A resistive pulse sensing device is able to extract quantities such as concentration and size distribution of particles, e.g. cells or microspheres, as they flow through the device's sensor region, i.e. channel, in an electrolyte solution. The dynamic range of detectable particle sizes is limited by the channel dimensions. In addition, signal interference from multiple particles transiting the channel simultaneously, i.e. coincidence event, further hinder the dynamic range. Coincidence data is often considered unusable and is discarded, reducing the throughput and introducing possible biases and errors into the distributions. Here, we propose a two-step solution. We code the channel such that the system response results in a Manchester encoded Barker-Code sequence, allowing us to take advantage of the code's pulse compression properties. We pose the parameter estimation problem as a sparse inverse problem, which enables estimation of particle sizes and velocities while resolving coincidences, and solve it with a successive interference cancellation algorithm. We introduce modifications to the algorithm to account for device fabrication variations and natural stochastic variations in flow. We demonstrate the ability to resolve coincidences and possible increases in the device's dynamic range by screening particles of different size through a Barker encoded device.