A self-correcting signal quantization based on error correcting codes
摘要
We propose a quantization method that makes a signal correctable after it has been corrupted by noise. The principle is to replace each bit level in the binary representation of each vector of time or time-frequency samples by a codeword of the same length, provided by an error-correction coder. Thus, assuming that the amount of errors does not exceed the correction capabilities, decoding each bit level of the noisy signal can suppress the noise. We demonstrate how to determine the necessary error correction capability for each bit level based on the signal and noise probability density functions along with the desired binary error probability. The codewords are chosen from codebooks with the adequate error correction capabilities so as to minimize the quadratic error between the original and the quantized signals, utilizing a modified matching pursuit algorithm. Applying this quantization method on a speech signal transmitted through a noisy channel demonstrates that it is possible to choose a set of coders so that the noise resulting from the quantizing-channel-decoding chain is less annoying than the channel noise alone.