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6.0 Error Propagation

Differential encoding incurs a bit error penalty because received code symbols influence more than one decoded bit. First consider a single symbol detection error in current symbol E’ which is labeled _k. The following sequence of decoding steps shows how the error propagates. Since the E channel was chosen as current, decoding starts with equation (M-4a). The single detection error creates two sequential decoding errors. By symmetry we can state that the same result occurs if a single error occurs in O’.

Next is the case of two symbol detection errors occurring consecutively on E’ and O’, i.e., detectors emit error symbols E’_k=_k and O’_k+1=_k+1. Starting again with equation (M-4a) yields: