Novel Repair-by-Transfer Codes and Systematic Exact-MBR Codes with Lower Complexities and Smaller Field Sizes

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 (₂ⁿ) ton; ii) the encoding complexity is decreased from n⁴ to n³. Our simulation results 2 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 ton; ii) the fast Reed-Solomon erasure coding algorithms can be applied on the proposed exact-MBR codes to reduce the time complexities.