ERROR MECHANISMS FOR CONVOLUTIONAL CODES.
MASSACHUSETTS INST OF TECH CAMBRIDGE RESEARCH LAB OF ELECTRONICS
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Upper and lower bounds to the probability of error for convolutional codes are presented. The lower bound is derived for an optimum decoder with convolutional codes in which each of the V channel symbols generated per encoder shift may have a different constraint length. The Fano sequential decoding algorithm is also investigated. An upper bound to the a th moment of decoder computation is obtained for arbitrary decoder bias B and a or 1. An upper bound on error probability with sequential decoding is derived for both systematic and nonsystematic convolutional codes. This error bound involves the exact value of the decoder bias B. There is a trade-off between sequential decoder computation and error probability as the bias B is varied. Also, for many values of B, sequential decoding of systematic convolutional codes gives an exponentially larger error probability than sequential decoding of nonsystematic convolutional codes when both codes are designed with exponentially equal optimum decoder error probabilities. Author