Transformer channel decoders, such as the Error Correction Code Transformer (ECCT), have shown strong empirical performance in channel decoding, yet their generalization behavior remains theoretically unclear. This paper studies the generalization performance of ECCT from a learning-theoretic perspective. By establishing a connection between multiplicative noise estimation errors and bit-error-rate (BER), we derive an upper bound on the generalization gap via bit-wise Rademacher complexity. The resulting bound characterizes the dependence on code length, model parameters, and training set size, and applies to both single-layer and multi-layer ECCTs. We further show that parity-check-based masked attention induces sparsity that reduces the covering number, leading to a tighter generalization bound. To the best of our knowledge, this work provides the first theoretical generalization guarantees for this class of decoders.

Recently, deep learning has demonstrated improvements over classical decoding algorithms in various families of error-correcting codes with short to moderate block lengths. Neural decoders like neural belief propagation (NBP), constructed based on the Tanner graphs of linear codes, have been extensively studied, but their application to longer codes is limited due to increased network complexity with longer block lengths. This complexity leads to higher computational costs and deployment challenges, such as GPU memory usage. To address this, we propose a novel revolving framework for NBP-like decoders tailored to cyclic and QC-LDPC codes, a commonly used class of error correction codes. Our approach leverages the cyclic structure and section-wise cyclic structure inherent in cyclic and QC-LDPC codes respectively, significantly simplifying the complexity of the network. Experimental results demonstrate the effectiveness of our method across various cyclic and QC-LDPC codes. Especially, compared to the traditional decoding scheme based on the section-wise cyclic structure, our proposed decoder shows substantial improvements on 5G LDPC codes, exhibits better performance than the traditional min-sum decoder, and approaches the sum-product decoder without a noticeable error floor within the investigated noise levels.

Recently, deep learning has demonstrated improvements over classical decoding algorithms in various families of error-correcting codes with short to moderate block lengths. Neural decoders like neural belief propagation (NBP), constructed based on the Tanner graphs of linear codes, have been extensively studied, but their application to longer codes is limited due to increased network complexity with longer block lengths. This complexity leads to higher computational costs and deployment challenges, such as GPU memory usage. To address this, we propose a novel revolving framework for NBP-like decoders tailored to QC-LDPC codes, a commonly used class of error correction codes. Our approach leverages the section-wise cyclic structure inherent in QC-LDPC codes, significantly simplifying the complexity of the network. Experimental results demonstrate the effectiveness of our method across various QC-LDPC codes. Especially, compared to the traditional decoding scheme based on the section-wise cyclic structure, our proposed decoder shows substantial improvements on 5G LDPC codes, exhibits better performance than the traditional min-sum decoder, and approaches the sum-product decoder without a noticeable error floor within the investigated noise levels.

Different from data-oriented communication systems that primarily focus on how to accurately transmit every bit of data, task-oriented semantic communication systems only transmit the specific semantic information required by downstream tasks, strive to minimize the communication overhead and maintain competitive tasks execution performance in the presence of channel noise. However, it is worth noting that in many scenarios, the transmitted semantic information needs to be dynamically modified according to the users' preferences in a conversational and interactive way, which few existing works take into consideration. In this paper, we propose a novel cross-modal editable semantic communication system, named Editable-DeepSC, to tackle this challenge. By utilizing inversion methods based on StyleGAN priors, Editable-DeepSC takes cross-modal text-image pairs as the inputs and transmits the edited information of images based on textual instructions. Extensive numerical results demonstrate that our proposed Editable-DeepSC can achieve remarkable editing effects and transmission efficiency under the perturbations of channel noise, outperforming existing data-oriented communication methods.

As a pioneering and deep-learning driven neural channel code, Product Autoencoder (ProductAE) shows significant superiority over Turbo Autoencoder (TurboAE) and other classical codes. However, received noisy codewords with different noise levels have different decoding difficulties for the neural decoder of ProductAE. The existing neural decoder processes all noisy codewords equally without discrimination, and neglects the prior knowledge of signal-to-noise ratio (SNR), thus leading to high decoding complexity. In this paper, we propose a new approach to speed up the decoding process of ProductAE. Intuitively, noisy codewords with different SNR can be recovered by decoders of different complexity, and our proposed novel pipeline, Adaptive ProductAE, an SNR-aware adaptive decoding strategy, adopts deep decoders to different SNR. Specifically, adaptive ProductAE combines an encoding module, an additional classification module, and two independent decoding branches in a unified framework. After receiving noisy codewords, it first judges the decoding difficulty of each signal and assigns them to different branches to get the decoded messages. Furthermore, we introduce a novel training strategy with a gap loss to maintain the classification and decoding performance. It can thus switch to a simpler branch of decoding networks automatically when it comes to signals with a higher SNR, and the overall computational cost can be reduced. Experiments show that our adaptive ProductAE saves up to 30.4% FLOPs for a moderate-length code of parameters (225, 100) and 25.5% FLOPs for a code of parameters (441, 196) in a higher SNR range.