Interference Channels
A two-user interference channel is a canonical model for multiple one-to-one communications, where two transmitters wish to communicate with their receivers via a shared medium, examples of which include pairs of base stations and handsets near the cell boundary that suffer from interference. Practical codes and the fundamental limit of communications are unknown for interference channels as mathematical analysis becomes intractable. Hence, simple heuristic coding schemes are used in practice to mitigate interference, e.g., time division, treating interference as noise, and successive interference cancellation. These schemes are nearly optimal for extreme cases: when interference is strong or weak. However, there is no optimality guarantee for channels with moderate interference. Here we combine deep learning and network information theory to overcome the limitation on the tractability of analysis and construct finite-blocklength coding schemes for channels with various interference levels. We show that carefully designed and trained neural codes using network information theoretic insight can achieve several orders of reliability improvement for channels with moderate interference.
Problem Setup
The problem setup is illustrated below. We focus on the symmetric two-user real AWGN interference channel, i.e. \(\textbf{Y}_1 = \textbf{C}_1 + h \textbf{C}_2 + \textbf{Z}_1, \textbf{Y}_2 = \textbf{C}_2 + h \textbf{C}_1 + \textbf{Z}_2\), where \(\textbf{Z}_1, \textbf{Z}_2 \sim \mathcal{N}(0,\sigma^2I)\), \(\mathbf{C}_i\) denotes the \(i\)-th encoder’s transmitted signal, and \(h\) is the interference coefficient. We assume that each encoder has a length \(K\) random binary sequence to communicate, i.e., \(\mathbf{b}_i \in [0,1]^K\) and generates a codeword of length \(n\), \(\mathbf{C}_i \in \mathbb{R}^n\). The \(i\)-th decoder estimates the desired message \(\mathbf{\hat{b}}_i \in [0,1]^K\) based on \(\mathbf{Y}_i \in \mathbb{R}^n\).
The encoders and decoders are replaced by TurboAE encoders and decoders respectively, described below.
Background on Turbo Autoencoder (TurboAE)
In this section, we review Turbo Autoencoder (TurboAE), one of the state-of-the-art neural network-based channel codes for point-to-point AWGN channels.
The encoder consists of three learnable blocks \(g_{\theta_1}\), \(g_{\theta_2}\) and \(g_{\theta_3}\) placed in parallel, followed by a power normalizing layer \(d(.)\). Each learnable block consists of a 1-D CNN followed by a linear layer. For the upper two branches, each message sequence \(\textbf{b}\) is encoded into 3 sequences \(\textbf{c}_1\), \(\textbf{c}_2\) and \(\textbf{c}_3\). For the third branch, the message sequence \(\textbf{b}\) first goes through an interleaver \(\pi\) before being encoded.
Inspired by the dynamic programming decoder, we let the decoder update the belief iteratively. Let \(\textbf{y}_1\), \(\textbf{y}_2\) and \(\textbf{y}_3\) be the noisy versions of \(\textbf{c}_1\), \(\textbf{c}_2\) and \(\textbf{c}_3\) respectively. The decoder goes through multiple iterations. Each iteration makes use of two sequential blocks of a 1-D CNN followed by a linear layer. At the last iteration, the message bits \(\hat{\textbf{b}}\) are estimated. The encoder and decoder architectures are shown below.
Encoder:
Decoder:
Results
In the figure below, we plot the Bit Error Rate (BER) vs Eb/N0. We show the results of time division (Turbo TD), treating interference as noise (Turbo TIN), our scheme (DeepIC+ Pretrained), and a previous iteration of our scheme (DeepIC). We notice that our scheme has the best performance.
Analysis
In the figure figure, we plot the codewords \(\textbf{C}_1\) and \(\textbf{C}_2\) for randomly generated bit sequences \(\textbf{b}_1\) and \(\textbf{b}_2\) for $K=100\(information bits and level of interference\)h=0.8$$. We notice that DeepIC+ learned partial time division (TD). (Full TD happens in the first 100 and last 100 positions, while some joint coding happens in the middle 100 positions). We conjecture that the joint coding is the reason DEEPIC+ outperforms classical TD for h=0.8.
References
DeepIC+: Learning Codes for Interference Channels, Karl Chahine, Yihan Jiang, Joonyoung Cho, Hyeji Kim. IEEE Transactions on Wireless Communications, 2023.
Turbo Autoencoder: Deep learning based channel codes for point-to-point communication channels, Yihan Jiang, Hyeji Kim, Himanshu Asnani, Sreeram Kannan, Sewoong Oh, Pramod Viswanath. NeurIPS, 2019.