Performance Evaluation of PAC Decoding with Deep Neural Networks

TL;DR

Three types of DNN decoders for PAC codes are proposed: multi-layer perceptron (MLP), convolutional neural network (CNN), and recurrent neural network (RNN), and numerical results show that the MLP decoder has the best error-correction performance under a similar model parameter number.

Abstract

By concatenating a polar transform with a convolutional transform, polarization-adjusted convolutional (PAC) codes can reach the dispersion approximation bound in certain rate cases. However, the sequential decoding nature of traditional PAC decoding algorithms results in high decoding latency. Due to the parallel computing capability, deep neural network (DNN) decoders have emerged as a promising solution. In this paper, we propose three types of DNN decoders for PAC codes: multi-layer perceptron (MLP), convolutional neural network (CNN), and recurrent neural network (RNN). The performance of these DNN decoders is evaluated through extensive simulation. Numerical results show that the MLP decoder has the best error-correction performance under a similar model parameter number.

Figures (9)

• Figure 1: Architecture of MLP, which has an input layer, an output layer, and three hidden layers.
• Figure 2: Architecture of CNN, which consists of several convolution layers, pooling layers, and a fully-connected layer.
• Figure 3: Architecture of LSTM, where $\boldsymbol{h}_{t}$, $\boldsymbol{c}_{t}$, and $\boldsymbol{y}_{t}$ represent the hidden state, cell state, and input vector at time $t$, respectively.
• Figure 4: The system framework of the proposed DNN decoders in this paper, where the decoding loss function corresponds to the equation (7).
• Figure 5: NVE performance of DNN decoders with different training $E_{b}/N_{0}$ for PAC code (16, 8). (a) MLP decoder. (b) CNN decoder. (c) RNN decoder.