scholarly journals New lower bounds for the Shannon capacity of odd cycles

2016 ◽  
Vol 84 (1-2) ◽  
pp. 13-22 ◽  
Author(s):  
K. Ashik Mathew ◽  
Patric R. J. Östergård
Keyword(s):  
Lower Bounds ◽  
Shannon Capacity ◽  
Odd Cycles

scholarly journals On the Interactive Capacity of Finite-State Protocols

Entropy ◽  
2020 ◽  
Vol 23 (1) ◽  
pp. 17
Author(s):  
Assaf Ben-Yishai ◽  
Young-Han Kim ◽  
Rotem Oshman ◽  
Ofer Shayevitz
Keyword(s):  
Lower Bounds ◽  
Upper Bound ◽  
Noisy Channel ◽  
Shannon Capacity ◽  
Finite State

The interactive capacity of a noisy channel is the highest possible rate at which arbitrary interactive protocols can be simulated reliably over the channel. Determining the interactive capacity is notoriously difficult, and the best known lower bounds are far below the associated Shannon capacity, which serves as a trivial (and also generally the best known) upper bound. This paper considers the more restricted setup of simulating finite-state protocols. It is shown that all two-state protocols, as well as rich families of arbitrary finite-state protocols, can be simulated at the Shannon capacity, establishing the interactive capacity for those families of protocols.

scholarly journals On The Independence Number Of Some Strong Products Of Cycle-Powers

2015 ◽  
Vol 40 (2) ◽  
pp. 133-141 ◽  
Author(s):  
Marcin Jurkiewicz ◽  
Marek Kubale ◽  
Krzysztof Ocetkiewicz
Keyword(s):  
Lower Bounds ◽  
Independence Number ◽  
Computational Results ◽  
Shannon Capacity ◽  
Noisy Channels ◽  
Running Time ◽  
The Third ◽  
Independence Numbers

Abstract In the paper we give some theoretical and computational results on the third strong power of cycle-powers, for example, we have found the independence numbers α((C102)√3) = 30 and α((C144)√3) = 14. A number of optimizations have been introduced to improve the running time of our exhaustive algorithm used to establish the independence number of the third strong power of cycle-powers. Moreover, our results establish new exact values and/or lower bounds on the Shannon capacity of noisy channels.

Two Lower Bounds for Shortest Double-Base Number System

2015 ◽  
Vol E98.A (6) ◽  
pp. 1310-1312 ◽  
Author(s):  
Parinya CHALERMSOOK ◽  
Hiroshi IMAI ◽  
Vorapong SUPPAKITPAISARN
Keyword(s):  
Lower Bounds ◽  
Number System ◽  
Base Number ◽  
Double Base

Lower bounds on the dimension of the Rauzy gasket

2020 ◽  
Vol 148 (2) ◽  
pp. 321-327
Author(s):  
Rodolfo Gutiérrez-Romo ◽  
Carlos Matheus
Keyword(s):  
Lower Bounds
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