Related papers: Decoding of scroll codes
This work studies certain aspects of graphs embedded on surfaces. Initially, a colored graph model for a map of a graph on a surface is developed. Then, a concept analogous to (and extending) planar graph is introduced in the same spirit as…
This paper investigates the concept of self-dual convolutional code. We derive the basic properties of this interesting class of codes and we show how some of the techniques to construct self-dual linear block codes generalize to self-dual…
We examine the topological characteristic cohomology classes of complexified vector bundles. In particular, all the classes coming from the real vector bundles underlying the complexification are determined.
The decoding of error syndromes of surface codes with classical algorithms may slow down quantum computation. To overcome this problem it is possible to implement decoding algorithms based on artificial neural networks. This work reports a…
This paper deals with a universal coding problem for a certain kind of multiterminal source coding network called a generalized complementary delivery network. In this network, messages from multiple correlated sources are jointly encoded,…
We introduce a characterization of topological order based on bulk oscillations of the entanglement entropy and the definition of an `entanglement gap', showing that it is generally applicable to pure and disordered quantum systems. Using…
We consider large uniform labeled random graphs in different classes with prescribed decorations in their modular decomposition. Our main result is the estimation of the number of copies of every graph as an induced subgraph. As a…
On a Goppa code whose structure polynomial has coefficients in the symbol field, the Frobenius acts. Its fixed codewords form a subcode. Deleting the naturally occurred redundance, we obtain a new code. It is proved that these new codes…
An important class of codes widely used in applications is the class of convolutional codes. Most of the literature of convolutional codes is devoted to con- volutional codes over finite fields. The extension of the concept of convolutional…
Several recently proposed code-based cryptosystems base their security on a slightly generalized version of the classical (syndrome) decoding problem. Namely, in the so-called restricted (syndrome) decoding problem, the error values stem…
Convolutional codes are constructed, designed and analysed using row and/or block structures of unit algebraic schemes. Infinite series of such codes and of codes with specific properties are derived. Properties are shown algebraically and…
The order statistics based list decoding techniques for linear binary block codes of small to medium block length are investigated. The construction of the list of the test error patterns is considered. The original order statistics…
In this paper we study the dual codes of a wide family of evaluation codes on norm-trace curves. We explicitly find out their minimum distance and give a lower bound for the number of their minimum-weight codewords. A general geometric…
Finding optimal correction of errors in generic stabilizer codes is a computationally hard problem, even for simple noise models. While this task can be simplified for codes with some structure, such as topological stabilizer codes,…
We present a formal language with expressions denoting general symbol structures and queries which access information in those structures. A sequence-to-sequence network processing this language learns to encode symbol structures and query…
In source coding, either with or without side information at the decoder, the ultimate performance can be achieved by means of random binning. Structured binning into cosets of performing channel codes has been successfully employed in…
Using linear functional-based duality of modules, we generalize the syndrome decoding algorithm of linear codes over finite fields to those over finite commutative rings. Moreover, If the ring is local the algorithm is simplified by…
Polynomial evaluation codes hold a prominent place in coding theory. In this work, we study the problem of list decoding for a general class of polynomial evaluation codes, also known as Toric codes, that are defined for any given convex…
Graphs are ubiquitous data structures for representing interactions between entities. With an emphasis on the use of graphs to represent chemical molecules, we explore the task of learning to generate graphs that conform to a distribution…
Staircase codes play an important role as error-correcting codes in optical communications. In this paper, a low-complexity method for resolving stall patterns when decoding staircase codes is described. Stall patterns are the dominating…