Abstract
Deep learning has a wide application in the area of natural language processing and image processing due to its strong ability of generalization. In this paper, we propose a novel neural network structure for jointly optimizing the transmitter and receiver in communication physical layer under fading channels. We build up a convolutional autoencoder to simultaneously conduct the role of modulation, equalization, and demodulation. The proposed system is able to design different mapping scheme from input bit sequences of arbitrary length to constellation symbols according to different channel environments. The simulation results show that the performance of neural network-based system is superior to traditional modulation and equalization methods in terms of time complexity and bit error rate under fading channels. The proposed system can also be combined with other coding techniques to further improve the performance. Furthermore, the proposed system network is more robust to channel variation than traditional communication methods.
深度學習由於其較強的泛化能力，在自然語言處理和圖像處理領域有着廣泛的應用。本文提出了一種新型的神經網絡結構，用於在衰減信道下聯合優化通信物理層中的發射機和接收機。我們建立了一個卷積自動編碼器，同時進行調製、均衡和解調的作用。所提出的系統能夠根據不同的信道環境，從輸入任意長度的比特序列到星座符號設計不同的映射方案。仿真結果表明，在衰落信道下，基於神經網絡的系統在時間複雜度和誤碼率方面的性能優於傳統的調製和均衡方法。所提出的系統還可以與其他編碼技術相結合，進一步提高性能。此外，與傳統通信方法相比，所提出的系統網絡對信道變化的適應性更強。
II. DEEP LEARNING BASICS
The structure of layers we are going to use are plotted in Fig. 1. Dense layer is the layer that has each neuron connected with every neuron in the previous layer. In convolutional layer, each neuron is only connected to several nearby neurons in the previous layer (no more than 3 neurons in Fig. 1), and the parameters for each neuron are shared. The locally-connected layer works similarly to the convolutional layer, except that weights are unshared, that is, a different set of filters is applied at each different patch of the input. And the time-distributed dense layer is a layer that only processes every temporal slice of its input instead of all the elements of the input. Under our case, it is essentially a convolutional layer with kernel size = 1. Taking the application in communication PHY into consideration, we will provide further comparison between dense layer and convolutional layer in Section III.
我們要使用的層的結構如圖1所示。稠密層是指每個神經元都與上一層的每個神經元相連的層。在卷積層中，每個神經元只與上一層中幾個附近的神經元相連（圖1中神經元不超過3個），每個神經元的參數是共享的。局部連接層的工作原理與卷積層類似，只是權重是不共享的，即在輸入的每個不同的補丁處應用不同的濾波器組。而時間分佈稠密層是一個只處理輸入的每個時間片而不是輸入的所有元素的層。在我們的情況下，它本質上是一個卷積層，內核大小=1。考慮到在通信PHY中的應用，我們將在第三節對稠密層和卷積層進行進一步的比較。
III. SYSTEM MODEL
A. Traditional Communication PHY Structure
B. Comparison Between Machine Learning Techniques
Inspired by recent progress in machine learning, we may view the traditional communication system as a general optimization problem provided parameterized representation of g1 and g3. Since it remains unclear how to do parametrization and optimization, we briefly compare existing representative machine learning techniques, including boosted tree,dense neural network autoencoder (DNN-AE) and convolutional neural network autoencoder (CNN-AE). In most of previous literatures [20]–[23], DNN-AE is adopted as the basic structure of design.
受機器學習最新進展的啓發，我們可以將傳統的通信系統看作是一個一般的優化問題，提供參數化表示的g1和g3。由於目前仍不清楚如何進行參數化和優化，我們簡單比較一下現有的代表性機器學習技術，包括boosted tree、稠密神經網絡自動編碼器（DNN-AE）和卷積神經網絡自動編碼器（CNN-AE）。在以往的文獻[20]-[23]中，大多采用DNN-AE作爲設計的基本結構。
Although DNN-AE may have a similar error rate as CNN-AE, we would like to point out that there is a huge computation complexity gap between these two network structures. Consider a simple case when a k-bit input sequence is processed by a one-layer CNN or DNN with 1 dimension. Assume the window size of CNN is c1 and the number of neurons for DNN is c2. Then the number of parameters in CNN is approximately c1 + 1, which does not scale with k, while the number of parameters in DNN is c2(k + 1). In practice, we tend to deal with input bits that are quite long even under block code setting. Thus it is more computationally efficient to train a CNN based autoencoder. As a concrete example, assuming that we are processing 12000 bits as input, if we assume the overall rate is 1/4, then the middle layers must have at least 6000 neurons, which could result in a huge number of parameters (at least 12000*6000) that makes the neural network hard to train.
雖然DNN-AE可能具有與CNN-AE相似的錯誤率，但我們要指出的是，這兩種網絡結構之間存在着巨大的計算複雜性差距。考慮一個簡單的案例，當一個k位的輸入序列被一個1維的單層CNN或DNN處理。假設CNN的窗口大小爲c1，DNN的神經元數量爲c2。那麼CNN的參數數大約爲c1+1，不隨k的增加而增加，而DNN的參數數爲c2(k+1)。在實際工作中，我們往往會處理相當長的輸入位，即使在塊碼設置下也是如此。因此，訓練一個基於CNN的自動編碼器在計算上更有效率。舉個具體的例子，假設我們要處理12000位的輸入，如果我們假設總碼率爲1/4，那麼中間層至少要有6000個神經元，這可能會導致大量的參數（至少12000*6000），導致神經網絡難以訓練。
Furthermore, it is also important that the proposed structure is able to be adapted to input with different lengths after training. However, for DNN-AE and boosted tree, one needs to retrain the whole model for input of different lengths. It is natural to adopt a CNN based structure since traditional communication system is mostly on a convolutional or similar scheme (e.g. convolution code, QAM and PSK modulation etc.). We summarized our discussion on different machine learning methods in Table I. Based on the properties of different machine learning methods, we propose to use a CNN autoencoder for joint transceiver optimization for the complexity consideration.
此外，同樣重要的是，所提出的結構能夠在訓練後適應不同長度的輸入。然而，對於DNN-AE和boosted tree來說，人們需要對整個模型進行再訓練，以適應不同長度的輸入。由於傳統的通信系統多采用卷積或類似的方案(如卷積碼、QAM和PSK調製等)，因此採用基於CNN的結構是很自然的。我們在表一中總結了對不同機器學習方法的討論。根據不同機器學習方法的特性，出於複雜度的考慮，我們提出採用CNN自動編碼器進行聯合收發優化。
IV. AUTOENCODER FOR TIME DOMAIN TRANSMISSION
A. Network Structure
The property of neural network enables us to train the model using only input bit sequences under different channel states. We jointly optimize the transmitter and receiver with an autoencoder structure. Convolutional neural network is used considering the sequential property of the input sequence. The network structure is shown in Fig. 3.
神經網絡的特性使我們能夠在不同的信道狀態下，只使用輸入位序列來訓練模型。我們用自動編碼器結構聯合優化發射機和接收機。考慮到輸入序列的順序性，採用卷積神經網絡。網絡結構如圖3所示。
We compress the length of the input from k×M to M in the first convolutional layer with stride size = k. And we combine the usage of time-distributed dense layer with convolutional layer to introduce further correlation and nonlinearity in the transmitter. We increase the number of parameters in the second convolutional layer to further improve the representability of the network. This is inspired by the traditional practice in communication of first doing coding to introduce redundancy and then conducting modulation to compress the data. The transmitted symbol X = [real(x);imag(x)] is of size M × 2 as a complex vector. In the channel layer, the input symbols are first normalized to satisfy the power constraint. For AWGN channel, only additive white gaussian noise is added to the normalized symbols. For fading channels, the normalized symbols first convolve with the impulse response in the time domain. The convolution in complex number is implemented as in equation (4). In neural networks, it can be represented by a 1D convolutional layer that convolves X with a 3D tensor.
在第一卷積層中，我們將輸入的長度從k×M壓縮到M，步幅大小=k，並結合時間分佈密集層和卷積層的使用，在發射機中進一步引入相關性和非線性。我們增加了第二卷積層的參數數量，以進一步提高網絡的可表示性。這是受傳統通信中先做編碼引入冗餘，再進行調製壓縮數據的做法的啓發。傳輸的符號X=[real(x);imag(x)]是大小爲M×2的複數向量。在信道層，首先對輸入符號進行歸一化處理，以滿足功率約束。對於AWGN信道，只在歸一化符號中加入加性白高斯噪聲。對於衰落信道，歸一化後的符號首先與時域的脈衝響應進行卷積。複數卷積的實現方式如式(4)。在神經網絡中，可以用一個1D卷積層來表示，用3D張量來卷積X。
Generally a neural network suffers from the restriction of input shape, i.e. the length of input for testing shall be the same as that in training procedure. However, due to the locallyconnected property of convolutional layer and time-distributed layer, the proposed network structure is able to accept input sequences of any length without the need of retraining the whole model. Thus the system can process long sequences while trained on short ones.
一般來說，神經網絡受到輸入形狀的限制，即用於測試的輸入長度應與訓練過程中的輸入長度相同。然而，由於卷積層和時間分佈層的局部連接特性，所提出的網絡結構能夠接受任何長度的輸入序列，而不需要重新訓練整個模型。因此該系統可以在對短序列進行訓練的同時處理長序列。
We conduct massive experiments to analyze the performance of our model. We train our model separately on AWGN channel and fading channel. In the rest part of this chapter, we give a thorough analysis on the result of the learned system.
我們進行了大量的實驗來分析我們模型的性能。我們分別在AWGN信道和衰落信道上訓練我們的模型。在本章的其餘部分，我們對學習系統的結果進行了全面的分析。
B. Setting
In our experiment, we set k = 6 and compare the learned system with 64QAM for AWGN channel, and 64QAM plus minimum mean square error (MMSE) estimation [28] for fading channel. We also test the proposed model on k = 8 case with 256QAM+MMSE in fading channel to prove the extensibility of our model. The modulation scheme is selected considering the throughput fairness. For the training and testing our model, we randomly generate i.i.d. bit sequences. The generated dataset is separated arbitrarily into training set, validation set and test set. The property of convolutional neural network enables the network to process input sequence of any length without changing network parameters. The change in the length of the input sequence would not affect the performance of our system. Thus we fix M to be 400.
在實驗中，我們設置k=6，並將學習到的系統與AWGN信道的64QAM和衰落信道的64QAM加最小均方誤差(MMSE)估計[28]進行比較。我們還在k=8的情況下用256QAM+MMSE在衰落信道中測試所提出的模型，以證明我們模型的可擴展性。調製方案的選擇考慮了吞吐量的公平性。對於訓練和測試我們的模型，我們隨機生成i.i.d.比特序列。生成的數據集被任意分離爲訓練集、驗證集和測試集。卷積神經網絡的特性使得網絡可以在不改變網絡參數的情況下處理任意長度的輸入序列。輸入序列長度的改變不會影響我們系統的性能。因此我們將M固定爲400。
We train the autoencoder with 30,000 training samples and test that with 10,000 test data. The learning rate is set to be 0.001 and the batch size is 32. We use mean squared error as the loss function. We run for 300 epochs. The kernel size of each convolutional layer is set to be 12 and we use tanh as activation function. We train the system at a specific signal to noise ratio (SNR) but test at a wide range of SNR, as well as robustness and adaptivity to deviations from the AWGN and fading setting. We would like to show that although the state space of input bit sequence is as large as 
, the model can generalize well with mere 30,000 training samples.
In the time domain transmission system, we test three different channels, one AWGN channel and two fading channels. The amplitude and delay for two fading channels are plotted in Fig. 4. The integer in x-axis is the delay of each path in the unit of symbols. Note that the phase information is omitted in the figure.
我們用30000個訓練樣本訓練自動編碼器，用10000個測試數據進行測試。學習率設置爲0.001，批次大小爲32。我們使用均方誤差作爲損失函數。我們運行了300個epochs。每個卷積層的內核大小設置爲12，我們使用tanh作爲激活函數。我們在特定的信噪比（SNR）下對系統進行訓練，但在很寬的SNR範圍內進行測試，以及對AWGN和衰減設置的偏差進行魯棒性和適應性測試。我們想證明，雖然輸入比特序列的狀態空間大到
，但僅用3萬個訓練樣本，模型就能很好地泛化。
在時域傳輸系統中，我們測試了三個不同的信道，一個AWGN信道和兩個衰落信道。圖4中繪製了兩個衰落信道的振幅和延遲。x軸中的整數是以符號爲單位的每條路徑的延遲。注意圖中省略了相位信息。
C. AWGN Channel
D. Fading Channel
low-density parity-check（LDPC）
E. Robustness
F. Time Complexity Comparison
We provide both simulation and numerical analysis for analyzing time complexity. We first test the time complexity by running demodulation plus detection algorithms and the receiver part in neural network on a Intel (R) Corel (TM) i7-7700HQ CPU @ 2.80GHz CPU and an NVIDIA GeForce GTX 1060 GPU. The platform in this experiment is python+keras [31]. For AWGN channel, only demodulation is needed to recover the bit sequence. For fading channel, MMSE is also included in the receiver, which takes long for the FFT step. We test both methods for 100 sets of data and take the average. The comparison is shown in Table.II.
我們提供仿真和數值分析來分析時間複雜度。我們首先在英特爾(R)Corel(TM)i7-7700HQ @ 2.80GHz CPU和NVIDIA GeForce GTX 1060 GPU上運行解調加檢測算法和神經網絡中的接收器部分，測試時間複雜度。本實驗中的平臺是python+keras[31]。對於AWGN信道，只需要解調恢復比特序列。對於衰落信道，接收機中還包含MMSE，這需要很長的FFT步驟。我們對兩種方法進行100組數據測試，取平均值。比較結果如表.II所示。
For transmitted bit sequence with length n, the time complexity for both CNN and QAM demodulation is O(n). However, for MMSE detection, FFT requires a O(nlogn). CNN is able to substitute the demodulation plus detection algorithm with a lower time complexity in theory and higher accuracy. Thus CNN based framework is quite suitable for designing communication system in fading channels.
對於長度爲n的傳輸位序列，CNN和QAM解調的時間複雜度均爲O(n)。但對於MMSE檢測，FFT需要O(nlogn)。CNN能夠替代解調加檢測算法，理論上時間複雜度更低，精度更高。因此基於CNN的框架相當適用於設計衰落信道中的通信系統。
With the development of neural network, the dimension of the CNN can be potentially reduced with techniques such as network pruning and distillation. Parallelization is also possible in the multiplicative units in the neural network, as well as pipelining. Neural network can be further accelerated by specially designed hardware framework like GPU, FPGA and TPU etc. These designs along with a careful analysis of the fixed point arithmetic requirements of the different weights are under active research. The efficiency of neural network can be further improved in the future.
隨着神經網絡的發展，CNN的維度可以通過網絡修剪和提煉等技術進行潛在的降低。神經網絡中的乘法單元也可以實現並行化，以及管道化。神經網絡可以通過專門設計的硬件框架，如GPU、FPGA和TPU等進一步加速。這些設計以及對不同權重的定點運算要求的仔細分析正在積極研究中。未來可以進一步提高神經網絡的效率。
V. AUTOENCODER FOR FREQUENCY DOMAIN TRANSMISSION
A. Network Structure
In the previous chapter, we studied the effect of the multipath fading channel. In Orthogonal Frequency Division Multiplexing (OFDM) [32] system, the inter-symbol interference can be eliminated by introducing guard interval between each subcarrier. Cyclic prefix is a typical guard interval, which makes each subcarrier orthogonal to each other. In the following part of this chapter, we assume perfect cyclic prefix as guard interval. Thus there is no inter-symbol inference and inter-channel inference. However, there is still fading on each subcarrier. One of the most common equalization methods for this issue is zero forcing (ZF) [33]. Since the fading on individual subcarrier might be quite significant, it is hard to recover the signal from those subcarriers due to poor SNR. The information carried by some subcarriers might experience deep fading and thus get lost during transmission. A zero order equalization system would cause inevitable loss of information [34]. By introducing correlation between subcarriers, the information can be carried by nearby subcarriers. Thus the burst error on subcarriers with deep fading can be decreased.
在上一章中，我們研究了多徑衰落信道的影響。在正交頻分複用(OFDM)[32]系統中，可以通過在每個子載波之間引入保護間隔來消除符號間的干擾。循環前綴是一個典型的保護間隔，它使每個子載波之間正交。在本章的下面部分，我們假設完美的循環前綴作爲保護間隔。因此，不存在符號間推理和信道間推理。然而，在每個子載波上仍然存在衰減。對於這個問題，最常用的均衡方法之一是迫零均衡（ZF）[33]。由於單個子載波上的衰落可能相當大，由於SNR較差，很難從這些子載波上恢復信號。一些子載波所攜帶的信息可能會經歷深度衰落，從而在傳輸過程中丟失。零階均衡系統會造成不可避免的信息丟失[34]。通過引入子載波之間的相關性，信息可以由附近的子載波攜帶。因此可以降低具有深度衰落的子載波的突發誤差。
Based on previous network structure, we design a frequency domain equalization system that is able to retrieve more information than ZF. Since the fading on each subcarrier is different, a convolutional layer that shares weight along the whole input sequence may not be suitable. Here locally connected layer is used to substitute some of the convolutional layers in previous structure. The locally connected layer works similarly as the convolutional layer, except that weights of kernels are unshared. That is, a different set of filters is applied at each different patch of the input. The whole network structure is shown in Fig. 13.
在以往網絡結構的基礎上，我們設計了一個頻域均衡系統，它能夠檢索到比ZF更多的信息。由於每個子載波上的衰落是不同的，沿整個輸入序列共享權重的卷積層可能並不合適。這裏使用局部連接層來替代前面結構中的一些卷積層。局部連接層的工作原理與卷積層類似，只是核的權重是不共享的。也就是說，在輸入的每一個不同的batch上都應用了一組不同的濾波器。整個網絡結構如圖13所示。
The only difference between time domain and frequency domain is the substitution of some convolutional layer. The reason to substitute convolutional layer with the more general locally connected layer lies in the fact that channel may bring different level of fading effects to different symbols on the coded sequence. Intuitively, the symbols that suffer from severe fading would need to spread its information to nearby symbols, while the symbols with strong energy also need to help carry more information. If we are merely using convolutional layer, then each symbol is treated equally, energy allocation is impossible to be done.
時域和頻域之間唯一的區別就是替換了一些卷積層。用更一般的局部連接層代替卷積層的原因在於，信道可能會給編碼序列上的不同符號帶來不同程度的衰落影響。直觀地講，受到嚴重衰減影響的符號需要將其信息傳播給附近的符號，而能量強的符號也需要幫助攜帶更多的信息。如果我們僅僅使用卷積層，那麼每個符號都被平等對待，能量分配是不可能完成的。
B. Simulation
We test the new structure under the case of an OFDM system transmission. The bit sequence is modulated and transmitted in frequency domain. All other settings are the same as the previous example. We consider the frequency transformation of channel B in Fig. 4. The frequency selective fading channel in frequency domain is shown in Fig. 14. We train and test our model on the same channel. And compare that with 64QAM+ZF method. Here ZF is assumed to have accurate channel state information. But the zero points in the fading plot would prohibit a significant number of subcarriers from transmitting information to the receiver.
我們在OFDM系統傳輸的情況下測試了新的結構。比特序列在頻域內被調製和傳輸。所有其他設置與前面的示例相同。我們在圖4中考慮信道B的頻率變換。頻域中的頻率選擇性衰落信道如圖14所示。我們在同一個頻道上訓練和測試我們的模型。並與64QAM+ZF法進行比較。這裏假設ZF具有準確的信道狀態信息。但是，衰落圖中的零點將禁止大量的子載波向接收機發送信息。
VI. DISCUSSION
From previous two sections, we provide empirical justification on the superiority of our design. We are comparing the trained CNN-AE with mostly 64QAM+MMSE as a baseline. In communication area there are much more complex algorithms and techniques, e.g. iterative demodulation and decoding algorithm, that are able to achieve near-capacity performance in terms of BER. However, we justify the fairness of our comparison from the following three aspects.
在前兩部分中，我們提供了我們的設計優越性的經驗證明。我們正在比較訓練的CNN-AE和大部分64QAM+MMSE作爲基線。在通信領域，有很多複雜的算法和技術，例如迭代解調和解碼算法，能夠在誤碼率方面達到接近容量的性能。但是，我們從以下三個方面來證明我們的比較是公平的。
- The running time in Table II shows that our algorithm is comparable in efficiency to QAM+MMSE system. And there have been many mature ideas to make large neural networks practically implementable in small devices with due accuracy and faster speed [36]. For example, the idea of distilling the knowledge in a large network to a smaller network and the idea of binarization of weights and data in order to avoid complex multiplication operations could further speed up CNN-AE based communication system.
- The designed CNN-AE does not include an iterative decoding structure. We believe that with appropriate iterative decoding design, the performance could be further improved and comparable with other coding and decoding methods using iterative schemes. For example, one may introduce another network as the second decoder and cascade that with the first decoder for the iterative decoding. Since the output of network can be viewed as the probability, it is naturally suitable for soft-decoding.
- With the help of interleaving, CNN-AE can also be combined with existing coding scheme to further improve its performance. We have shown previously that it can be combined with LDPC code in Fig. 8.
- 從表二的運行時間可以看出，我們的算法在效率上與QAM+MMSE系統相當。而爲了使大型神經網絡在小型設備中實際實現，並具有應有的精度和更快的速度，已經有很多成熟的想法[36]。例如，將大型網絡中的知識提煉爲一個較小的網絡，以及將權值和數據二值化以避免複雜的乘法運算的思想，可以進一步加快基於CNN-AE的通信系統的速度。
- 所設計的CNN-AE不包括迭代解碼結構。我們認爲，如果採用適當的迭代解碼設計，可以進一步提高性能，與其他採用迭代方案的編解碼方法相媲美。例如，可以引入另一個網絡作爲第二解碼器，與第一解碼器級聯，進行迭代解碼。由於網絡的輸出可以看作是概率，所以自然適合軟解碼。
- 在交織的幫助下，CNN-AE還可以與現有的編碼方案相結合，進一步提高其性能。前面我們已經展示了它可以與LDPC碼結合，如圖8。
Another issue with most of deep learning based communication system is that the BER stops decreasing after reaching some low BER level. This also shows up in our Figs. 11 and 15. However, for practice use, we propose to combine CNN-AE with some other coding scheme. When the coding is powerful enough, the system can reach much lower BER as long as the performance of CNN-AE is better within 
region.
Furthermore, we would like to point out that our goal is to show that CNN-AE is able to learn the way of mapping and demapping for any channel without prior mathematic model and analysis, thus being promising for communication system design without expertise. We also believe that some other autoencoder-based structures, e.g. combining resnet with autoencoder, may also lead to improvement on existing structures.
大多數基於深度學習的通信系統的另一個問題是，誤碼率在達到一些低誤碼率水平後就停止下降。這在我們的圖11和圖15中也有體現。但在實際使用中，我們建議將CNN-AE與其他編碼方案相結合。當編碼足夠強大時，只要CNN-AE的性能在
區域內更好，系統可以達到更低的誤碼率。
此外，我們想指出的是，我們的目標是證明CNN-AE能夠在不需要事先建立數學模型和分析的情況下學習任何信道的映射和解映射方式，因此在沒有專業知識的情況下，很有希望用於通信系統設計。我們也相信，其他一些基於自動編碼器的結構，例如將resnet與自動編碼器結合起來，也可能會帶來對現有結構的改進。
VII. CONCLUSION
In this paper, we propose a convolutional autoencoder structure that is able to automatically design communication physical layer scheme according to different channel status. The system has no restriction on the length of input bit sequence. We conduct massive experiment to give empirical evidence for the superiority of the proposed system. The neural network has lower time complexity and higher accuracy especially for fading channel, and is also quite robust to channel variation. The framework can also be extended to OFDM system which transmits in frequency domain.
本文提出一種卷積自動編碼器結構，能夠根據不同的信道狀態自動設計通信物理層方案。該系統對輸入位序列的長度沒有限制。我們進行了大量的實驗，爲所提出的系統的優越性提供了實證。該神經網絡具有較低的時間複雜度和較高的精度，特別是對於衰落信道，對信道變化也具有相當的魯棒性。該框架還可以擴展到頻域傳輸的OFDM系統。
There is still a lot of work to be done in combining machine learning techniques with communication PHY. We may further explore the feasibility and utility of neural network based communication methods in following aspects.
在機器學習技術與通信PHY的結合上，還有很多工作要做。我們可以從以下幾個方面進一步探討基於神經網絡的通信方法的可行性和實用性。
- One of the most important goals of designing a communication system is to maximize the capacity, i.e. the mutual information between input and output. However, since the constellation diagram in neural network based system is continuously distributed in the complex plane. It is hard for us to estimate the mutual information accurately, let alone optimizing the mutual information within neural network. A framework for analyzing mutual information in neural network based communication system may significantly enlarge our knowledge about both neural network and communication system.
- An iterative, soft-input soft-output receiver can significantly improve the BER performance. Designing a receiver with both log likelihood ratio and received symbol as input using neural network may also enable iteration inside receiver, thus improving the current performance.
- The performance of neural network is still not as good in high SNR regime. It is important to figure out how autoencoder can learn a communication physical layer that outperforms existing communication techniques even in the high-SNR regions.
- 設計一個通信系統最重要的目標之一是最大限度地提高容量，即輸入和輸出之間的相互信息。然而，由於基於神經網絡的系統中的星座圖是連續分佈在複雜平面上的。我們很難準確地估計互信息，更不用說優化神經網絡內部的互信息了。一個基於神經網絡的通信系統中的互信息分析框架，可能會大大擴展我們對神經網絡和通信系統的認識。
- 迭代的軟輸入軟輸出接收機可以顯著提高誤碼率性能。利用神經網絡設計一個同時以對數似然比和接收符號爲輸入的接收機，也可以實現接收機內部的迭代，從而改善目前的性能。
- 在高SNR體制下，神經網絡的性能還是不盡如人意。重要的是要弄清楚自動編碼器如何學習一個通信物理層，即使在高SNR區域也能優於現有的通信技術。