Optimal Index Assignment for Multiple Description Scalar Quantization With Translated Lattice Codebooks

Abstract

We provide a method for designing an optimal index assignment for scalar K-description coding. The method stems from a construction of translated scalar lattices, which provides a performance advantage by exploiting a so-called staggered gain. Interestingly, generation of the optimal index assignment is based on a lattice in K − 1 dimensional space. The use of the K − 1 dimensional lattice facilitates analytic insight into the performance and eliminates the need for a greedy optimization of the index assignment. It is shown that that the optimal index assignment is not unique. This is illustrated for the two-description case, where a periodic index assignment is selected from possible optimal assignments and described in detail. The new index assignment is applied to design of a K-description quantizer, which is found to outperform a reference K-description quantizer at high rates. The performance advantage due to the staggered gain increases with increasing redundancy among the descriptions. Index TermsMultiple description quantization, Index assignment.

Repairing multiple description quantizers in distributed storage systems

“…K and the centroid of the tuple u c . As shown in [7], this procedure can be expressed as a geometric minimization problem in a K − 1 dimensional space.…”

“…This is due to the way humans perceive media files, meaning that the message can still be conveyed from imperfect representations of the source. In this direction, Multiple Description (MD) codes [5], [6] and quantizers [7] can be employed in order to ensure that the reconstruction quality is an increasing function of the available nodes k.…”

“…Fig 1 depicts such a system and follows a set of nodes through a failure and repair. In this paper, we address this problem by proposing a repair technique for the MD scalar quantization proposed in [7]. More specifically, in section II a review of preliminaries and related work is presented.…”

Index assignment for multiple description repair in distributed storage systems

“…Furthermore, an estimate of the source can be acquired even when less that k units are available, while the reconstruction quality keeps improving even when more than k units are received. In this direction, Multiple Description (MD) codes [5], [6] and quantizers [7] can be employed in order to ensure that the reconstruction quality is an increasing function of the available nodes k. Independently of the coding technique, a common problem in distributed storage systems is how to repair the nodes that are bound to fail from time to time. When a node fails, the information it stored is lost forever but it may be possible to perfectly or approximately recover it using the redundancy information stored across the distributed storage system.…”

Index assignment capable of detecting one bit errors for multiple description scalar quantizers

“…For the case of 2DSQ's one approach toward this is to start from a 2DSQ with an initial IA that is good for the conventional 2DSQ problem [6]- [8] and apply a permutation to the indices of each description. Such a technique does not change the performance of the 2DSQ in the conventional sense, i.e., when the descriptions are not corrupted by bit errors, but it has the potential of increasing the error resilience at the central decoder by detecting or even correcting a higher proportion of errors when a higher d min is achieved.…”