Coding for Fading Channels with Imperfect CSI at the Transmitter and Quantized Feedback

2026-01-10

arXiv.org

AI Summary

This study addresses the extension of the classical Schalkwijk–Kailath (SK) coding scheme to multipath fading channels with memory, particularly under the practical constraint that the transmitter has only quantized and imperfect channel state information. For quasi-static multipath channels with noisy feedback, two approaches are proposed: for two-path channels, the secondary path is treated as an amplify-and-forward relay to exploit interference for rate enhancement; for general multipath channels, a time–frequency transformation is employed to construct an equivalent frequency-domain MIMO model, enabling adaptation of SK-type coding. This work presents the first successful generalization of SK coding to multipath fading environments, preserving its low complexity and exponential error decay while establishing a novel equivalence framework between time-domain multipath and frequency-domain MIMO systems, thereby offering new pathways for ultra-reliable communication.

Technology Category

• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Machine Learning: Multi-class/Multi-label Learning & Extreme Classification

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements
• Web Mining and Content Analysis: Models for Web evolution

Abstract

The classical Schalkwijk-Kailath (SK) scheme for the additive Gaussian noise channel with noiseless feedback is highly efficient since its coding complexity is extremely low and the decoding error doubly exponentially decays as the coding blocklength tends to infinity. However, how to extend the SK scheme to channel models with memory has yet to be solved. In this paper, we first investigate how to design SK-type scheme for the 2-path quasi-static fading channel with noiseless feedback. By viewing the signal of the second path as a relay and adopting an amplify-and-forward (AF) relay strategy, we show that the interference path signal can help to enhance the transmission rate. Besides this, for arbitrary multi-path fading channel with feedback, we also present an SK-type scheme for such a model, which transforms the time domain channel into a frequency domain MIMO channel.

Problem

• fading channels
• imperfect CSI
• quantized feedback
• Schalkwijk-Kailath scheme
• channel with memory

Innovation

• Schalkwijk-Kailath scheme
• fading channels
• amplify-and-forward relay
• frequency-domain MIMO
• noiseless feedback