Compressed Coding, AMP Based Decoding and Analog Spatial Coupling

TL;DR

The state evolution analysis of AMP is derived and it is shown that compressed-coding can approach Gaussian capacity at a very low compression ratio, and the results are extended to systems involving non-linear effects such as clipping.

Abstract

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.

Figures (9)

• Figure 1: Graphic illustrations for (a) system model, (b) the receiver structures and (c) state evolution. ENC and DEC denote the encoder and decoder, respectively.
• Figure 2: Graphic illustrations for (a) an SE recursion with a general decoding function $\psi$ and (b) the optimal $\psi^{opt}$ satisfying the matching condition. The functions $\phi$ in two figures are the same.
• Figure 3: Examples of transfer functions for GAMP.
• Figure 4: (a) A modified version of Fig. \ref{['system']}(a) with $W = 3$. (b) An SC-CC system based on (a) with $W = 3$.
• Figure 5: Examples of $\phi$ and $\psi$ in typical scenarios.