SNR-ADAPTIVE DEEP JOINT SOURCE-CHANNEL CODING
FOR WIRELESS IMAGE TRANSMISSION

According to Shannon’s separation theorem [1], it is known that under the premise of unlimited time delay and complexity, separate optimization of source coding and channel coding can also achieve the optimal performance. Therefore, most modern communication systems apply a two-step encoding process: First use source coding algorithm to compress source data to remove its redundancy. Then transmit the compressed bitstream over the channel by using a channel coding algorithm. Moreover, current communication systems employ highly efficient source coding algorithms (e.g., JPEG, JPEG2000, BPG) and near-optimal channel codes (e.g., LDPC, Turbo, polar codes) to approach the theoretical optimality. All the source and channel coding algorithms mentioned above have undergone long-term development and are quite effective.

However, in practice, Shannon’s hypothesis is not applicable in many cases. Even under these assumptions that Shannon mentioned, the separate approach breaks down in multi-user scenarios [2, 3], or non-ergodic source or channel distributions [4, 5]. Moreover, in some applications joint source-channel coding (JSCC) scheme is known to be better than the separate approach [6].

In this paper, we consider the design of practical JSCC scheme. The proposed JSCC scheme can be adaptive to different SNRs and able to be applied to multi-user scenarios (The SNRs of the users might be different) by using pilot signal as an additional input to the decoder. In actual wireless transimission, the transmitter can send pilot signal known to the receiver. According to the pilot signal, the receiver can estimate the SNR to assist the decoding process.

This work is mainly inspired by recent work on deep JSCC and recent success of deep neural networks (DNNs) (in particular, the autoencoder architectures [7, 8]). There are many examples of designs about JSCC using autoencoder architectures, e,g., [9, 10, 11, 12, 13, 14, 15]. The first work that used neural networks to solve the problem of JSCC is [9], where simple neural network architectures were used as encoder and decoder for Gauss-Markov sources over additive white gaussian noise (AWGN) channel. And in [16], they considered the problem of JSCC of structured data such as natural language. In [17], they proposed an deep JSCC model which was mainly inspired by low-variance gradient estimation for variational learning of discrete latent variable models. Kurka $et$ $al$. presented several deep JSCC schemes, among which [18] provided graceful degradation with the SNR, [19] fully exploited channel output feedback, [20] achieved successive refinement of images. This presented work is most relevant to theirs, especially with [18]. The reference [18] is their first contribution and this current paper will take it as the baseline.

To the best of our knowledge, this is the first work about deep JSCC scheme that can be adaptive to different SNRs and able to be applied to multi-user scenarios. Although in [18], they presented graceful degradation with the SNR, their results are not quite satisfactory. We conduct sufficient experiments to verify the performance of our proposed SNR-adaptive deep JSCC scheme and compare it with [18], which is state-of-the-art. It can be seen that, the proposed method can better adapt to the changes of the SNR and it is robust to noisy estimation of the SNR.

The rest of the paper is organized as follows. In Section 2, we introduce the system model and general encoding and decoding process. The proposed model architecture is introduced in Section 3. Section 4 presents the evaluation of the SNR-adaptability of the proposed deep JSCC scheme, and its comparison with the baseline. Moreover, Section 4 includes analysis on robustness of the proposed method to noisy SNR estimation. Finally, the paper is concluded in Section 5.

Fig. 1 presents the multi-user wireless image transmission which is adaptive to the SNR. Each user has a different channel but the same decoder. First, the encoder maps $n$-dimensional image $x\in$ $R^{n}$ to a $k$-dimensional vector of complex numbers $y\in$ $C^{k}$. Then apply an average power constraint to $y$ and $y$ satisfies $\frac{1}{k}$$E[y^{*}y]$ $\leq$ $P$. $y^{*}$ is the conjugate transpose of $y$. $P$ is the average transmit power constraint [18]. $k/n$ is defined as the bandwidth ratio. And the encoder function $f_{\theta}:R^{n}\rightarrow C^{k}$ is parameterized using a CNN with parameters $\theta$. After encoding, $y$ is transimitted over an AWGN channel and the channel output $z_{i}=y+n_{i}$, where $n_{i}$ is the independent and identically distributed circularly symmetric complex Gaussian noise component with zero mean and variance $\sigma^{2}_{i}$. Based on the pilot signal, the decoder can estimate the average SNR and serve it as auxiliary decoding information. SNR = $10log_{10}\frac{P}{\sigma^{2}_{i}}$. Without loss of generality, we assume that $P=1$, in following experiments. And the SNR can be changed by adjusting $\sigma^{2}_{i}$. In subsequent experiments, we actually use $\sigma^{2}_{i}$ obtained by the SNR. Finally, the decoder maps $\sigma^{2}_{i}$ and $z_{i}$ to the reconstructed image $\hat{x}_{i}\in R^{n}$. And the decoding function $g_{\varphi}:C^{k}\rightarrow R^{n}$ is parameterized using a CNN with parameters $\varphi$.

The proposed model is mainly based on autoencoder. From Fig. 2(a), it can be seen that, the encoder consists of five convolutional layers and uses PReLU [21] activation functions. The notation $K*F*F/S$ denotes a convolutional layer with $K$ filters of spatial extent (or size) $F$ and stride $S$. In the subsequent experimental results, $n$ remains unchanged in encoding. By adjusting the number of filters (C) in the last convolutional layer of the encoder, $k$ can be changed, leading to the change in the bandwidth ratio $k/n$. The decoder consists of deconvolutional layers and also uses PReLU and Sigmoid activation functions. The most important thing is that there are two improvements to the decoder.

The above models are implemented in Tensorflow and optimized using the Adam algorithm [26]. The loss function is the average mean squared error (MSE) between the original input image $x$ and reconstruction $\hat{x}$ output from the decoder, defined as:

where $d(x,\hat{x})=\frac{1}{n}\|x-\hat{x}\|^{2}$. PSNR is used to evaluate the performance of the proposed method. The PSNR metric measures the ratio between the maximum possible power of the signal and the power of the noise that corrupts the signal. We evaluate the performance of our model on the CIFAR-10 image dataset [27], which has a training set of 50000 32*32 images and a testing set of 10000 images. Before conducting the experiment, the dataset is preprocessed first. The images in the dataset are 24-bit RGB images. Normalize them and convert the pixel value range from [0,255] to [0,1]. During model training, the learning rate is initially set to $10^{-4}$ and the batch size is 64. Reduce the learning rate to 0.9 times of the original every 10 epochs. Then continue training the model until the test performance no longer shows any improvement. In addition, we first set a training SNR list : [0, 5, 10, 15, 20, 25] (dB) and a testing SNR list : [0, 5, 10, 15, 20] (dB). During training, a SNR is randomly selected from

this traning SNR list in each iteration as the SNR in the transmission process. During the test, the SNR in the testing SNR list is used in the transmission process in turn.

In this paper, a novel SNR-adaptive deep JSCC scheme is proposed for multi-user wireless image transmission.

In this scheme, the decoder estimates the SNR from the pilot signal to assist the decoding process and achieve SNR-adaptability. To the best of our knowledge, this is the first method that focuses on the adaptability for different SNRs and can be applied to multi-user scenarios. We present the advantages of the proposed method by comparing it with state-of-the-art. It can be seen from the experiment results that the SNR-adaptability of the method proposed is better than that of the baseline. Since the proposed model is adaptive to the SNR, it has the potential to be applied to multi-user scenarios. What’s more, we explored the robustness of our proposed model to noisy estimation of the SNR at the decoder. The results show that even if there exist noise in the estimations of the SNR at the decoding end, the performance of the proposed model only drops slightly even when the noise is relatively strong.