A pulse power drilling system includes a pulse power drill string to be positioned in a borehole formed in a subsurface formation. The pulse power drill string is to drill the borehole based on periodic pulsing of an electrical discharge into the subsurface formation. The pulse power drill string includes a generator to generate electrical power, an electrode to emit the electrical discharge out to the subsurface formation based on the electrical power, and a controller communicatively coupled to the generator and the electrode. The controller is to control at least one discharge parameter of the electrical discharge to encode a data communication within the electrical discharge.