Estimates of the bit error probabilities for linear block codes and symmetric binary-input memoryless channels

A coset representation of the bit error probabilities for binary linear block codes and arbitrary symmetric memoryless channels is derived. Such a representation leads to simple upper bounds on the bit error probabilities for code components expressed via 2n code spectra, where n is the code length, and to a "bounded distance decoding" algorithm. The performance of the algorithm is illustrated for the (23,12) Golay code and a particular channel having non-binary output alphabet where it attains a sub-optimum performance.