Adaptive interactive scheme for Gaussian fading two-way channels

Shuo SHAO, Kangning MA, Dengfeng XIA, Bin DAI

Journal of Tsinghua University(Science and Technology) ›› 2025, Vol. 65 ›› Issue (11) : 2042-2052.

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Journal of Tsinghua University(Science and Technology) ›› 2025, Vol. 65 ›› Issue (11) : 2042-2052. DOI: 10.16511/j.cnki.qhdxxb.2025.27.044
Frontiers in New-Quality Communication Technology

Adaptive interactive scheme for Gaussian fading two-way channels

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Abstract

Objective: This study addresses the key challenge of designing adaptive coding schemes for nonstationary two-way communication channels, where forward and feedback links experience time-varying fading governed by Markovian memory. While traditional Schalkwijk-Kailath (S-K) coding frameworks perform well over static channels, they rely on offline, precomputed power allocation strategies that are unsuitable for channels with dynamically evolving conditions. Such static approaches fail to track Markov-correlated channel fluctuations, resulting in degraded signal-to-noise ratio (SNR) scaling over successive communication rounds, and, particularly under channel memory effects, thereby degrading error rate performance. Aiming to address this limitation, a novel S-K-inspired coding architecture that adaptively adjusts power allocation based on delayed channel state information (CSI). This adaptive design enhances the robustness and reliability of two-way communication over channels exhibiting Markov fading. Methods: Aiming to achieve this goal, a reinforcement-inspired, real-time optimization framework integrated within the S-K coding structure is introduced. The core innovation of the approach lies in its capability to dynamically allocate transmission energy for each communication round based on three critical inputs: 1) the channel state of the historical round (quantized via finite Markov states), 2) the Markov transition matrix of the channel (used to predict the next likely state), and 3) the instantaneous channel state at current iteration (causal CSI). In contrast to conventional S-K schemes that rely on static, offline power allocation, the proposed method reformulates power allocation as a sequential decision-making problem. This reformulation is realized through a dual optimization strategy that jointly considers coupled system parameters to maximize the expected cumulative equivalent SNR across multiround interactions. The optimization strategy begins with the derivation of relaxed constraints based on specific bidirectional transmission requirements (power budgets and error thresholds), and proceeds by employing greedy algorithms to allocate power for equivalent SNR maximization. A critical component of the scheme is its integration of predictive Markov state transition adjustments, enabling proactive power adjustments in anticipation of future channel variations. This predictive capability supports suboptimal yet resilient communication quality across rounds. Collectively, these strategies enable the proposed scheme to maintain high interaction reliability while supporting elevated transmission rates. Results: Simulation results and mathematic analysis show that the proposed scheme consistently outperforms conventional S-K-type schemes in a two-way Markov fading channel. Under ideal conditions, when the channels are in a stable state, the proposed scheme automatically reduces to the classical S-K solution for additive white Gaussian noise channels. In more general fading scenarios involving multiple random channel states, the scheme yields substantial performance gains over conventional S-K baselines by strategically leveraging noisy feedback to enhance communication robustness. Notably, even when compared to enhanced Markov channel models with idealized noise-free feedback, whose capacities represent the theoretical upper bound for the studied model, the numerical results reveal that the proposed scheme asymptotically approaches this limit through successive rounds of interaction. Conclusion: This study presents an adaptive feedback coding scheme for Gaussian channels with memory under unstable fading conditions. By dynamically adjusting encoding parameters using dual optimization in coupled systems, the proposed approach extends the S-K framework to achieve suboptimal yet robust transmission rates. Numerical simulations and mathematical analysis demonstrate that the scheme outperforms classical S-K methods in fading environments, particularly in the presence of channel fluctuations. By balancing causal adaptation with predictive optimization, the proposed architecture offers a promising solution for reliable communication in 5G/6G systems operating under nonstationary feedback conditions.

Key words

feedback communication / Gaussian fading channels / Schalkwijk-Kailath feedback scheme

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Shuo SHAO , Kangning MA , Dengfeng XIA , et al. Adaptive interactive scheme for Gaussian fading two-way channels[J]. Journal of Tsinghua University(Science and Technology). 2025, 65(11): 2042-2052 https://doi.org/10.16511/j.cnki.qhdxxb.2025.27.044

References

1
KENT M L , LANE A . Two-way communication, symmetry, negative spaces, and dialogue[J]. Public Relations Review, 2021, 47 (2): 102014.
2
POPOVSKI P , CHIARIOTTI F , HUANG K B , et al. A perspective on time toward wireless 6G[J]. Proceedings of the IEEE, 2022, 110 (8): 1116- 1146.
3
LI R , XIAO Y , YANG P , et al. UAV-aided two-way relaying for wireless communications of intelligent robot swarms[J]. IEEE Access, 2020, 8, 56141- 56150.
4
SHANNON C E. Two-way communication channels [C]// Proceedings of the 4th Berkeley Symposium on Mathematical Statistics and Probability. Berkeley, USA: University of California Press, 1961: 611-644.
5
HAYASHI M , VÁZQUEZ-CASTRO Á . Two-way physical layer security protocol for Gaussian channels[J]. IEEE Transactions on Communications, 2020, 68 (5): 3068- 3078.
6
SCHALKWIJK J , KAILATH T . A coding scheme for additive noise channels with feedback-Ⅰ: No bandwidth constraint[J]. IEEE Transactions on Information Theory, 1966, 12 (2): 172- 182.
7
SCHALKWIJK J . A coding scheme for additive noise channels with feedback-Ⅱ: Band-limited signals[J]. IEEE Transactions on Information Theory, 1966, 12 (2): 183- 189.
8
HORSTEIN M . Sequential transmission using noiseless feedback[J]. IEEE Transactions on Information Theory, 1963, 9 (3): 136- 143.
9
BEN-YISHAI A , SHAYEVITZ O . Interactive schemes for the AWGN channel with noisy feedback[J]. IEEE Transactions on Information Theory, 2017, 63 (4): 2409- 2427.
10
SHANNON C . The zero error capacity of a noisy channel[J]. IRE Transactions on Information Theory, 1956, 2 (3): 8- 19.
11
OZAROW L . The capacity of the white Gaussian multiple access channel with feedback[J]. IEEE Transactions on Information Theory, 1984, 30 (4): 623- 629.
12
VISWANATHAN H . Capacity of Markov channels with receiver CSI and delayed feedback[J]. IEEE Transactions on Information Theory, 1999, 45 (2): 761- 771.
13
LIU J L , ELIA N , TATIKONDA S . Capacity-achieving feedback schemes for Gaussian finite-state Markov channels with channel state information[J]. IEEE Transactions on Information Theory, 2015, 61 (7): 3632- 3650.
14
CHANCE Z , LOVE D J . Concatenated coding for the AWGN channel with noisy feedback[J]. IEEE Transactions on Information Theory, 2011, 57 (10): 6633- 6649.
15
XIA D F , YANG C C , DAI B . Two-way full-duplex Gaussian channels with or without eavesdropper: Revisit[J]. IEEE Transactions on Communications, 2022, 70 (8): 5434- 5450.
16
MALKAMAKI E , LEIB H . Performance of truncated type-Ⅱ hybrid ARQ schemes with noisy feedback over block fading channels[J]. IEEE Transactions on Communications, 2000, 48 (9): 1477- 1487.
17
MAKKI B , AMAT A G I , ERIKSSON T . On noisy ARQ in block-fading channels[J]. IEEE Transactions on Vehicular Technology, 2014, 63 (2): 731- 746.
18
BIGLIERI E , PROAKIS J , SHAMAI S . Fading channels: Information-theoretic and communications aspects[J]. IEEE Transactions on Information Theory, 1998, 44 (6): 2619- 2692.
19
TSE D , VISWANATH P . Fundamentals of wireless communication[M]. Cambridge: Cambridge University Press, 2005.
20
GOLDSMITH A J , VARAIYA P P . Capacity, mutual information, and coding for finite-state Markov channels[J]. IEEE Transactions on Information Theory, 1996, 42 (3): 868- 886.
21
RUBINSTEIN R Y , KROESE D P . Simulation and the Monte Carlo method[M]. Hoboken: John Wiley & Sons, Inc., 2016.

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