A method implemented in a digital subscriber line (DSL) system is described for minimizing a misdetection probability at a far-end coded message receiver during transmission of a coded message. The method comprises jointly determining, at the far-end coded message receiver, a P matrix and a modulation scheme. The method further comprises encoding a message into a coded message with a systematic linear block code, the systematic linear block code having a generator matrix [I P], where I represents a linear block code component identity matrix and P represents the determined P matrix. The method also comprises modulating the encoded message to one or more tones forming a discrete multi-tone (DMT) symbol according to the determined modulation scheme.