AbstractTransmission channels in mobile communication are extremely unstable due to the effect of multipath fading. Therefore the realization of high‐reliability communication necessitates the introduction of error control in the form of error‐correction coding.This paper considers the decoding of error‐correcting codes that are adapted to digital mobile communication operating under Rayleigh fading conditions. A soft decision Viterbi decoding using the received carrier level is studied for the case of convolutional codes. This soft decision method is based on the level of the received carrier by adaptively determining the metric used in the decoding. In this way a metric is obtained for digital mobile communication.This paper also presents an estimation method using error exponent which provides effective means to realize such a soft decision method. If the channel can be considered memoryless due for example to interleaving, then this method provides an easy way to estimate: (1) the figure of merit for quantizing thresholds, and (2) the gains of the soft decision.First, it is shown that using this kind of estimation in the case of channels which can be considered sufficiently memoryless due to interleaving, extremely large gain is obtained by the soft decision method discussed in this paper.Next, simulations are performed and the efficiency of the estimation method is demonstrated. Finally, the bit error rate characteristics are shown for the case when the channel is not made sufficiently memoryless by interle