how to merge 1 mp4 video with a looping mp3 audio?

I have a .mp4 mpeg-4 video which has no audio track and is about 11 minutes long and a mp3 file which is about 30 seconds long. I would like to combine the two, with the audio looping. Also I would like to keep the base resolution of the video. Is this possible to merge the two without re-encoding, or what would be the best approach to do this?