Skip to main content

Computer Science > Information Theory

arXiv:2504.05959 (cs)
[Submitted on 8 Apr 2025]

Title:Old and New Results on Alphabetic Codes

Authors:Roberto Bruno, Roberto De Prisco, Ugo Vaccaro
View PDF HTML (experimental)
Abstract:This comprehensive survey examines the field of alphabetic codes, tracing their development from the 1960s to the present day. We explore classical alphabetic codes and their variants, analyzing their properties and the underlying mathematical and algorithmic principles. The paper covers the fundamental relationship between alphabetic codes and comparison-based search procedures and their applications in data compression, routing, and testing. We review optimal alphabetic code construction algorithms, necessary and sufficient conditions for their existence, and upper bounds on the average code length of optimal alphabetic codes. The survey also discusses variations and generalizations of the classical problem of constructing minimum average length alphabetic codes. By elucidating both classical results and recent findings, this paper aims to serve as a valuable resource for researchers and students, concluding with promising future research directions in this still-active field.
Comments: Published in: Information Theory and Related Fields, Lecture Notes in Computer Science
Subjects: Information Theory (cs.IT); Data Structures and Algorithms (cs.DS)
Cite as: arXiv:2504.05959 [cs.IT]
  (or arXiv:2504.05959v1 [cs.IT] for this version)
  https://doi.org/10.48550/arXiv.2504.05959
Journal reference: Information Theory and Related Fields, Lecture Notes in Computer Science, Springer, vol. 14620, pp. 151-194, 2025
Related DOI: https://doi.org/10.1007/978-3-031-82014-4_7

Submission history

From: Roberto Bruno [view email]
[v1] Tue, 8 Apr 2025 12:15:53 UTC (856 KB)
Full-text links:

Access Paper:

license icon view license

Current browse context:

cs.IT
< prev   |   next >
new | recent | 2025-04
Change to browse by:
cs
cs.DS
math
math.IT

References & Citations

Bookmark

BibSonomy Reddit

Bibliographic and Citation Tools

Bibliographic Explorer (What is the Explorer?)
Connected Papers (What is Connected Papers?)
Litmaps (What is Litmaps?)
scite Smart Citations (What are Smart Citations?)

Code, Data and Media Associated with this Article

alphaXiv (What is alphaXiv?)
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub (What is DagsHub?)
Gotit.pub (What is GotitPub?)
Hugging Face (What is Huggingface?)
ScienceCast (What is ScienceCast?)

Demos

Replicate (What is Replicate?)
Hugging Face Spaces (What is Spaces?)
TXYZ.AI (What is TXYZ.AI?)

Recommenders and Search Tools

Influence Flower (What are Influence Flowers?)
CORE Recommender (What is CORE?)

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)