Variable-Length Non-Overlapping Codes
@article{Bilotta2017VariableLengthNC, title={Variable-Length Non-Overlapping Codes}, author={Stefano Bilotta}, journal={IEEE Transactions on Information Theory}, year={2017}, volume={63}, pages={6530-6537} }
We define a variable-length code having the property that no (non-empty) prefix of each its codeword is a suffix of any other one, and vice versa. This kind of code can be seen as an extension of two well-known codes in the literature, called, respectively, fix-free code and non-overlapping code. In this paper we present constructive algorithms for such codes and some numerical results about their cardinality.
7 Citations
Variable dimension non-overlapping matrices
- Computer Science
- 2020
This paper uses non-overlapping variable length strings as rows of the matrices and imposing the avoidance of two consecutive patterns of length k, gets the desired sets of non-ovelapping matrices with variable dimension.
Non-overlapping matrices via Dyck words
- MathematicsEnumerative Combinatorics and Applications
- 2021
We define a set of binary matrices where any two of these can not be placed one on another such that the corresponding entries coincide. The rows of the matrices are obtained by means of Dyck words.…
Non-overlapping Dyck matrices
- Mathematics
- 2018
We define a set of binary matrices where any two of them can not be placed one on the other in a way such that the corresponding entries coincide. The rows of the matrices are obtained by means of…
Q-ary non-overlapping codes: a generating function approach
- Computer ScienceIEEE Trans. Inf. Theory
- 2022
An exact formula is given for the number of fixed-length words that do not contain the codewords in a variable-length non-overlapping code as subwords that thereby solves an open problem by Bilotta and induces a recursive upper bound on the maximum size of variable- length non- overlapping codes.
A construction for variable dimension strong non-overlapping matrices
- Mathematics, Computer Science
- 2022
We propose a method for the construction of sets of variable dimension strong non-overlapping matrices basing on any strong non-overlapping set of strings.
Mutual Borders and Overlaps
- MathematicsIEEE Transactions on Information Theory
- 2022
This paper gives a recurrence for the number of mutually bordered pairs of words and shows that the expected shortest overlap between pairs of Words is bounded above by a constant.
References
SHOWING 1-10 OF 34 REFERENCES
Non-Overlapping Codes
- Computer ScienceIEEE Transactions on Information Theory
- 2015
This work provides a simple construction for a class of non-overlapping codes which has optimal cardinality whenever n divides q, and shows that a code from this class is close to optimal, in the sense that it has cardinality within a constant factor of an upper bound due to Levenshtein from 1970.
Prefix partitioned gray codes for particular cross-bifix-free sets
- Computer ScienceCryptography and Communications
- 2014
This work provides an efficient generating algorithm producing Gray codes for a remarkable family of cross-bifix-free sets.
Cross-Bifix-Free Codes Within a Constant Factor of Optimality
- Computer ScienceIEEE Transactions on Information Theory
- 2013
A new construction of cross-bifix-free codes is provided which generalizes the construction by Bajic to longer code lengths and to any alphabet size, and the codes are shown to be nearly optimal in size.
On variable length codes for iterative source/channel decoding
- Computer ScienceProceedings DCC 2001. Data Compression Conference
- 2001
A bit-level soft-in/soft-out decoder based on this trellis is used as an outer component decoder in an iterative decoding scheme for a serially concatenated source/channel coding system.
Variable-length binary encodings
- Computer Science
- 1959
This paper gives a theoretical treatment of several properties which describe certain variable-length binary encodings of the sort which could be used for the storage or transmission of information.…
On an application of semi groups methods to some problems in coding
- MathematicsIRE Trans. Inf. Theory
- 1956
A simple suboptimal construction of cross-bifix-free codes
- MathematicsCryptography and Communications
- 2013
A general construction method for cross-bifix-free sequences based on kernels, applicable to a limited number of so-called “regular kernel sets”, is proposed and properties of such sequences with an outline for further research are discussed.
Avoiding cross-bifix-free binary words
- Computer ScienceActa Informatica
- 2013
The problem of associating a word to a path in the generating tree obtained by the succession rule is solved by introducing an algorithm which constructs all binary words having more 1’s than 0’'s and then kills those containing the forbidden patterns.