Bandwidth Cost of Code Conversions in Distributed Storage: Fundamental Limits and Optimal Constructions

Erasure codes have become an integral part of distributed storage systems as a tool for providing data reliability and durability under the constant threat device failures. In such systems, [ n, k ] code over finite field F q encodes xmlns:xlink="http://www.w3.org/1999/xlink">k message symbols from into xmlns:xlink="http://www.w3.org/1999/xlink">n codeword which are then stored on different nodes in system. Recent work has shown that significant savings space can be obtained by tuning to variations failure rates. Such necessitates xmlns:xlink="http://www.w3.org/1999/xlink">code conversion : process converting already encoded initial xmlns:xlink="http://www.w3.org/1999/xlink">nI, kI its equivalent final xmlns:xlink="http://www.w3.org/1999/xlink">nF, kF code. The default approach conversion is re-encode new code, places burden system resources. xmlns:xlink="http://www.w3.org/1999/xlink">Convertible codes recently proposed class enabling resource-efficient conversions. Existing convertible focused minimizing access cost, i.e., number accessed during conversion. Bandwidth, corresponds amount read transferred, another important resource optimize this paper, we study fundamental limits bandwidth used present constructions bandwidth-optimal codes. First, model problem using network information flow graphs with variable capacity edges. Second, focusing MDS parameter regime called merge regime, derive tight lower bounds bandwidth. derived show significantly reduced compared even regions where it been cost cannot reduced. Third, construction matches bound thus