Channel coding is vital for reliable sixth-generation (6G) data transmission, employing diverse error correction codes for various application scenarios. Traditional decoders require dedicated hardware for each code, leading to high hardware costs. Recently, artificial intelligence (AI)-driven approaches, such as the error correction code Transformer (ECCT) and its enhanced version, the foundation error correction code Transformer (FECCT), have been proposed to reduce the hardware cost by leveraging the Transformer to decode multiple codes. However, their excessively high computational complexity ofO(N2) due to the self-attention mechanism in the Transformer limits scalability, whereNrepresents the sequence length. To reduce computational complexity, we propose a unified Transformer-based decoder that handles multiple linear block codes within a single framework. Specifically, a standardized unit is employed to align code length and code rate across different code types, while a redesigned low-rank unified attention module, with computational complexity ofO(N), is shared across various heads in the Transformer. Additionally, a sparse mask, derived from the parity-check matrix’s sparsity, is introduced to enhance the decoder’s ability to capture inherent constraints between information and parity-check bits, improving decoding accuracy and further reducing computational complexity by 86%. Extensive experimental results demonstrate that the proposed unified Transformer-based decoder outperforms existing methods and provides a high-performance, low-complexity solution for next-generation wireless communication systems.

Neural network-based decoding methods show promise in enhancing error correction performance but face challenges with punctured codes. In particular, existing methods struggle to adapt to variable code rates or meet protocol compatibility requirements. This paper proposes a unified long short-term memory (LSTM)-based neural decoder for punctured convolutional and Turbo codes to address these challenges. The key component of the proposed LSTM-based neural decoder is puncturing-aware embedding, which integrates puncturing patterns directly into the neural network to enable seamless adaptation to different code rates. Moreover, a balanced bit error rate training strategy is designed to ensure the decoder’s robustness across various code lengths, rates, and channels. In this way, the protocol compatibility requirement can be realized. Extensive simulations in both additive white Gaussian noise (AWGN) and Rayleigh fading channels demonstrate that the proposed neural decoder outperforms conventional decoding techniques, offering significant improvements in decoding accuracy and robustness.

Electromagnetic information theory (EIT) is one of the emerging topics for 6G communication due to its potential to reveal the performance limit of wireless communication systems. For EIT, one of the most important research directions is degree of freedom (DoF) analysis. Existing research works on DoF analysis for EIT focus on asymptotic conclusions of DoF, which do not well fit the practical wireless communication systems with finite spatial regions and finite frequency bandwidth. In this paper, we provide mathematical definitions of the DoF for continuous electromagnetic fields. Moreover, we theoretically prove that the channel DoF is upper-bounded by the proposed functional DoF of electromagnetic fields. Furthermore, we use the theoretical analyzing tools from the Slepian concentration problem and extend them to three-dimensional space domains and four-dimensional space-time domains under electromagnetic constraints. Then we provide asymptotic DoF conclusions and non-asymptotic DoF analyzing scheme, which suits practical scenarios better, under different scenarios like three-dimensional antenna array. Finally, we use numerical analysis to provide some insights about the optimal spatial sampling interval of the antenna array, the DoF of three-dimensional antenna array, the impact of unequal antenna spacing, the orthogonal space-time patterns, etc.

In extremely large-scale multiple-input-multiple-output (XL-MIMO) systems for future sixth-generation (6G) communications, codebook-based beam training stands out as a promising technology to acquire channel state information (CSI). Despite their effectiveness, existing beam training methods suffer from significant achievable rate degradation for remote users with low signal-to-noise ratio (SNR). To tackle this challenge, leveraging the error-correcting capability of channel codes, we incorporate channel coding theory into beam training to enhance the training accuracy, thereby extending the coverage area. Specifically, we establish the duality between hierarchical beam training and channel coding, and build on it to propose a general coded beam training framework. Then, we present two specific implementations exemplified by coded beam training methods based on Hamming codes and convolutional codes, during which the beam encoding and decoding processes are refined respectively to better accommodate to the beam training problem. Simulation results have demonstrated that, the proposed coded beam training method can enable reliable beam training performance for remote users with low SNR, while keeping training overhead low.