Errors introduced on most channels including radio channels are not independent and cannot be adequately represented by the classical memory less model. Further, error processes on real channels differ one another in varying degrees of burstiness. Thus, in selecting the most suitable error control technique to overcome charmel errors, we need to investigate how well the channel memory (statistical dependence in the occurrence of transmission errors) can be used for the effective design of wireless ATM error control schemes. For this we first develop a bit-level Markovian error model and obtain recurrence relations for the dependency of bit error distributions. Next, by aggregating the bit-level model, we develop a block-level (i.e., cell-level) model and derive the joint probability distribution of errors between two adjacent blocks of equal sizes. The block-level model can be extended to a two-state Markov chain describing the error correlation structure between blocks, in which each block is divided into two states according to whether more than a specified number of bits are in error. Particularly we concentrate on a special case named as the simplest Markovian block error pattern. We present numerical and simulation results for the simplest Markovian block error pattern and compare this to the conventional memoryless model in order to understand the relationships between several parameters of the derived model.