Index Assignment for Robust Multiple Description Scalar Quantizer

Conventional multiple description coding (MDC) is a source coding technique which provides resilience against packet loss. On the other hand, the correlation introduced between descriptions can be used to combat bit errors as well. While the latter feature of MDC has been attested and exploited in prior work, only few attempts have been made to design MDC with higher bit error resilience ability. This thesis makes some progress in the latter direction by addressing the problem of robust (i.e., bit error resilient) index assignment (IA) design for two description scalar quantizers. Our approach is to start from an initial IA which is known to be good for the conventional two description problem, and then apply permutations to indices in each description to increase a minimum Hamming distance-like performance measure. The criterion of increasing the minimum Hamming distance between valid index pairs (dmin), has been considered in prior work, however an efficient IA construction was presented only for the case of dmin = 2 and low redundancy. The contribution of this thesis is the following. For the scenario when one description is known to be error free, a new measure for IA robustness is proposed, which is termed minimum side Hamming distance (dside,min). This quantity is defined as the minimum Hamming distance between valid indices of one description for fixed index iii of the other description. It is further shown that the problem of robust permutations design under the new criterion is closely connected to the anti-bandwidth problem in a certain graph derived from a hypercube. Leveraging this connection, permutations achieving dside,min = 2 are proposed for all redundancy levels. Furthermore, for general values of dside,min, a simple construction of permutations achieving dside,min is presented, based on channel codes of appropriate block length and rate, and with minimum distance dside,min + 1, respectively, dside,min, for two types of initial IA (diagonal, respectively, square-based). The application of this result to achieve IA with dside,min = 3 is further discussed for a wide range of redundancy levels. Finally, for the scenario when both descriptions may carry bit errors, simple constructions of permutations achieving dmin = 3 are proposed for the high redundancy case.