Compressed Coding, AMP Based Decoding and Analog Spatial Coupling

Abstract

This paper considers a compressed coding (CC) 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 the CC scheme. We show that the CC scheme can approach Gaussian capacity at a very high 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 (ASC) is used to avoid sophisticated low-rate code design. In the end, we study ASC-CC in a multiuser environment, where ASC can be realized in a distributive way. The overall block length can be shared by many users, which reduces block length per-user.