Novel Repair-by-Transfer Codes and Systematic Exact-MBR Codes with Lower Complexities and Smaller Field Sizes
Sian-Jheng Lin, Wei‐Ho Chung · IEEE Transactions on Parallel and Distributed Systems · 2014
The$(n,k,d)$regenerating code is a class of$(n,k)$erasure codes with the capability to recover a lost code fragment from other$d$existing code fragments. In this paper, we focus on the design of exact regenerating codes at minimum bandwidth regenerating (MBR) points. For$d=n-1$, a class of$(n,k,d=n-1)$exact-MBR codes, termed as repair-by-transfer codes, have been developed in prior work to avoid arithmetic operations in node repairing process. The first result of this paper presents a new class of repair-by-transfer codes via congruent transformations. As compared with prior works, the advantages of proposed codes include: i) the minimum of field size is significantly reduced from$n \atopwithdelims ()2$to$n$; ii) the encoding complexity is decreased from$n^4$to$n^3$. Our simulation results show that the proposed code achieves faster operations than the prior approach does under large$n$. The second result of this paper presents a new form of coding matrix for product-matrix exact-MBR codes. The proposed coding matrix includes the following advantages: i) the minimum of finite field size is reduced from$n-k+d$to$n$; ii) the fast Reed-Solomon erasure coding algorithms can be applied on the proposed exact-MBR codes to reduce the time complexities.