  This paper considers a compressed-coding scheme that combines compressed
sensing with forward error control coding. Approximate message passing (AMP) is
used to decode the message. Based on the state evolution analysis of AMP, we
derive the performance limit of compressed-coding. We show that
compressed-coding can approach Gaussian capacity at a very low compression
ratio. Further, the results are extended to systems involving non-linear
effects such as clipping. We show that the capacity approaching property can
still be maintained when generalized AMP is used to decode the message.
  To approach the capacity, a low-rate underlying code should be designed
according to the curve matching principle, which is complicated in practice.
Instead, analog spatial-coupling is used to avoid sophisticated low-rate code
design. In the end, we study the coupled scheme in a multiuser environment,
where spatial-coupling can be realized in a distributive way. The overall block
length can be shared by many users, which reduces block length per-user.
