Successive coding of correlated sources
IEEE Transactions on Information Theory
Successive refinement of vector sources under individual distortion criteria
IEEE Transactions on Information Theory
| Hi-index | 754.96 |
Methods for determining and computing the rate-distortion (RD) bound for N-layer scalable source coding of a finite memoryless source are considered. Optimality conditions were previously derived for two layers in terms of the reproduction distributions qy1 and qy2|y1. However, the ignored and seemingly insignificant boundary cases, where qy1=0 and qy2|y1 is undefined, have major implications on the solution and its practical application. We demonstrate that, once the gap is filled and the result is extended to N-layers, it is, in general, impractical to validate a tentative solution, as one has to verify the conditions for all conceivable qyi+1,...,yN|y1,...,yi at each (y1,...,yi) such that qy1,...,yi=0. As an alternative computational approach, we propose an iterative algorithm that converges to the optimal joint reproduction distribution qy1,...,yN, if initialized with qy1,...,yN0 everywhere. For nonscalable coding (N=1), the algorithm specializes to the Blahut-Arimoto (1972) algorithm. The algorithm may be used to directly compute the RD bound, or as an optimality testing procedure by applying it to a perturbed tentative solution q. We address two additional difficulties due to the higher dimensionality of the RD surface in the scalable (N1) case, namely, identifying the sufficient set of Lagrangian parameters to span the entire RD bound; and the problem of efficient navigation on the RD surface to compute a particular RD point.