Capacity-Achieving Sparse Regression Codes via Vector Approximate Message Passing
- Resource Type
- Conference
- Authors
- Xu, Yizhou; Liu, YuHao; Liang, ShanSuo; Wu, Tingyi; Bai, Bo; Barbier, Jean; Hou, TianQi
- Source
- 2023 IEEE International Symposium on Information Theory (ISIT) Information Theory (ISIT), 2023 IEEE International Symposium on. :785-790 Jun, 2023
- Subject
- Communication, Networking and Broadcast Technologies
Computing and Processing
Signal Processing and Analysis
AWGN channels
Codes
Error probability
Message passing
Decoding
Sparse matrices
Resource management
- Language
- ISSN
- 2157-8117
Sparse regression codes (SPARCs) are a promising coding scheme that can approach the Shannon limit over Additive White Gaussian Noise (AWGN) channels. Previous works have proven the capacity-achieving property of SPARCs with Gaussian design matrices. We generalize these results to right orthogonally invariant ensembles that allow for more structured design matrices. With the Vector Approximate Message Passing (VAMP) decoder, we rigorously demonstrate the exponentially decaying error probability for design matrices that satisfy a certain criterion with the exponentially decaying power allocation. For other spectra, we design a new power allocation scheme to show that the information theoretical threshold is achievable.