@article{Xia2025, 
author = {Dengfeng Xia and Fan Cheng and Shenghao Yang and Han Cai and Peng Xu and Bin Dai},
title = {Feedback Coding Schemes for Gaussian Parallel Relay Networks},
year = {2025},
journal = {Tsinghua Science and Technology},
keywords = {feedback, Gaussian channel, relay network, Schalkwij−Kailath (SK) scheme},
url = {https://www.sciopen.com/article/10.26599/TST.2025.9010042},
doi = {10.26599/TST.2025.9010042},
abstract = {Previously, it has been shown that the destination-to-source feedback helps to significantly increase the achievable rate of the Gaussian Relay Network (GRN) with single source-destination, and the proposed feedback scheme is based on the well-known Schalkwijk−Kailath (SK) scheme and the Amplify-and-Forward (AF) relay strategy. In this paper, we would like to know whether additional feedback links help to further enhance the transmission rate, and if there does not exist destination-source feedback, how to design feedback scheme for the single source-destination GRN with destination-relay and relay-source feedback links? To answer the aforementioned questions, first, we study the Gaussian Parallel Relay Network (GPRN) with feedback links from destination to both source and relay nodes. A new hybrid scheme, which combines the SK scheme with AF and compute-and-forward relay strategies, is proposed. We show that this new scheme may further enhance the achievable rate for the same model with only destination-source feedback. Next, we study the GPRN with destination-relay and relay-source feedback links. A time sharing scheme which combines the SK-type schemes for the broadcast channel and the multiple-access channel is proposed. Numerical results show that even without destination-source feedback, other feedback links can still provide rate gain for some cases.}
}