scholarly journals Optimal Linear Error Correcting Delivery Schemes for Two Optimal Coded Caching Schemes

Entropy ◽  
2020 ◽  
Vol 22 (7) ◽  
pp. 766
Author(s):  
Nujoom Sageer Karat ◽  
Anoop Thomas ◽  
Balaji Sundar Rajan
Keyword(s):  
Closed Form ◽  
Average Rate ◽  
Cache Memory ◽  
Peak Rate ◽  
Index Coding ◽  
Memory Size ◽  
Optimal Linear ◽  
Coded Caching

For coded caching problems with small buffer sizes and the number of users no less than the amount of files in the server, an optimal delivery scheme was proposed by Chen, Fan, and Letaief in 2016. This scheme is referred to as the CFL scheme. In this paper, an extension to the coded caching problem where the link between the server and the users is error prone, is considered. The closed form expressions for average rate and peak rate of error correcting delivery scheme are found for the CFL prefetching scheme using techniques from index coding. Using results from error correcting index coding, an optimal linear error correcting delivery scheme for caching problems employing the CFL prefetching is proposed. Another scheme that has lower sub-packetization requirement as compared to CFL scheme for the same cache memory size was considered by J. Gomez-Vilardebo in 2018. An optimal linear error correcting delivery scheme is also proposed for this scheme.

Optimal Linear Broadcast Rates of Some Two-Sender Unicast Index Coding Problems

2019 ◽  
Vol 67 (6) ◽  
pp. 3965-3977 ◽  
Author(s):  
Chinmayananda Arunachala ◽  
Vaneet Aggarwal ◽  
B. Sundar Rajan
Keyword(s):  
Index Coding ◽  
Optimal Linear

An Alternative Explanation for Lower Repeat Rates after Promotion Purchases

1989 ◽  
Vol 26 (2) ◽  
pp. 205-213 ◽  
Author(s):  
Scott A. Neslin ◽  
Robert W. Shoemaker
Keyword(s):  
Monte Carlo ◽  
Closed Form ◽  
Research Methodology ◽  
Alternative Explanation ◽  
Choice Model ◽  
Average Rate ◽  
Future Research ◽  
Management Research ◽  
Disproportionate Number ◽  
Purchase Rate

Several authors have observed that average repeat rates are lower after a promotion purchase. One interpretation of this result is that a media-coupon or cents-off promotion undermines the consumer's repeat purchase rate. The authors describe an alternative explanation. The explanation is that the promotion temporarily attracts a disproportionate number of households with low purchase probabilities. When the repeat rates of these households are averaged with the repeat rates of those that would have bought the brand even without a promotion, the average rate after a promotion purchase is lower. This effect is demonstrated by means of a numerical example, a closed-form equation for repeat rates, a Monté Carlo purchase simulation, and a logit choice model. An exploratory empirical analysis supports these arguments. Implications for marketing management, research methodology, and future research are discussed.

scholarly journals Constructions of Coded Caching Schemes With Flexible Memory Size

2019 ◽  
Vol 67 (6) ◽  
pp. 4166-4176 ◽  
Author(s):  
Minquan Cheng ◽  
Jing Jiang ◽  
Qifa Yan ◽  
Xiaohu Tang
Keyword(s):  
Memory Size ◽  
Coded Caching

scholarly journals An Umbrella Converse for Data Exchange: Applied to Caching, Computing, and Shuffling

Entropy ◽  
2021 ◽  
Vol 23 (8) ◽  
pp. 985
Author(s):  
Prasad Krishnan ◽  
Lakshmi Natarajan ◽  
Vadlamani Lalitha
Keyword(s):  
Distributed Computing ◽  
Data Exchange ◽  
Specific Problem ◽  
Independence Number ◽  
Index Coding ◽  
Communication Problems ◽  
Generic Data ◽  
General Data ◽  
Problem Formulations ◽  
Coded Caching

The problem of data exchange between multiple nodes with storage and communication capabilities models several current multi-user communication problems like Coded Caching, Data Shuffling, Coded Computing, etc. The goal in such problems is to design communication schemes which accomplish the desired data exchange between the nodes with the optimal (minimum) amount of communication load. In this work, we present a converse to such a general data exchange problem. The expression of the converse depends only on the number of bits to be moved between different subsets of nodes, and does not assume anything further specific about the parameters in the problem. Specific problem formulations, such as those in Coded Caching, Coded Data Shuffling, and Coded Distributed Computing, can be seen as instances of this generic data exchange problem. Applying our generic converse, we can efficiently recover known important converses in these formulations. Further, for a generic coded caching problem with heterogeneous cache sizes at the clients with or without a central server, we obtain a new general converse, which subsumes some existing results. Finally we relate a “centralized” version of our bound to the known generalized independence number bound in index coding and discuss our bound’s tightness in this context.

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