|Eliminating Pairing Loss for Coded Caching with Three Erasure-Coded Servers
|Aniruddha Phatak, Mahesh K. Varanasi, University of Colorado Boulder, United States
|N.3: Coded Caching I
|Networking and Network Coding
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|A three-server coded caching scheme was presented recently by Luo et al. that extends the single-server coded caching scheme by Maddah-Ali and Niesen. Forming user sets as in the single-server case, Luo et al. show that by "pairing" such user sets that satisfy certain conditions, the rate of the three-server scheme may be reduced to less than two-thirds of the rate of the single-server scheme. Yet, in some cases, the pairing is not perfect (i.e., some of the sets are left unpaired) and the requirements of the unpaired sets must then be satisfied by a sub-optimal scheme. This results in the so-called "pairing loss", leading to a transmission rate greater than one-half of the single-server scheme due to imperfect pairing. In this paper, it is shown that instead of just pairing user sets, groups of 2 and 6 user sets can be formed, enabling a more efficient organization. It is shown that within groups of size 6 (and 2), the user demands can be satisfied at a rate equal to one-half that of the single-server scheme. Then, through a specific example, a grouping algorithm is given that forms all user sets into such groups of size 2 or 6. Hence, the three-server rate may be uniformly reduced to exactly half the single-server rate, eliminating the pairing loss altogether.