Rateless DeepJSCC for Broadcast Channels: a Rate-Distortion-Complexity Tradeoff

Zijun Qin; Jingxuan Huang; Zesong Fei; Haichuan Ding; Yulin Shao; Xianhao Chen

cs.ITMar 23, 2026

Rateless DeepJSCC for Broadcast Channels: a Rate-Distortion-Complexity Tradeoff

Authors: Zijun Qin, Jingxuan Huang, Zesong Fei, Haichuan Ding, Yulin Shao, Xianhao Chen

Organizations: Department of Electrical and Computer Engineering, University of Hong Kong, Pok Fu Lam, Hong Kong S.A.R., China · School of Information and Electronics, Beijing Institute of Technology, Beijing, China · School of Cyberspace Science and Technology, Beijing Institute of Technology, Beijing, China

Abstract

In recent years, numerous data-intensive broadcasting applications have emerged at the wireless edge, calling for a flexible tradeoff between distortion, transmission rate, and processing complexity. While deep learning-based joint source-channel coding (DeepJSCC) has been identified as a potential solution to data-intensive communications, most of these schemes are confined to worst-case solutions, lack adaptive complexity, and are inefficient in broadcast settings. To overcome these limitations, this paper introduces nonlinear transform rateless source-channel coding (NTRSCC), a variable-length JSCC framework for broadcast channels based on rateless codes. In particular, we integrate learned source transformations with physical-layer LT codes, develop unequal protection schemes that exploit decoder side information, and devise approximations to enable end-to-end optimization of rateless parameters. Our framework enables heterogeneous receivers to adaptively adjust their received number of rateless symbols and decoding iterations in belief propagation, thereby achieving a controllable tradeoff between distortion, rate, and decoding complexity. Simulation results demonstrate that the proposed method enhances image broadcast quality under stringent communication and processing budgets over heterogeneous edge devices.

Figures & tables

Variable	Definition
$\mathbf{x}$	Source image
$\bf{y},{\bf{b}}$	Latent representation and quantized vector
$\bf{z},\bar{\bf{z}},\tilde{\bf{z}}$	Hyperprior latent variables and quantized / relaxed version
$\mathbf{v}$	Rateless coded symbols
$\mathbf{u}$	Channel input symbols
$\hat{\mathbf{u}}_{j}$	Channel output symbols at user $j$

TABLE I: List of important notations in this paper

Fig. 1: Schematic diagram for nonlinear transform rateless source-channel coding. At the transmitter, the analysis transform $g_{a}$ extracts semantic information ${\bf{y}}$ from source image, the analysis transform $h_{a}$ produces auxiliary variable $\bf{z}$ , the synthesis transforms $h_{s}$ and $h_{c}$ predict bit likelihoods ${\bm{\mu}}$ and LT parameters ${\bm{\rho}}$ , ${\bm{\Omega}}$ to generate rateless symbols $\bf{v}$ . At the receiver, the synthesis transforms $h_{s}$ and $h_{c}$ predict bit likelihoods and LT parameters, the scaling function $f_{s}$ estimates the number of received symbols $\bf{n}$ and decoding iterations $\bm{\eta}$ to perform BP decoding on demodulator soft values ${\bf{\hat{v}}}$ , the synthesis transform ${g_{s}}$ takes soft decoder outputs $\mathcal{M}$ and recovers image information.

	$\displaystyle{\mathbb{E}_{p\left({\bf{x}}\right)}}$	$\displaystyle{D_{KL}}\left[{\left.{q({\bf{\tilde{z}}},{\bf{\hat{u}}}\mid{\bf{x}})}\right\\|p({\bf{\tilde{z}}},{\bf{\hat{u}}}\mid{\bf{x}})}\right]$
		$\displaystyle={\mathbb{E}_{p\left({\bf{x}}\right)}}{\mathbb{E}_{q({\bf{\tilde{z}}},{\bf{\hat{u}}}\mid{\bf{x}})}}\left[{\ln q({\bf{\hat{u}}}\mid{\bf{x}})+\ln q({\bf{\tilde{z}}}\mid{\bf{x}})-\ln p({\bf{\tilde{z}}})-\ln p({\bf{\hat{u}}}\mid{\bf{\tilde{z}}})-\ln p(\left.{\bf{x}}\right\|{\bf{\tilde{z}}},{\bf{\hat{u}}})+\ln p\left({\bf{x}}\right)}\right]$
		$\displaystyle\mathop{=}\limits^{\left(a\right)}{\mathbb{E}_{p\left({\bf{x}}\right)}}{\mathbb{E}_{q({\bf{\tilde{z}}}\mid{\bf{x}})}}{\mathbb{E}_{q({\bf{\hat{u}}}\mid{\bf{x}})}}\left[{\ln\frac{{q({\bf{\hat{u}}}\mid{\bf{x}})}}{{p({\bf{\hat{u}}}\mid{\bf{\tilde{z}}})}}+\ln q({\bf{\tilde{z}}}\mid{\bf{x}})-\ln p({\bf{\tilde{z}}})-\ln{\mathbb{E}_{p\left({\left.{\mathcal{M}}\right\|{\bf{\tilde{z}}},{\bf{\hat{u}}}}\right)}}p(\left.{\bf{x}}\right\|{\mathcal{M}})}\right]+{\mathbb{E}_{p\left({\bf{x}}\right)}}\ln p\left({\bf{x}}\right)$
		$\displaystyle={\mathbb{E}_{p\left({\bf{x}}\right)}}\left\{{{\mathbb{E}_{q({\bf{\tilde{z}}}\mid{\bf{x}})}}{D_{KL}}\left[{\left.{q({\bf{\hat{u}}}\mid{\bf{x}})}\right\\|p({\bf{\hat{u}}}\mid{\bf{\tilde{z}}})}\right]+{\mathbb{E}_{q({\bf{\tilde{z}}}\mid{\bf{x}})}}{\mathbb{E}_{q({\bf{\hat{u}}}\mid{\bf{x}})}}\left[{\ln q({\bf{\tilde{z}}}\mid{\bf{x}})-\ln p({\bf{\tilde{z}}})-\ln{\mathbb{E}_{p\left({\left.{\mathcal{M}}\right\|{\bf{\tilde{z}}},{\bf{\hat{u}}}}\right)}}p(\left.{\bf{x}}\right\|{\mathcal{M}})}\right]}\right\}+{\mathbb{E}_{p\left({\bf{x}}\right)}}\ln p\left({\bf{x}}\right)$
		$\displaystyle\mathop{=}\limits^{\left(b\right)}{\mathbb{E}_{p\left({\bf{x}}\right)}}\left\{{{\mathbb{E}_{q({\bf{\tilde{z}}}\mid{\bf{x}})}}n{D_{KL}}\left[{\left.{q(\hat{u}\mid{\bf{x}})}\right\\|p(\hat{u}\mid{\bf{\tilde{z}}})}\right]+{\mathbb{E}_{q({\bf{\tilde{z}}}\mid{\bf{x}})}}{\mathbb{E}_{q({\bf{\hat{u}}}\mid{\bf{x}})}}\left[{\ln q({\bf{\tilde{z}}}\mid{\bf{x}})-\ln p({\bf{\tilde{z}}})-\ln{\mathbb{E}_{p\left({\left.{\mathcal{M}}\right\|{\bf{\tilde{z}}},{\bf{\hat{u}}}}\right)}}p(\left.{\bf{x}}\right\|{\mathcal{M}})}\right]}\right\}+{\mathbb{E}_{p\left({\bf{x}}\right)}}\ln p\left({\bf{x}}\right)$
		$\displaystyle\mathop{=}\limits^{\left(c\right)}{\mathbb{E}_{p\left({\bf{x}}\right)}}\left\{{n{D_{KL}}\left[{\left.{q(\hat{u}\mid{\bf{x}})}\right\\|p(\hat{u}\mid{\bf{\tilde{z}}})}\right]-\ln p({\bf{\tilde{z}}})-{\mathbb{E}_{q({\bf{\hat{u}}}\mid{\bf{x}})}}\ln{\mathbb{E}_{p\left({\left.{\mathcal{M}}\right\|{\bf{\tilde{z}}},{\bf{\hat{u}}}}\right)}}p(\left.{\bf{x}}\right\|{\mathcal{M}})}\right\}+{\mathbb{E}_{p\left({\bf{x}}\right)}}\ln p\left({\bf{x}}\right)$
		$\displaystyle\mathop{\leq}\limits^{\left(d\right)}{\mathbb{E}_{p\left({\bf{x}}\right)}}\left\{{n{D_{KL}}\left[{\left.{q(\hat{u}\mid{\bf{x}})}\right\\|p(\hat{u}\mid{\bf{\tilde{z}}})}\right]-\ln p({\bf{\tilde{z}}})-{\mathbb{E}_{q({\bf{\hat{u}}}\mid{\bf{x}})}}{\mathbb{E}_{p\left({\left.{\mathcal{M}}\right\|{\bf{\tilde{z}}},{\bf{\hat{u}}}}\right)}}\ln p(\left.{\bf{x}}\right\|{\mathcal{M}})}\right\}+{\mathbb{E}_{p\left({\bf{x}}\right)}}\ln p\left({\bf{x}}\right)$

Table 3

Operation	Count	Operation	Count
$\tanh(\cdot)$	$E+n$	$\tanh^{-1}(\cdot)$	$E$
$/$	$2E+n$	$\times$	$2E+n$
$+$	$E+k$	$-$	$E$

TABLE II: Arithmetic operations per BP decoding iteration

Fig. 2: The LT encoding and decoding process in NTRSCC. Consider the j-th feature channel. The extracted latent features ${\bf{y}}_{j}$ are quantized to obtain bitstream ${\bf{b}}_{j}$ . ${\bf{y}}_{j}$ also produces dimension-wise prior ${\bm{\mu}}_{j}$ , which guides the prediction of degree distributions ${\bm{\Omega}}_{j}$ and ${\bm{\rho}}_{j}$ . While the rateless symbols are produced indefinitely, the encoder employs a polling strategy based on the sum log-probability of each feature channel to generate channel symbols ${\bf{v}}_{j}$ . The decoder stops receiving more rateless channel symbols when the total number of collected symbols reaches $\bf{n}$ . The BP decoder processes demodulated LLR ${\bf{\hat{v}}}_{j}$ and the prior LLR ${\bm{\mu}}_{j}$ , until the number of iterations reach ${\left\lceil\eta\right\rceil}$ , and the final outputs are the soft likelihoods $\mathcal{M}_{j}$ .

Panel of Figure 6 — Fig. 3: Rate-distortion tradeoff comparisons.

Panel of Figure 7 — Fig. 4: Complexity-distortion tradeoff comparisons.

Panel of Figure 8 — Fig. 5: broadcasting efficiency comparisons

Joint Source-Channel Coding

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Apr 24, 2026

Selective Depthwise Separable Convolution for Lightweight Joint Source-Channel Coding in Wireless Image Transmission

Depthwise separable convolutional (DSConv) layers have been successfully applied to deep learning (DL)-based joint source-channel coding (JSCC) schemes to reduce computational complexity. However, a systematic investigation of the layerwise and ratio-wise replacement of standard convolutional (Conv) layers with DSConv layers in JSCC systems for wireless image transmission remains largely unexplored. In this letter, we propose a configurable lightweight JSCC framework that incorporates a selective replacement strategy, enabling flexible Conv-to-DSConv replacement at different replacement ratios and positions. By varying the replacement ratio, we obtain models with different computational complexities and analyze their impact on reconstruction performance. Furthermore, we investigate how replacements at different encoder and decoder depths influence reconstruction quality under a fixed replacement ratio. Our results show that Conv-to-DSConv replacement at the intermediate layers of the encoder and decoder achieves a favorable complexity-performance trade-off, revealing layer-wise redundancy in DL-based JSCC systems. Extensive experiments further demonstrate that the proposed framework achieves substantial parameter reduction with only slight performance degradation, enabling flexible complexity-performance trade-offs for resource-constrained edge devices.

Ming Ye, Kui Cai, Cunhua Pan +3

Singapore University of Technology and Design, Singapore 487372 · National Mobile Communications Research Laboratory, Southeast University, Nanjing 210096, China · School of Electronic and Optical Engineering, Nanjing University of Science and Technology, Nanjing 210094, China

Deep Joint Source-Channel Coding Wireless Communications Convolutional Neural Networks Depthwise Separable Convolution Joint Source-Channel Coding

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Oct 8, 2026

Neural Network Verification for Deep Joint Source-Channel Coding

Deep joint source-channel coding (DeepJSCC) transmits data end-to-end over wireless channels using a neural encoder-decoder, but reconstruction quality can degrade sharply under adversarial perturbations and channel disturbances; no method formally bounds this degradation for DeepJSCC. We present the first bound-propagation framework for verifying DeepJSCC's decoder, bounding worst-case reconstruction error over a given wireless channel's noise region. Current deep neural network (DNN) verifiers do not support three DeepJSCC decoder components: parametric rectified linear activations (PReLU), transposed convolutions, and Rayleigh fading. We extend state-of-the-art techniques for optimization of linear relaxation in DNN verification for PReLU, replace the transposed convolution with its restricted upsample-then-convolution form, and formulate Rayleigh fading as a structural perturbation prepended directly into the decoder, thereby reducing the dimensionality of the verification problem. We also instantiate Lipschitz-regularized global robustness training, denoted GloRo, improving global robustness and enabling tight certification of DeepJSCC models for the first time. On DeepJSCC model for image transmission, this global robustness training procedure combined with structural encoding lowers the median certified bound by up to 41% and certifies about ten times more safe cases (192 against 19) than GloRo with interval encoding at a 10-degree error in channel estimation. Over-the-air validation with an orthogonal frequency-division multiplexing (OFDM) implementation on software-defined radio devices confirm the certificate holds on real hardware, with a worst observed error on radio link at 0.082 against a certified bound of 0.128.

Thanh Le, Hai Duong, Takeshi Matsumura +1

Wireless Systems Laboratory, National Institute of Information and Communication Technology, Yokosuka, Kanagawa, Japan · George Mason University, Fairfax, VA, USA

Deep Joint Source-Channel Coding Certified Robustness Neural Network Verification Joint Source-Channel Coding Wireless Communications

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Jun 11, 2026

JSCGC: Joint Source-Channel-Generation Coding for Wireless Generative Communications

Conventional communication systems, including both separation-based coding and learning-based joint source-channel coding (JSCC), are typically designed under Shannon's rate-distortion theory. However, relying on generic distortion metrics fails to capture complex human visual perception, often resulting in blurred or unrealistic reconstructions. In this paper, we propose Joint Source-Channel-Generation Coding (JSCGC), a generative communication paradigm that replaces the conventional decoder with a generative model at the receiver. The received signal is treated as a condition that controls the sampling process into the learned conditional distribution, reformulating communication from deterministic reconstruction for distortion minimization to controlled generation for mutual information maximization under perceptual constraints. Based on this formulation, we develop a unified joint training and efficient stochastic sampling framework, and provide theoretical analysis of its effectiveness in both learning and inference stages. Extensive experiments on latent-space image transmission demonstrate that the JSCGC consistently improves feature-based, semantic-level, and distributional quality across diverse channel conditions, while exhibiting a distinct error behavior characterized by semantic inconsistency rather than distortion.

Tong Wu, Zhiyong Chen, Guo Lu +4

Cooperative Medianet Innovation Center, the School of Information Science and Electronic Engineering, Shanghai Jiao Tong University, Shanghai 200240, China

Joint Source-Channel Coding Wireless Communications Conditional Generative Modeling

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	$\displaystyle{\mathbb{E}_{p\left({\bf{x}}\right)}}$	$\displaystyle{D_{KL}}\left[{\left.{q({\bf{\tilde{z}}},{\bf{\hat{u}}}\mid{\bf{x}})}\right\\|p({\bf{\tilde{z}}},{\bf{\hat{u}}}\mid{\bf{x}})}\right]$
		$\displaystyle={\mathbb{E}_{p\left({\bf{x}}\right)}}{\mathbb{E}_{q({\bf{\tilde{z}}},{\bf{\hat{u}}}\mid{\bf{x}})}}\left[{\ln q({\bf{\hat{u}}}\mid{\bf{x}})+\ln q({\bf{\tilde{z}}}\mid{\bf{x}})-\ln p({\bf{\tilde{z}}})-\ln p({\bf{\hat{u}}}\mid{\bf{\tilde{z}}})-\ln p(\left.{\bf{x}}\right\|{\bf{\tilde{z}}},{\bf{\hat{u}}})+\ln p\left({\bf{x}}\right)}\right]$
		$\displaystyle\mathop{=}\limits^{\left(a\right)}{\mathbb{E}_{p\left({\bf{x}}\right)}}{\mathbb{E}_{q({\bf{\tilde{z}}}\mid{\bf{x}})}}{\mathbb{E}_{q({\bf{\hat{u}}}\mid{\bf{x}})}}\left[{\ln\frac{{q({\bf{\hat{u}}}\mid{\bf{x}})}}{{p({\bf{\hat{u}}}\mid{\bf{\tilde{z}}})}}+\ln q({\bf{\tilde{z}}}\mid{\bf{x}})-\ln p({\bf{\tilde{z}}})-\ln{\mathbb{E}_{p\left({\left.{\mathcal{M}}\right\|{\bf{\tilde{z}}},{\bf{\hat{u}}}}\right)}}p(\left.{\bf{x}}\right\|{\mathcal{M}})}\right]+{\mathbb{E}_{p\left({\bf{x}}\right)}}\ln p\left({\bf{x}}\right)$
		$\displaystyle={\mathbb{E}_{p\left({\bf{x}}\right)}}\left\{{{\mathbb{E}_{q({\bf{\tilde{z}}}\mid{\bf{x}})}}{D_{KL}}\left[{\left.{q({\bf{\hat{u}}}\mid{\bf{x}})}\right\\|p({\bf{\hat{u}}}\mid{\bf{\tilde{z}}})}\right]+{\mathbb{E}_{q({\bf{\tilde{z}}}\mid{\bf{x}})}}{\mathbb{E}_{q({\bf{\hat{u}}}\mid{\bf{x}})}}\left[{\ln q({\bf{\tilde{z}}}\mid{\bf{x}})-\ln p({\bf{\tilde{z}}})-\ln{\mathbb{E}_{p\left({\left.{\mathcal{M}}\right\|{\bf{\tilde{z}}},{\bf{\hat{u}}}}\right)}}p(\left.{\bf{x}}\right\|{\mathcal{M}})}\right]}\right\}+{\mathbb{E}_{p\left({\bf{x}}\right)}}\ln p\left({\bf{x}}\right)$
		$\displaystyle\mathop{=}\limits^{\left(b\right)}{\mathbb{E}_{p\left({\bf{x}}\right)}}\left\{{{\mathbb{E}_{q({\bf{\tilde{z}}}\mid{\bf{x}})}}n{D_{KL}}\left[{\left.{q(\hat{u}\mid{\bf{x}})}\right\\|p(\hat{u}\mid{\bf{\tilde{z}}})}\right]+{\mathbb{E}_{q({\bf{\tilde{z}}}\mid{\bf{x}})}}{\mathbb{E}_{q({\bf{\hat{u}}}\mid{\bf{x}})}}\left[{\ln q({\bf{\tilde{z}}}\mid{\bf{x}})-\ln p({\bf{\tilde{z}}})-\ln{\mathbb{E}_{p\left({\left.{\mathcal{M}}\right\|{\bf{\tilde{z}}},{\bf{\hat{u}}}}\right)}}p(\left.{\bf{x}}\right\|{\mathcal{M}})}\right]}\right\}+{\mathbb{E}_{p\left({\bf{x}}\right)}}\ln p\left({\bf{x}}\right)$
		$\displaystyle\mathop{=}\limits^{\left(c\right)}{\mathbb{E}_{p\left({\bf{x}}\right)}}\left\{{n{D_{KL}}\left[{\left.{q(\hat{u}\mid{\bf{x}})}\right\\|p(\hat{u}\mid{\bf{\tilde{z}}})}\right]-\ln p({\bf{\tilde{z}}})-{\mathbb{E}_{q({\bf{\hat{u}}}\mid{\bf{x}})}}\ln{\mathbb{E}_{p\left({\left.{\mathcal{M}}\right\|{\bf{\tilde{z}}},{\bf{\hat{u}}}}\right)}}p(\left.{\bf{x}}\right\|{\mathcal{M}})}\right\}+{\mathbb{E}_{p\left({\bf{x}}\right)}}\ln p\left({\bf{x}}\right)$
		$\displaystyle\mathop{\leq}\limits^{\left(d\right)}{\mathbb{E}_{p\left({\bf{x}}\right)}}\left\{{n{D_{KL}}\left[{\left.{q(\hat{u}\mid{\bf{x}})}\right\\|p(\hat{u}\mid{\bf{\tilde{z}}})}\right]-\ln p({\bf{\tilde{z}}})-{\mathbb{E}_{q({\bf{\hat{u}}}\mid{\bf{x}})}}{\mathbb{E}_{p\left({\left.{\mathcal{M}}\right\|{\bf{\tilde{z}}},{\bf{\hat{u}}}}\right)}}\ln p(\left.{\bf{x}}\right\|{\mathcal{M}})}\right\}+{\mathbb{E}_{p\left({\bf{x}}\right)}}\ln p\left({\bf{x}}\right)$

Abstract

Joint Source-Channel Coding

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