Based on an initial idea of Shannon, we investigate an approach, named Shannon mapping, for transmission of analog messages, that is fundamentally different from current digital communication methods. We investigate 1:2 bandwidth expansion Shannon mapping based on two specific mapping curves. We demonstrate that bandwidth expansion Shannon mapping using a mapping curve does not introduce any delay and its encoding and decoding processes exhibit very low complexity. More importantly, our simulations show that the distortion performance of 1:2 bandwidth expansion Shannon mapping is significantly better than the rate-distortion bound without bandwidth expansion at moderate to high SNRs, and about 3-5 dB inferior to the rate-distortion bound with the same bandwidth expansion.