Repairing multiple description quantizers in distributed storage systems

Abstract

Abstract-Distributed storage systems have been receiving increasing attention lately due to the developments in cloud and grid computing. Furthermore, a major part of the stored information comprises of multimedia, whose content can be communicated even with a lossy reconstruction. In this context, Multiple Description Quantizers (MDQ) can be employed to encode such sources for distributed storage. However, a question which naturally arises is how to repair lost descriptions which are due to node failures. In this paper, we employ MDQs based on translated lattices and a common decoding method through averaging over the available descriptions. The descriptions of failed nodes are repaired by quantizing the estimate of common decoding and then by reusing the same side codebook. Based on simulations, we study the effect of system size and number of failures on the distortion of the reconstructed source. As expected, the distortion deteriorates with the number of failures but the degradation is graceful especially for large systems.

Index assignment for multiple description repair in distributed storage systems

“…In Figure 3, the setup is similar to Figure 2, but with the main difference being that we have consecutive MDLQ systems, with the possibility of repairing the lost descriptions in each step [11]. We call this system the multiple description lattice quantizer with repairs (MDLQR).…”

“…To the authors' knowledge, this was first investigated in [11] from an experimental point of view. This paper builds on [11], presenting an analytical model of the lossy repair problem and introducing three different repair techniques. For one of the techniques, we derive a result that shows how to construct the optimal encoder.…”

“…The first equality holds by noting that a fixed λ 2 i in the left hand double sum of (10) (9) over j, using the formula in (11), and collecting terms, we get…”