Rate-based versus distortion-based optimal joint source-channel coding

We consider a joint source-channel coding system that protects an embedded wavelet bitstream against noise using a finite family of channel codes with error detection and error correction capability. The performance of this system may be measured by the expected distortion or by the expected number of correctly received source bits subject to a target total transmission rate. Whereas a rate-based optimal solution can be found in linear time, the computation of a distortion-based optimal solution is prohibitive. Under the assumption of the convexity of the operational distortion-rate function of the source coder, we give a lower bound on the expected distortion of a distortion-based optimal solution that depends only on a rate-based optimal solution. Then we show that a distortion-based optimal solution provides a stronger error protection than a rate-based optimal solution and exploit this result to reduce the time complexity of the distortion-based optimization. Finally, we propose a fast iterative improvement algorithm that starts from a rate-based optimal solution and converges to a local minimum of the expected distortion. Experimental results for a binary symmetric channel with the SPIHT coder and JPEG 2000 show that our lower bound is close to optimal. Moreover, the solution given by our local search algorithm has about the same quality as a distortion-based optimal solution, whereas its complexity is much lower than that of the previous best solution.