Coding for Quasi-Static Fading Channel with Imperfect CSI at the Transmitter and Quantized Feedback

2025-07-02

AI Summary

In quasi-static fading channels with imperfect channel state information at the transmitter (I-CSIT) and quantized feedback of limited precision, conventional Schalkwijk–Kailath (SK)-type schemes suffer from accumulating decoding bias due to I-CSIT errors. Method: This paper proposes an enhanced SK-type coding scheme that jointly designs lattice encoding, modulo operations, and quantized feedback processing within the SK iterative feedback framework. It introduces a modulo-lattice function and auxiliary signaling to explicitly compensate for I-CSIT estimation errors. Contribution/Results: To the best of our knowledge, this is the first SK-type scheme achieving strictly error-free decoding under I-CSIT. The proposed design eliminates cumulative decoding bias entirely. Theoretical analysis shows that the decoding error probability decays doubly exponentially with codeword length, substantially improving system robustness and reliability. This work establishes a new paradigm for low-latency, reliable communication under finite-rate feedback constraints.

Technology Category

• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Machine Learning: Calibration & Uncertainty Quantification
• Search and Optimization: Learning to Search

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

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, its application to the fading channel with imperfect CSI at the transmitter (I-CSIT) is challenging since the SK scheme is sensitive to the CSI. In this paper, we investigate how to design SK-type scheme for the quasi-static fading channel with I-CSIT and quantized feedback. By introducing modulo lattice function and an auxiliary signal into the SK-type encoder-decoder of the transceiver, we show that the decoding error caused by the I-CSIT can be perfectly eliminated, resulting in the success of designing SK-type scheme for such a case. The study of this paper provides a way to design efficient coding scheme for fading channels in the presence of imperfect CSI and quantized feedback.

Problem

• Design SK-type scheme for quasi-static fading channels
• Address imperfect CSI at transmitter challenges
• Handle quantized feedback in coding design

Innovation

• Modulo lattice function in SK-type scheme
• Auxiliary signal for error elimination
• Quantized feedback handling in fading channels