Abstract: A method for detecting errors in data that comprises encoding the data into a codeword using a generation polynomial, transmitting the codeword over a channel, receiving the transmitted codeword, generating syndromes for the received codeword using the generation polynomial, the syndromes comprising a plurality of syndrome symbols, providing a plurality of syndrome windows, each of the syndrome windows comprising a plurality of sub-windows and corresponding to a set of syndrome symbols, determining a number of non-zero terms of sub-windows of each of the syndrome windows, and selecting at least one syndrome window having a least number of non-zero terms of sub-windows.

Abstract: A signal processing system that comprises a sampling device for converting a continuous signal into a discrete signal, a quantizing device for converting the discrete signal into a first bit stream, each bit in the bit stream having a first value, a detector for determining whether at least one bit in the first bit stream includes a second value different from the first value of the at least one bit, and a demultiplexer for converting a section of the first bit stream into a first modulation code, and converting a section of a second bit stream into a second modulation code, the second bit stream being formed by replacing the first value of the at least one bit in the first bit stream with the second value.