Read-Write-Codes: An Erasure Resilient Encoding System for Flexible Reading and Writing in Storage Networks

We introduce the Read-Write-Coding-System (RWC) – a very flexible class of linear block codes that generate efficient and flexible erasure codes for storage networks. In particular, given a message x of k symbols and a codeword y of n symbols, an RW code defines additional parameters k \leq r,w \leq n that offer enhanced possibilities to adjust the fault-tolerance capability of the code. More precisely, an RWC provides linear $\left(n,k,d\right)$-codes that have (a) minimum distance d=n-r+1 for any two codewords, and (b) for each codeword there exists a codeword for each other message with distance of at most w. Furthermore, depending on the values r,w and the code alphabet, different block codes such as parity codes (e.g. RAID 4/5) or Reed-Solomon (RS) codes (if r=k and thus, w=n) can be generated. In storage networks in which I/O accesses are very costly and redundancy is crucial, this flexibility has considerable advantages as r and w can optimally be adapted to read or write intensive applications; only w symbols must be updated if the message x changes completely, what is different from other codes which always need to rewrite y completely as x changes. In this paper, we first state a tight lower bound and basic conditions for all RW codes. Furthermore, we introduce special RW codes in which all mentioned parameters are adjustable even online, that is, those RW codes are adaptive to changing demands. At last, we point out some useful properties regarding safety and security of the stored data.