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Computation and analysis of the N-Layer scalable rate-distortion function

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2 Author(s)
Tuncel, E. ; Dept. of Electr. & Comput. Eng., Univ. of California, Santa Barbara, CA, USA ; Rose, K.

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,...,yN>0 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 (N>1) 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.

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Information Theory, IEEE Transactions on  (Volume:49 ,  Issue: 5 )