In this paper, we propose a parameter allocation scheme in a parallel array bistable stochastic resonance-based communication system (P-BSR-CS) to improve the performance of weak binary pulse amplitude modulated (BPAM) signal transmissions. The optimal parameter allocation policy of the P-BSR-CS is provided to minimize the bit error rate (BER) and maximize the channel capacity (CC) under the adiabatic approximation condition. On this basis, we further derive the best parameter selection theorem in realistic communication scenarios via variable transformation. Specifically, the P-BSR structure design not only brings the robustness of parameter selection optimization, where the optimal parameter pair is not fixed but variable in quite a wide range, but also produces outstanding system performance. Theoretical analysis and simulation results indicate that in the P-BSR-CS the proposed parameter allocation scheme yields considerable performance improvement, particularly in very low signal-to-noise ratio (SNR) environments.