Shocks in the asymmetric simple exclusion process in a discrete-time update

We study the dynamics of a shock distribution as an initial state for a one-dimensional asymmetric simple exclusion process with sub-lattice parallel update. The time evolution of the shock distribution can be calculated exactly if the two initial densities of the shock satisfy a special relation which results from its U(q)[SU(2)] symmetry. The resulting distribution is a linear combination of shock measures. The motion of the shock position can be interpreted as if it would perform a biased discrete-time random walk, with hopping rules related to that of a single particle in the exclusion process. The shock diffusion constant and the shock velocity are calculated exactly. We obtain simple expressions for these quantities in terms of the shock densities and currents which we argue to be valid for any pair of shock densities.