Near-optimal multi-version codes

Motivated by applications to distributed storage and computing, the multi-version coding problem was formulated by Wang and Cadambe in [4]. In this problem, a client sequently over time stores v independent versions of a message in a storage system with n server nodes. It is assumed that, a message version may not reach some servers, and that each server is unaware of what has been stored in other servers. The problem requires that any c servers must be able to reconstruct their latest common version. An extended multi-version problem introduced in [5] relaxes the above requirement by requiring any c servers to be able to reconstruct their latest common version or any version later than that. The objective in both the original and extended multi-version problem is to minimize the worst case storage cost. In this work, we propose codes for both the multi-version problem and its extension. For the original multi-version coding problem, we show that the storage cost of our proposed codes are near-optimal. For the extended multi-version coding problem, we show that the storage cost of our first algorithm is optimal when v|c - 1. Our second proposed extended multi-version code shows that storage cost of strictly less than one is achievable even when v is 50% larger than c. This is interesting, as the storage cost of existing codes becomes one as soon as v becomes larger than c.