Block error-correcting codes for systems with a very high BER: Theoretical analysis and application to the protection of watermarks

摘要

This paper addresses the problem of error-correction for extremely noisy channels (BER from 0.1 to 0.5), such as those obtained for image or video watermarking. Minimum distance arguments are used to identify a region for which no other code is as efficient as repetition codes, whatever the rate, at least when bounded decoding is considered. However, in order to obtain a reasonable and sufficiently low BER, repetition codes are not very efficient. We present a coding scheme concatenating a repetition code with another one, and design rules in order to select these codes for a given watermarking application are developed. The repetition code lowers the huge channel BER, as no other code can do this part of the job. Then, the second more powerful code working at a lower BER achieves a larger BER reduction. In this paper, this role is devoted to BCH codes, as members of a classical family. Thanks to their moderate decoding complexity, they turn out to be an interesting cost versus performance trade-off, while more efficient coding schemes based on soft decoding are far more complex. However, we also provide an idea of the solutions to consider for watermarking applications with fewer complexity limitations, for which more powerful decoding techniques can be implemented.