A mathematical model for the non-linear optical loop mirror (NOLM) demultiplexer, operating with a soliton-shaped pulse for both control and data, is presented. The model can be used: to optimise system parameters (control pulse width, walk-off time etc.) for maximising peak transmittance of the switching profile; to calculate the switching profile width; and to estimate the switching profile through a new convolution approach. The simulation results are verified by numerically solving the non-linear Schrodinger equation. The NOLM model is then integrated into an optical receiver model for a bit error rate (BER) analysis. Simulation results show that BER, timing jitter noise and cross-talk are strongly dependent on the walk-off time between control and signal pulses in NOLM demultiplexing. The dependence of the BER on walk-off time agrees qualitatively with experimental results reported elsewhere.