Bit error rate bounds for Viterbi decoding with modem implementation errors

A useful technique is derived for upper bounding the bit error rate of convolutional coding-Viterbi decoding in the presence of modern implementation errors or cochannel interference. This method utilizes the state transition matrix to find the contribution of each error event. By slightly underestimating the distance of each error path, the randomness of the implementation errors or interference can be averaged on a bit-by-bit basis. This produces an effective reduction of signal-to-noise ratio, and the elements of the state transition matrix merely reflect this reduction. The resulting bound is both accurate and very simple to apply. Application of the bound shows that coding is quite robust to implementation errors compared against the performance without coding. Thus, modem synchronization requirements may be relaxed considerably when coding is employed. This is an important finding since, with coding, the input CNR may be sufficiently low that tight synchronization becomes difficult to realize.