 corrupted codewordŝ as the condition. The generator f g is trained to map the received samplesŝ from a fixed distribution pŝ |x to the real distribution p x|s, where pŝ |x is determined by the encoder function f e and channel transition function W. d LPIPS denotes the perceptual LPIPS loss function [7]. As the learning-based LPIPS metric has many different configurations, we exemplarily adopt the Alexnet-based [15] LPIPS loss to help model training in a perception-aware way. d MSE denotes the regular MSE distortion function. β d, β p, β m control the trade-off between three distortion terms.
• Training the discriminator f d with the loss function L D : The channel corrupted sequenceŝ is associated with the source image sample x in (3), i.e.,ŝ = W (f e (x)). The discriminator f d is mapping the input tuple (x, s) to the probability that it is a sample from the real distribution p x|s rather than the fake sample generated by f g.
III. NETWORK ARCHITECTURE Our network architecture is shown in Fig. 3, including the encoder f e, generator f g, and discriminator f d. The encoder f e uses convolution neural networks (CNNs) to extract features of the source image x and reshape them to power normalized channel-input symbols s. The decoder f g performs the inverse operations of the encoder.
Our discriminator network f d is basically the same as that in PatchGAN [16], which penalizes structure at the scale of image patches, i.e., it tries to identify if each patch of the reconstruction is real or fake. The patch size is set to 16 × 16 pixels in our implementation. Besides, we also make use of the structure of cGAN [13] by concatenating the reconstructed image with an upscaled deep JSCC codeword to provide the contextual information. In particular, four cascaded modules of the form "convolution-SpectrualNorm-LeackyReLU" [17] is used to downsample the concatenated feature map progressively, and the number of kernels in convolutions C i is 64, 128, 256, and 512, respectively. After the last layer, a convolution with the Sigmoid activation indicates the discriminator's true or false judgments for each patch.
During the model training, we firstly pretrain the encoder f e and generator f g only using the perceptual loss d LPIPS and   the regular MSE loss d MSE. The function of the pretraining step is to accelerate the experiments and makes them more stable. In the second step, we freeze the encoder f e and generator f g and only optimize the discriminator f d, which enables it to penalize structure at image patches produced by pretrained weights. Finally, we adopt an iterative approach to alternately training the generative network (f e and f g ) and the discriminator network (f d ).

A. Experimental setup 1) Training Details:
The training set consists of 720,000 images sampled from the Open Images dataset [18]. During training, we form a batch of 12 patches by randomly cropping a 256 × 256 patch from each image. We first pretrain the network except for the discriminator f d by about 100,000 iterations jointly using the LPIPS perceptual loss and the regular MSE loss with β p = 1.0 and β m = 10 −5 under a uniform distribution of SNR train ∈ {1, 4, 7, 10, 13} dB. Then, we freeze the encoder and generator and optimize the discriminator for about 10,000 iterations. Finally, we alternately train the generative network (f e and f g ) by setting β g = 10 −3. We use the Adam optimizer with a learning rate of 10 −4.
2) Evaluation Protocols: We evaluate our method on the widely-used Kodak dataset [19] (24 images, 768 × 512 pixels) and the test set of the CLIC2021 dataset [20] (60 images, up to 2048 × 1890 pixels). The comparison schemes include the deep JSCC optimized for MSE (marked as "deep JSCC (MSE)") and the classical coded transmission schemes (BPG + LDPC). In particular, for the deep JSCC scheme, we adopt the Deep JSCC (no feedback) scheme in [2], which achieves better performance than the original paper [1]. For traditional coded transmission schemes, we employ the BPG [3] image codec for source coding and LDPC followed by quadrature amplitude modulation (QAM) for channel coding and modulation. We further adopt BPG combined with an ideal capacity-achieving channel code, which can be viewed as the performance upper bound of the traditional coded transmission scheme. For brevity, "BPG + LDPC" and "BPG + Capacity" refers to the two comparison schemes, respectively.

3) Metrics:
We evaluate our models and the comparison schemes in classical metric PSNR and MS-SSIM [5] as well as the emerging deep learning based perceptual metric LPIPS [7], DISTS [21], FID [22]. PSNR corresponds to the regular MSE distortion in (2). MS-SSIM is the most widely used perceptual metric despite failing to account for many nuances of human perception [7]. LPIPS and DISTS both can predict well with human perceptual judgment by computing the distance in the feature space of the image classification network. FID is widely used to assess the quality and diversity of generated images especially from GAN, which measures the similarity between the distribution of reference images and generated images in the feature space of an Inception network. As the image resolutions vary in a large range, we use the nonoverlapping 2155 patches size of 256 pixels for the CLIC2021 dataset and 144 same size patches for the Kodak dataset.
Inspired by [6], we also carry out a user study to more holistically evaluate the visual quality of our results. Considering the tiny distortion between the original image x and the reconstructed imagex at the high CBR, we design the user study for two models with CBR = 1/48 and CBR = 1/24 and BPG at CBR ranging from 0.029 to 0.058 at SNR = 10dB. We crop the reconstructed images on the Kodak dataset to 256 × 256 patches which are respectively produced from our models and BPG + LDPC. Then we compose a questionnaire comprising of 46 reconstructed patch pairs. Each patch pair include two patches produced by different methods but from the same patch. 20 random participants are asked to choose which patch corresponds to human visual perception. We report the mean percentage of preference for each choice. Fig. 4 shows SNR-distortion and SNR-perception results at the CBR = 1/48 on the Kodak dataset and the CLIC2021 testset. Solid red line and solid green line plot the performance of our model and deep JSCC, where the training SNR value is consistent with the testing SNR value. For the BPG + LDPC scheme, we present the envelope of the best performing configurations at each SNR among different combinations of LDPC coding rate and modulations. Moreover, as shown in Fig. 5, we further present the CBR-perception and CBR-distortion curves over AWGN channel at SNR = 10dB on CLIC2021. For the BPG + LDPC scheme, following [2], we use a 2/3 rate (4096, 6144) LDPC code with 16-ary QAM to ensure reliable transmission and adjust the BPG to the largest compression rate within the CBR constraint.

1) Quantitative Comparison:
Results indicate that our model dominates in terms of all three perceptual quality indices (LPIPS, DISTS, and FID). In particular, our scheme can achieve comparable or even better perceptual quality values than other approaches while saving 2x to 4x bandwidth cost in the same SNR or otherwise achieving 4dB to 8dB SNR gain using the same CBR. It validates the effectiveness of the proposed compound loss function in (1). Even though perceptual metrics match better with human judgments [23], more convincing results can be made through subjective testing in the following user study. Besides, we also note that our scheme presents some performance degradation in the PSNR metric compared to the MSE optimized deep JSCC scheme. These verify that our scheme prefers to generate clear textures instead of a blur, resulting in lower pixel-wise metrics than comparison schemes. Performance degradation becomes negligible when considering another objective metric MS-SSIM, which is more correlated with perceptual quality than PSNR.
2) User Study: Fig 6 shows  the results at the CBR = 1/48. It can be seen that our method is the preferred scheme even if the CBR cost is 47% smaller than that of BPG + LDPC. It is well known that the BPG suffers blocky artifacts, which is unfriendly to human visual perception, but our method can well preserve global semantic information and synthesizes realistic texture. The lower figure shows the results at the CBR = 1/24, the overall image quality improvement leads to a relatively smaller gain of our model, but it is still preferred to the BPG + LDPC when saving 18% channel bandwidth cost. These results verify that our perceptual learned deep JSCC can reconstruct higher visual quality images by using less channel bandwidth cost.

C. Model Variants
As one type of ablation study, we explore the effects of introducing perceptual loss d LPIPS and adversarial loss. We fix the β p = 1.0 and vary the β m and β g to observe the visual results. Firstly we set the β g = 0 and compare the reconstructed images produced respectively from our models with β m = 10 −3, 10