulations, bounds on maximal coverages of partial codes and code isomorphisms are used to prune the search space.
Tabu search is used to construct asymmetric and unidirectional covering codesâwith several record-breaking codes for the former. A new definition for neighborhood is derived.
The traditional board game of go and computer go results are reviewed. The concept of entropy is introduced into the game context as a metric for complexity and for relevance (of featuresâlike distance to the previous move). Experimental results and questionnaire studies are presented to support the use of entropy
Two-batch liar games on a general bounded channel
We consider an extension of the 2-person R\'enyi-Ulam liar game in which lies
are governed by a channel , a set of allowable lie strings of maximum length
. Carole selects , and Paul makes -ary queries to uniquely
determine . In each of rounds, Paul weakly partitions and asks for such that . Carole responds with some
, and if , then accumulates a lie . Carole's string of
lies for must be in the channel . Paul wins if he determines within
rounds. We further restrict Paul to ask his questions in two off-line
batches. We show that for a range of sizes of the second batch, the maximum
size of the search space for which Paul can guarantee finding the
distinguished element is as ,
where is the number of lie strings in of maximum length . This
generalizes previous work of Dumitriu and Spencer, and of Ahlswede, Cicalese,
and Deppe. We extend Paul's strategy to solve also the pathological liar
variant, in a unified manner which gives the existence of asymptotically
perfect two-batch adaptive codes for the channel .Comment: 26 page
Asymmetric binary covering codes
An asymmetric binary covering code of length n and radius R is a subset C of
the n-cube Q_n such that every vector x in Q_n can be obtained from some vector
c in C by changing at most R 1's of c to 0's, where R is as small as possible.
K^+(n,R) is defined as the smallest size of such a code. We show K^+(n,R) is of
order 2^n/n^R for constant R, using an asymmetric sphere-covering bound and
probabilistic methods. We show K^+(n,n-R')=R'+1 for constant coradius R' iff
n>=R'(R'+1)/2. These two results are extended to near-constant R and R',
respectively. Various bounds on K^+ are given in terms of the total number of
0's or 1's in a minimal code. The dimension of a minimal asymmetric linear
binary code ([n,R]^+ code) is determined to be min(0,n-R). We conclude by
discussing open problems and techniques to compute explicit values for K^+,
giving a table of best known bounds.Comment: 16 page
Rewriting Codes for Joint Information Storage in Flash Memories
Memories whose storage cells transit irreversibly between
states have been common since the start of the data storage
technology. In recent years, flash memories have become a very
important family of such memories. A flash memory cell has q
statesâstate 0.1.....q-1 - and can only transit from a lower
state to a higher state before the expensive erasure operation takes
place. We study rewriting codes that enable the data stored in a
group of cells to be rewritten by only shifting the cells to higher
states. Since the considered state transitions are irreversible, the
number of rewrites is bounded. Our objective is to maximize the
number of times the data can be rewritten. We focus on the joint
storage of data in flash memories, and study two rewriting codes
for two different scenarios. The first code, called floating code, is for
the joint storage of multiple variables, where every rewrite changes
one variable. The second code, called buffer code, is for remembering
the most recent data in a data stream. Many of the codes
presented here are either optimal or asymptotically optimal. We
also present bounds to the performance of general codes. The results
show that rewriting codes can integrate a flash memoryâs
rewriting capabilities for different variables to a high degree
Communication and Interference Coordination
We study the problem of controlling the interference created to an external
observer by a communication processes. We model the interference in terms of
its type (empirical distribution), and we analyze the consequences of placing
constraints on the admissible type. Considering a single interfering link, we
characterize the communication-interference capacity region. Then, we look at a
scenario where the interference is jointly created by two users allowed to
coordinate their actions prior to transmission. In this case, the trade-off
involves communication and interference as well as coordination. We establish
an achievable communication-interference region and show that efficiency is
significantly improved by coordination
Protection of parity-time symmetry in topological many-body systems: non-Hermitian toric code and fracton models
In the study of -symmetric quantum systems with
non-Hermitian perturbations, one of the most important questions is whether
eigenvalues stay real or whether -symmetry is
spontaneously broken when eigenvalues meet. A particularly interesting set of
eigenstates is provided by the degenerate ground-state subspace of systems with
topological order. In this paper, we present simple criteria that guarantee the
protection of -symmetry and, thus, the reality of the
eigenvalues in topological many-body systems. We formulate these criteria in
both geometric and algebraic form, and demonstrate them using the toric code
and several different fracton models as examples. Our analysis reveals that
-symmetry is robust against a remarkably large class of
non-Hermitian perturbations in these models; this is particularly striking in
the case of fracton models due to the exponentially large number of degenerate
states.Comment: 20 pages, 6 figure
Design issues for the Generic Stream Encapsulation (GSE) of IP datagrams over DVB-S2
The DVB-S2 standard has brought an unprecedented degree of novelty and flexibility in the way IP datagrams or other network level packets can be transmitted over DVB satellite links, with the introduction of an IP-friendly link layer - he continuous Generic Streams - and the adaptive combination of advanced error coding, modulation and spectrum management techniques. Recently approved by the DVB, the Generic Stream Encapsulation (GSE) used for carrying IP datagrams over DVBS2 implements solutions stemmed from a design rationale quite different from the one behind IP encapsulation schemes over its predecessor DVB-S. This paper highlights GSE's original design choices under the perspective of DVB-S2's innovative features and possibilities
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