Globally Optimal Uneven Error-Protected Packetization of Scalable Code Streams

In this paper, we present a family of new algorithms for rate-fidelity optimal packetization of scalable source bit streams with uneven error protection. In the most general setting where no assumption is made on the probability function of packet loss or on the rate-fidelity function of the scalable code stream, one of our algorithms can find the globally optimal solution to the problem in $O(N^{2}L^{2})$ time, compared to a previously obtained $O(N^{3}L^{2})$ complexity, where $N$ is the number of packets and $L$ is the packet payload size. If the rate-fidelity function of the input is convex, the time complexity can be reduced to $O(NL^{2})$ for a class of erasure channels, including channels for which the probability function of losing $n$ packets is monotonically decreasing in $n$ and independent erasure channels with packet erasure rate no larger than ${{N}/{2(N+1)}}$. Furthermore, our $O(NL^{2})$ algorithm for the convex case can be modified to find an approximation solution for the general case. All of our algorithms do away with the expediency of fractional bit allocation, a limitation of some existing algorithms.