Progressive optimal error protection of embedded codes

The embedded wavelet image coders such as SPIHT [1] or JPEG 2000 [2] allow an efficient progressive transmission of digital images. However, the bitstreams generated by these coders are very sensitive to channel noise, and error
protection is necessary to ensure acceptable reconstruction fidelity. One of the most successful protection systems for embedded wavelet coders was recently proposed by Sherwood and Zeger [3] who partitioned the bitstream of information bits into packets of fixed length and protected these packets by using a concatenation of a cyclic redundancycheck (CRC) coder for error detection and a rate-compatible punctured convolutional (RCPC) coder for error correction. A challenging task is to find an optimal error protection for such systems [4]; that is, an assignment of the available channel rates to the packets that minimizes the expected reconstruction error (measured, for example, by the peaksignal-to-noise ratio (PSNR)) subject to a total bit rate constraint. An alternative proposed in [4] is to maximize the expected number of error-free received source bits for this target total bit rate. Though suboptimal in the PSNR sense, this approach has two advantages. First, an optimal protection
can be determined with a fast algorithm [4, 5]. Second, the solution is independent of both the source coder and the test image. Thus, the algorithm can also be implemented by the receiver, avoiding the need for sending side information, which would have to be strongly protected. In progressive decoding, a very good performance is desirable not only at the target total rate, but also at all intermediate rates. In particular, a good image quality at the lowest
rates is very useful in internet browsing because it allows the receiver to stop the transmission at an early stage whenever necessary. In this paper, we consider an error protection strategy that maximizes the average expected number of error-free received source bits over all intermediate rates. We prove many interesting properties of an optimal solution, present a linear-time algorithm (linear in the number of packets) for computing a solution, and compare its progressive
performance (number of error-free received source bits and PSNR) to that of the standard strategy that is optimal at the target total rate [4] for the SPIHT and JPEG
2000 source coders with a binary symmetric channel and an RCPC channel coder.