Efficient Rate–Distortion Optimal Packetization of Embedded Bitstreams Into Independent Source Packets

Abstract

This paper addresses the rate-distortion (R-D) optimal packetization (RDOP) of embedded bitstreams into independent source packets, in order to limit error propagation in transmission of images over packet noisy channels. The input embedded stream is assumed to be an interleaving of K independently decodable basic streams. To form independent source packets, the set of basic streams is partitioned into N groups. The streams within each group are then interleaved to generate a source packet. Error/erasure protection may be further applied along/across source packets, to produce the channel packets to be transmitted. The RDOP problem previously formulated by Wu et at. has the goal of finding the partitioning that minimizes the distortion when all source packets are decoded. We extend the problem formulation such that to also include the minimization of the expected distortion for general transmission scenarios that may apply uneven erasure/ error protection. Further, we show that the dynamic programming (DP) algorithm of Wu et al. can be extended to solve the general RDOP problem. The main contribution of this paper is a fast divide-and-conquer algorithm (D&C) to find the globally optimal solution, under the assumption that all basic streams have convex R-D curves. Instrumental in obtaining the fast solution is our result which proves that the problem can be formulated as a series of matrix search problems in totally monotone matrices. The proposed D&C reduces the running time from O(K(2)LN) where L is the size of each packet achieved by the DP solution to O(NKL log K). Experiments on SPIHT coded images demonstrate that the speedup is significant in practice.