Multiple-input multiple-output (MIMO) synthetic aperture radar (SAR) has been intensely investigated in recent years, due to its potential to achieve new system concepts such as high-resolution wide-swath imaging and multimodal operation. Among the proposed orthogonal waveforms, inter-pulse phase modulation outperforms by the immunity to the impact of Doppler shift arising from the movement of the platform, thus no compensation of the Doppler effect is needed before SAR imaging. However, the demodulation procedure requires oversampling in Doppler domain, which poses strict restriction on the pulse repetition frequency (PRF) and seriously limits its applications. In this paper, a novel azimuth discrete periodic phase coding scheme and the corresponding demodulation method is proposed. By using this method, the undersampled echoes could be separated from each other after multichannel reconstruction, thus feasible for high-resolution wide-swath imaging. Theoretical derivations and simulation results validate the effectiveness of the proposed coding scheme.