808 research outputs found
Improving the redundancy of Knuth's balancing scheme for packet transmission systems
A simple scheme was proposed by Knuth to generate binary balanced codewords
from any information word. However, this method is limited in the sense that
its redundancy is twice that of the full sets of balanced codes. The gap
between Knuth's algorithm's redundancy and that of the full sets of balanced
codes is significantly considerable. This paper attempts to reduce that gap.
Furthermore, many constructions assume that a full balancing can be performed
without showing the steps. A full balancing refers to the overall balancing of
the encoded information together with the prefix. We propose an efficient way
to perform a full balancing scheme that does not make use of lookup tables or
enumerative coding.Comment: 11 pages, 4 figures, journal article submitted to Turkish journal of
electrical and computer science
Enumerative Coding for Grassmannian Space
The Grassmannian space \Gr is the set of all dimensional subspaces of
the vector space~\smash{\F_q^n}. Recently, codes in the Grassmannian have
found an application in network coding. The main goal of this paper is to
present efficient enumerative encoding and decoding techniques for the
Grassmannian. These coding techniques are based on two different orders for the
Grassmannian induced by different representations of -dimensional subspaces
of \F_q^n. One enumerative coding method is based on a Ferrers diagram
representation and on an order for \Gr based on this representation. The
complexity of this enumerative coding is digit
operations. Another order of the Grassmannian is based on a combination of an
identifying vector and a reduced row echelon form representation of subspaces.
The complexity of the enumerative coding, based on this order, is
digits operations. A combination of the two
methods reduces the complexity on average by a constant factor.Comment: to appear in IEEE Transactions on Information Theor
Analysis of Carries in Signed Digit Expansions
The number of positive and negative carries in the addition of two
independent random signed digit expansions of given length is analyzed
asymptotically for the -system and the symmetric signed digit
expansion. The results include expectation, variance, covariance between the
positive and negative carries and a central limit theorem.
Dependencies between the digits require determining suitable transition
probabilities to obtain equidistribution on all expansions of given length. A
general procedure is described to obtain such transition probabilities for
arbitrary regular languages.
The number of iterations in von Neumann's parallel addition method for the
symmetric signed digit expansion is also analyzed, again including expectation,
variance and convergence to a double exponential limiting distribution. This
analysis is carried out in a general framework for sequences of generating
functions
Mutually Uncorrelated Primers for DNA-Based Data Storage
We introduce the notion of weakly mutually uncorrelated (WMU) sequences,
motivated by applications in DNA-based data storage systems and for
synchronization of communication devices. WMU sequences are characterized by
the property that no sufficiently long suffix of one sequence is the prefix of
the same or another sequence. WMU sequences used for primer design in DNA-based
data storage systems are also required to be at large mutual Hamming distance
from each other, have balanced compositions of symbols, and avoid primer-dimer
byproducts. We derive bounds on the size of WMU and various constrained WMU
codes and present a number of constructions for balanced, error-correcting,
primer-dimer free WMU codes using Dyck paths, prefix-synchronized and cyclic
codes.Comment: 14 pages, 3 figures, 1 Table. arXiv admin note: text overlap with
arXiv:1601.0817
Compositions into Powers of : Asymptotic Enumeration and Parameters
For a fixed integer base , we consider the number of compositions of
into a given number of powers of and, related, the maximum number of
representations a positive integer can have as an ordered sum of powers of .
We study the asymptotic growth of those numbers and give precise asymptotic
formulae for them, thereby improving on earlier results of Molteni. Our
approach uses generating functions, which we obtain from infinite transfer
matrices. With the same techniques the distribution of the largest denominator
and the number of distinct parts are investigated
On the Huffman and Alphabetic Tree Problem with General Cost Functions
We address generalized versions of the Huffman and Alphabetic Tree Problem where the cost caused by each individual leaf i, instead of being linear, depends on its depth in the tree by an arbitrary function. The objective is to minimize either the total cost or the maximum cost among all leaves. We review and extend the known results in this direction and devise a number of new algorithms and hardness proofs. It turns out that the Dynamic Programming approach for the Alphabetic Tree Problem can be extended to arbitrary cost functions, resulting in a time O(n (4)) optimal algorithm using space O(n (3)). We identify classes of cost functions where the well-known trick to reduce the runtime by a factor of n via a "monotonicity" property can be applied. For the generalized Huffman Tree Problem we show that even the k-ary version can be solved by a generalized version of the Coin Collector Algorithm of Larmore and Hirschberg (in Proc. SODA'90, pp. 310-318, 1990) when the cost functions are nondecreasing and convex. Furthermore, we give an O(n (2)logn) algorithm for the worst case minimization variants of both the Huffman and Alphabetic Tree Problem with nondecreasing cost functions. Investigating the limits of computational tractability, we show that the Huffman Tree Problem in its full generality is inapproximable unless P = NP, no matter if the objective function is the sum of leaf costs or their maximum. The alphabetic version becomes NP-hard when the leaf costs are interdependent.ArticleALGORITHMICA. 69(3): 582-604 (2014)journal articl
Proof Theory at Work: Complexity Analysis of Term Rewrite Systems
This thesis is concerned with investigations into the "complexity of term
rewriting systems". Moreover the majority of the presented work deals with the
"automation" of such a complexity analysis. The aim of this introduction is to
present the main ideas in an easily accessible fashion to make the result
presented accessible to the general public. Necessarily some technical points
are stated in an over-simplified way.Comment: Cumulative Habilitation Thesis, submitted to the University of
Innsbruc
- …