Related papers: Bifix codes and interval exchanges
We present several enumeration results holding in sets of words called neutral and which satisfy restrictive conditions on the set of possible extensions of nonempty words. These formulae concern return words and bifix codes. They…
Ideal dense coding protocols allow one to use prior maximal entanglement to send two bits of classical information by the physical transfer of a single encoded qubit. We investigate the case when the prior entanglement is not maximal and…
In this paper we go into the study of 2-limits and 2-colimits in the 2-category CAT the category of small categories. More precisely we show the commutation of filtered 2-colimits and finite 2-limits. It is a generalization of a classical…
Index coding and coded caching are two active research topics in information theory with strong ties to each other. Motivated by the multi-access coded caching problem, we study a new class of structured index coding problems (ICPs) which…
Why do bilingual speakers code-switch (mix their two languages)? Among the several theories that attempt to explain this natural and ubiquitous phenomenon, the Triggering Hypothesis relates code-switching to the presence of lexical…
The introduction of physical layer network coding gives rise to the concept of turning a collision of transmissions on a wireless channel useful. In the idea of physical layer network coding, two synchronized simultaneous packet…
We study the ergodic properties of compositions of interval exchange transformations and rotations. We show that for any interval exchange transformation T, there is a full measure set of \alpha in [0, 1) so that T composed with R_{\alpha}…
Let us call subdivision {\it good}, if 1) set corresponding to each symbol is convex (i.e. interval or (semi)closed interval). 2) If points $A$ and $B$ corresponds to the some color and interval $(A,B)$ has discontinuity point, then $f(A)$…
We approach the study of complete bifix decodings of (uniformly) recurrent languages with the help of the free profinite monoid. We show that the complete bifix decoding of a uniformly recurrent language $F$ by an $F$-charged rational…
Motivated by recent interests in predictive inference under distribution shift, we study the problem of approximating finite weighted exchangeable sequences by a mixture of finite sequences with independent terms. Various bounds are derived…
We compute the bi-free max-convolution which is the operation on bi-variate distribution functions corresponding to the max-operation with respect to the spectral order on bi-free bi-partite two-faced pairs of hermitian non-commutative…
In this paper we describe a class of codes called {\it permutation codes}. This class of codes is a generalization of cyclic codes and quasi-cyclic codes. We also give some examples of optimal permutation codes over binary, ternary, and…
Non-binary codes correcting multiple deletions have recently attracted a lot of attention. In this work, we focus on multiplicity-free codes, a family of non-binary codes where all symbols are distinct. Our main contribution is a new…
We consider the problem of optimal exchange which can be formulated as a kind of optimal transportation problem. The existence of an optimal solution and a duality theorem for the optimal exchange problem are proved in case of completely…
In this article we demonstrate the relationship between finitely exchangeable arrays and finitely exchangeable sequences. We then derive sharp bounds on the total variation distance between distributions of finitely and infinitely…
The fragmentation processes of exchangeable partitions have already been studied by several authors. In this paper, we examine rather fragmentation of exchangeable compositions, that means partitions of $\mathbb{N}$ where the order of the…
For complete graphs and n-cubes bounds are found for the possible number of colours in an interval edge colourings.
A typical interval exchange transformation has an infinite sequence of matrices associated to it by successive iterations of Rauzy induction. In 2010, W. A. Veech answered a question of A. Bufetov by showing that the interval exchange…
Multidimensional convolutional codes generalize (one dimensional) convolutional codes and they correspond under a natural duality to multidimensional systems widely studied in the systems literature.
The theoretical code-switching (CS) literature provides numerous pointwise investigations that aim to explain patterns in CS, i.e. why bilinguals switch language in certain positions in a sentence more often than in others. A resulting…