A geometric view of the service rates of codes problem and its application to the service rate of the first order Reed-Muller codes

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Kazemi, Fatemeh ; Kurz, Sascha ; Soljanin, Emina:
A geometric view of the service rates of codes problem and its application to the service rate of the first order Reed-Muller codes.
Bayreuth , 2020 . - 8 S.

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Abstract

We investigate the problem of characterizing the service rate region of a coded storage system by introducing a novel geometric approach. The service rate is an important performance metric that measures the number of users that can be simultaneously served by the storage system. One of the most significant advantages of our introduced geometric approach over the existing approaches is that it allows one to derive bounds on the service rate of a code without explicitly knowing the list of all possible recovery sets. As an illustration of the power of our geometric approach, we derive upper bounds on the service rate of the first order Reed-Muller codes and the simplex codes. Then, we show how these upper bounds can be achieved. Moreover, utilizing the same geometric technique, we show that given the service rate region of a code, a lower bound on the minimum distance of the code can be obtained.