Design of Storage Codes Based on Integer Arithmetic Modulo a Power of Two

Locally repairable code repairs storage node failure in distributed storage systems by accessing only a small number of nodes. Recent studies of locally repairable code have focused on constructing codes over finite fields. However, field multiplication and division operations can be costly, especially when the field size is large. Codes over binary fields are able to offer fast encoding and decoding speeds, but the achievable code parameters are more limited. In this paper, we exploit the advantages of the algebraic structure of unsigned integers, specifically utilizing rings of residue integers modulo power of 2. Multiplication of unsigned integers can be performed using microprocessor instructions with a latency of just one clock cycle. The processing speed can be comparable to logical XOR. The superior processing speed is achieved with only a slight increase in the number of redundant bits. In this paper, we demonstrate the benefits of this new methodology and outline the underlying design principles.