PaperlayerView exact revision on arXiv

Source-linked AI summary

OFDM-guided Deep Joint Source Channel Coding for Wireless Multipath Fading Channels

Mingyu Yang, Chenghong Bian, Hun-Seok Kim

arXiv:2109.05194v1eess.SP

TL;DR

Wireless image transmission over multipath fading channels challenges separate coding and prior deep JSCC approaches designed for simpler channels. The paper combines an autoencoder with differentiable OFDM and explicit channel-processing components, achieving a reported 2.5 - 4dB SNR gain over separate source and channel coding, with further improvement from CSI feedback.

  • Problem

    Separate coding is limited for short messages, while prior deep JSCC work does not specifically address multipath fading channels.

  • Method

    The method jointly trains neural encoder-decoder networks with non-trainable but differentiable OFDM and multipath-channel layers, using explicit channel estimation and equalization.

  • Results

    2.5 - 4dB SNR gain is reported over a traditional modularized scheme using state-of-the-art image compression and separate error correction coding.

  • Takeaways & Limitations

    CSI feedback further improves performance, while adversarial training improves perceptual quality and the scheme is robust to clipping and unseen channel conditions.

Abstract

from arXiv · show

We investigate joint source channel coding (JSCC) for wireless image transmission over multipath fading channels. Inspired by recent works on deep learning based JSCC and model-based learning methods, we combine an autoencoder with orthogonal frequency division multiplexing (OFDM) to cope with multipath fading. The proposed encoder and decoder use convolutional neural networks (CNNs) and directly map the source images to complex-valued baseband samples for OFDM transmission. The multipath channel and OFDM are represented by non-trainable (deterministic) but differentiable layers so that the system can be trained end-to-end. Furthermore, our JSCC decoder further incorporates explicit channel estimation, equalization, and additional subnets to enhance the performance. The proposed method exhibits 2.5 -- 4 dB SNR gain for the equivalent image quality compared to conventional schemes that employ state-of-the-art but separate source and channel coding such as BPG and LDPC. The performance further improves when the system incorporates the channel state information (CSI) feedback. The proposed scheme is robust against OFDM signal clipping and parameter mismatch for the channel model used in training and evaluation.

I. INTRODUCTION

The paper targets the limitations of separate coding and prior deep JSCC in realistic multipath fading channels by combining JSCC with OFDM and domain-knowledge-driven processing. Experiments report improved performance over modular baselines, with additional gains from CSI feedback and robustness across channel conditions.

  • Motivation: Separate source and channel coding can be suboptimal for short messages and may fail catastrophically below a channel-quality threshold.These limitations motivate jointly optimizing source and channel coding for low-latency or low-complexity communication.
  • Research gap: Prior deep JSCC studies largely focus on simple AWGN or Rayleigh flat-fading channels, leaving multipath fading specifically unaddressed.The paper identifies no existing JSCC work specifically designed and optimized for multipath fading channels.
  • Approach: The proposed method concatenates neural networks with differentiable OFDM and multipath-channel blocks, enabling end-to-end training for wireless image transmission.Encoded images are fed as frequency-domain OFDM baseband symbols, while channel and OFDM operations remain fixed but differentiable.
  • Extensions and robustness: CSI feedback further improves performance, while adversarial training enhances perceptual quality and the method remains robust to clipping, noise levels, and unseen channel conditions.The reported robustness includes variations in noise power, multipath count, and channel conditions not seen during training.
  • Results: 2.5 - 4dB SNR gain is reported over a traditional modularized scheme using state-of-the-art image compression and separate error correction coding.The comparison uses a conventional image-compression codec and separate channel code applied to OFDM.

II. PROPOSED METHOD

The proposed channel model represents multipath fading and Gaussian noise in discrete time, while differentiable channel realizations allow gradients to pass through the channel during end-to-end training. The model uses a learned encoder-decoder framework with explicit channel parameters and convolutional processing.

  • Deep JSCC channel model: The encoder maps a real-valued image to complex-valued baseband samples, and the decoder reconstructs the source from noisy multipath-channel outputs.Encoder and decoder parameters are learned neural-network parameters, while the channel is represented conditionally through channel statistics.
  • Multipath fading channel: The multipath channel is modeled in discrete time as convolution with a length-L complex impulse response followed by additive complex Gaussian noise.The channel impulse response contains L multipaths, and the noise has covariance σ^2I_k.
  • Multipath fading channel: Each path undergoes independent Rayleigh fading, with path powers following an exponential decay profile.The decay profile is governed by a time-decay or delay-spread constant γ.
  • Differentiable training: The channel transfer function is fully differentiable with respect to the transmitted signal for fixed random channel realizations.This allows decoder gradients to propagate through a particular multipath realization back to the encoder during gradient-based training.

B. JSCC with OFDM extension

The OFDM extension maps encoded image information into frequency-domain symbols, uses pilots for channel estimation, and transmits through a multipath channel with differentiable OFDM processing.

  • Packet and channel assumptions: Each image is transmitted in one OFDM packet containing N_p pilot symbols and N_s information symbols.Block-type pilots send known symbols on all subcarriers; synchronization is assumed within the cyclic-prefix length L_cp and without carrier frequency offset.
  • Encoder and OFDM mapping: The encoder reshapes complex-valued outputs into N_s × L_fft frequency-domain symbols for OFDM transmission.One half of the real-valued encoder output supplies the real component and the other half the imaginary component.
  • Receiver processing: The receiver removes the cyclic prefix and applies DFT to obtain frequency-domain pilots and data symbols from the noisy channel output.The received data follow ˆY[j,k] = H[k]Y[j,k] + V[j,k], where H[k] is the kth subcarrier response.
  • Decoder objective: The decoder estimates the source from transmitted pilots, received data symbols, and received pilots using a reconstruction objective based on MSE.The decoder input is (Y_p, ˆY, ˆY_p), and its output is the reconstructed source ˆx.
  • Differentiable implementation: OFDM processing remains trainable end-to-end because IDFT, DFT, and cyclic-prefix operations are fixed linear layers that pass gradients during back-propagation.

C. Decoder design with domain knowledge

The decoder combines explicit channel estimation and equalization with learned residual subnetworks, while jointly training source reconstruction and channel estimation.

  • Decoder alternatives: A direct generator-network decoder receives received data and pilot signals but treats the decoder as a black box, risking slow convergence and sub-optimal performance.
  • Explicit signal processing: Per-channel MMSE estimation and conventional MMSE equalization provide computationally efficient preprocessing before the generator network.Per-channel estimation uses element-wise operations and does not require second-order channel statistics.
  • Residual refinement: CE and EQ residual subnets learn to compensate errors remaining after explicit channel estimation and equalization.These lightweight networks are connected residually to the corresponding processing stages.
  • Auxiliary supervision: An additional channel-estimation loss encourages the equalizer input to remain a valid channel estimate.
  • End-to-end training: The system jointly optimizes reconstruction and channel-estimation losses, with λ_c weighting the channel-estimation term.The required derivatives of the channel-estimation and equalization functions are straightforward to obtain for back-propagation.

D. OFDM with PAPR reduction

The paper addresses OFDM’s high peak-to-average power ratio through signal clipping and also considers CSI-based precoding and adversarial image reconstruction.

  • PAPR motivation: High OFDM PAPR causes excessive power consumption at the power amplifier.For the transmit signal y[n], PAPR is defined as the maximum sample power divided by average sample power.
  • Clipping method: Signal clipping is investigated as a simple PAPR-reduction method that can be combined with the JSCC scheme.
  • Clipping operation: Clipping limits the amplitude of time-domain OFDM samples, after which normalization restores the original signal power without changing PAPR.The clipping ratio ρ and input signal power P_s determine the clipping operation.
  • CSI feedback: When CSI is available, an optional precoding block is enabled to evaluate the impact of exploiting channel knowledge.CSI feedback can support dynamic power allocation and adaptive modulation, although it does not increase memoryless-channel capacity.
  • Adversarial reconstruction: The adversarial extension adds a discriminator because PSNR may poorly reflect texture and content quality at low rates.The resulting minmax objective adds an adversarial-loss weight λ_g to the training objective.

III. TRAINING AND EVALUATION

The evaluation uses image datasets, CNN-based encoder and generator networks, and differentiable OFDM system components under defined training and transmission settings.

  • CIFAR-10 and CIFAR-100 contain 60,000 32×32-pixel images, while CelebA contains more than 200,000 celebrity images and is processed at 64×64 pixels.
  • Testing uses 10,000 unused images per dataset, transmitted five times through different random multipath-channel realizations, with PSNR and SSIM evaluating reconstruction quality.
  • The encoder uses down-scaling convolutional layers, residual blocks, and power normalization, with output channels controlling the compression rate.
  • The component evaluations report PSNR, SSIM, and channel-estimation mean square error when available, while Table III analyzes CIFAR-10 complexity.
  • The OFDM system uses L_fft = 64, L_cp = 16, L = 8, and γ = 4; the cyclic prefix must exceed channel delay spread to avoid inter-symbol interference.
  • All evaluations except Section III-D omit CSI feedback and use instantaneous receiver-defined SNR.

A. Effect of domain knowledge and residual connections

OFDM substantially improves deep JSCC over direct transmission in multipath fading, while explicit channel estimation and equalization provide SNR-dependent benefits. Compared with separate BPG-LDPC coding, the proposed scheme is strongest at low SNR and low rate.

  • Effect of domain knowledge: Explicit channel estimation and equalization slightly improve high-SNR performance but initially reduce PSNR and SSIM at 5dB SNR.
  • Residual connections and subnets: Adding a channel-estimation subnet and estimation loss improves reconstruction at both 5dB and 15dB SNR, while the complete CE-plus-EQ scheme performs best among variants.
  • Complexity: The methods have comparable complexity, and the proposed CE and EQ subnets add approximately 1.2% parameters relative to OFDM+CE+EQ.
  • Comparison with separate coding: The proposed JSCC consistently outperforms separate coding with perfect CSI, especially when the number of information symbols is small.
  • Comparison with separate coding: With only N_p = 1 pilot, JSCC’s advantage increases as per-channel MMSE estimation becomes less accurate, particularly at low SNR.
  • Pilot-information trade-off: Using fewer pilots can improve reconstruction because the additional information symbols provide more data-symbol redundancy than the lost channel-estimation accuracy costs.
  • Comparison with separate coding: At fixed N_s + N_p = 7, the proposed method exceeds the baseline’s perfect-CSI upper bound in both PSNR and SSIM across all SNRs.

C. Performance with PAPR reduction

PAPR reduction creates a trade-off between amplifier-friendly signals and image quality. Training with clipping makes the proposed JSCC degrade more gradually under aggressive clipping than the baseline.

  • Figure 8 evaluates clipping ratios ρ = 0.8, 1, 1.2, and 1.4 at N_s = 6 and N_p = 1 for 5dB and 15dB SNR.
  • Without PAPR reduction, PSNR is highest but PAPR is approximately 10dB, imposing a significant amplifier power-efficiency burden.
  • Carefully selected clipping ratios achieve PAPR below 2dB at both 5dB and 15dB SNR, with image-quality loss from constrained representation power.
  • The model is more resilient to clipping noise at 5dB than at 15dB because channel noise dominates at lower SNR, whereas clipping dominates total distortion at higher SNR.
  • The proposed JSCC shows a more gradual PSNR/SSIM degradation than the baseline as clipping becomes more aggressive.

D. Performance with CSI feedback

With perfect CSI feedback, the system removes channel estimation and activates a precoding network. CSI feedback improves the proposed JSCC for both image-quality metrics.

  • The proposed system removes its channel-estimation module and CE subnet and activates an optional precoding network when perfect CSI is available at transmitter and receiver.
  • Perfect CSI feedback improves the proposed JSCC performance for both PSNR and SSIM.
  • Against a separate-coding upper bound that fully attains channel capacity, JSCC provides similar PSNR and consistently better SSIM.
  • The CSI-feedback gain is larger for the proposed JSCC than for the baseline separate scheme.

E. Performance with adversarial loss

Adversarial training improves the perceptual quality of reconstructed images, especially at low SNR, while trading off PSNR and SSIM. The JSCC remains robust under SNR and multipath-model mismatch.

  • Adversarial-loss results: JSCC-adv achieves the highest classification accuracy, while original JSCC achieves the highest PSNR and SSIM at both evaluated SNRs.The comparison uses CIFAR-10 with CPP = 0.182 and assumes perfect CSI for the baseline.
  • Adversarial-loss results: Adversarial loss produces more high-frequency details, including human hair and background structure, despite lower PSNR and SSIM.The perceptual improvement aligns with the classification-accuracy improvement.
  • Robustness to channel mismatch: Performance is hardly affected when testing uses fewer than 8 paths than training, while more than 8 paths gradually degrade channel estimation and SSIM.The model was trained with an L = 8 multipath channel and evaluated at the same noise level.
  • Robustness to channel mismatch: Within a certain range of L, JSCC remains robust to channel mismatch and outperforms separated methods with perfect CSI.The mismatch test varies the number of multipaths used during evaluation relative to training.

G. Extension to larger images and qualitative results

The fully convolutional JSCC extends to high-resolution images and variable input sizes, and its perceptual advantages persist on Kodak. Adversarial training further improves fine-detail reconstruction despite lower distortion metrics.

  • Extension to larger images: The high-resolution model is trained on 200,000 Open Images V6 natural images using 256×256 random patches.It adds convolutional and residual layers relative to the smaller-image architecture.
  • Extension to larger images: The fully convolutional structure supports testing on multiple input sizes beyond 256×256.The Kodak benchmark contains 24 images at 768×512 resolution.
  • Qualitative results: JSCC reconstructions show better visual quality by SSIM-based measures, even when measured PSNR is lower than the baseline.This reflects the paper’s claim that PSNR is less reliable for subjective quality on high-resolution Kodak images.
  • Qualitative results: Adversarial loss further improves fine details such as bush, grass, and ground texture in reconstructed Kodak images.The paper reports that adversarial loss aligns better with human perception for large images.

APPENDIX A ABLATION STUDIES ON 𝜆𝑐AND 𝜆𝑔

The ablations show that explicit channel estimation is important for image quality and channel-estimation accuracy, while adversarial-loss weighting controls a perception-distortion trade-off. The structured network also benefits from OFDM and specialized subnets.

  • Ablation of λc: Setting λc = 0 causes significantly larger channel-estimation error, although PSNR is not sensitive to λc.Including the channel-estimation subnet Φce enhances image quality.
  • Ablation of λc: When Φce is included, image quality depends little on λc, but λc > 0 yields more interpretable channel-estimation-subnet results.The ablation uses Ns = 6, Np = 1, and SNR = 5dB.
  • Ablation of λg: Increasing λg lowers reconstruction PSNR while increasing classification accuracy.This establishes a perception-distortion trade-off for the adversarial-loss weight.
  • Ablation of λg: Excessively large λg causes generated content to differ from the original images, degrading both PSNR and classification accuracy.The ablation uses λc = 0.5, Ns = 6, Np = 1, and SNR = 5dB.
  • Network-structure comparison: The proposed structured network is compared with a direct network without OFDM and subnets on CIFAR-10 under AWGN and multipath fading channels.The comparison uses 384 channel usages per 32 × 32 image, corresponding to CPP = 0.375.
Loading 2109.05194v1…