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

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Apr 24, 2026J/K move · Enter open · S save

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

Ming Ye, Kui Cai, Cunhua Pan, Zhen Mei+2

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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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.

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

Abstract

Joint Source-Channel Coding

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