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We investigate the low density generator matrix (LDGM) codes for continuous phase modulation (CPM). The nonsystematic version of LDGM codes is used in the scheme. The overall system has linear encoding complexity due to the low complexity of the LDGM codes. A property of the check node degree of the LDGM code is shown. We use the EXIT chart/function to optimize the LDGM codes. The EXIT function of CPM with a fixed SNR (signal-to-noise-ratio) is shown. We derive the union bound to analyze the error floor performance. Design approaches for lowering error floors are suggested from the analysis process. Numerical results show that this scheme converges earlier (lower SNR) than best found serially concatenated CPM (SCCPM) for iterative decoding while maintaining comparable error floors.