A general class of nonlinear compound pulse position modulation (CPPM) codes is introduced to incorporate nonlinear low-rate PPM constraints directly into a Tanner-like code graph on which iterative decoding can be performed. The iterative decoding algorithm is specified for these codes, including the extrinsic message computations at the nonlinear constraint nodes. For a particular subclass of CPPM codes a simple but strange encoding algorithm is defined that encodes a variable number of source bits for each code block. The encoding algorithm is applied to calculate the average information rate of a particular type of parallel concatenated CPPM code ensemble called turbo PPM?.