IIIT Hyderabad Publications |
|||||||||
|
On Regenerating Codes with Cooperative and Centralized Repair for Two ErasuresAuthor: Rekha Devi Bhoopatiraju Date: 2019-07-03 Report no: IIIT/TH/2019/83 Advisor:Lalitha Vadlamani AbstractCooperative regenerating codes are regenerating codes designed to trade off storage for repair band-width in case of multiple node failures. Minimum storage cooperative regenerating codes (MSCR) are a class of cooperative regenerating codes which achieve the minimum storage point of the trade off. The main limitation in the practical implementation of these codes is its very large sub-packetization level. -MSR codes are a class of codes introduced to trade off sub-packetization level for a slight increase in the repair bandwidth for the case of single node failures. In this work, we introduce the framework of -MSCR codes which allow for a similar trade off for the case of multiple erasures. We present a construction of -MSCR codes, which can recover from two node failures, by concatenating a class of MSCR codes and scalar linear codes. We give two different repair procedures to repair the -MSCR codes in the event of two node failures (a) in a cooperative manner and (b) in a centralized manner. In cooperative method, repair takes places in two rounds and the failed nodes are allowed to communicate between themselves. The failed nodes do not communicate between themselves in a centralized repair model and there is a central node that recovers the contents of all the failed nodes. We calculate the repair bandwidth for each repair procedure and characterize the increase in repair bandwidth incurred by the method in comparison with the optimal repair bandwidth given by the respective cut-set bound for each case. We then show that the sub-packetization level of -MSCR codes scales logarithmically in the number of nodes and require a field size of the order of the number of nodes. The repair problem can be simplified with the help of codes with constant repairing subspaces. The existence of these codes have been proven for the case of single erasures. However, no such existence was proven for the case of multiple erasures. We prove the existence of such codes for the recovery of two failed nodes namely (a) for the failure of two systematic nodes, (b) for the failure of a systematic node and a parity node. We also give the rank conditions which need to be satisfied for successful recovery of the failed nodes for each case. Full thesis: pdf Centre for Communications |
||||||||
Copyright © 2009 - IIIT Hyderabad. All Rights Reserved. |