Scaling Deep Learning-Based Decoding of Polar Codes via Partitioning

Abstract

The training complexity of deep learning-based channel decoders scales exponentially with the codebook size and therefore with the number of information bits. Thus, neural network decoding (NND) is currently only feasible for very short block lengths. In this work, we show that the conventional iterative decoding algorithm for polar codes can be enhanced when sub-blocks of the decoder are replaced by neural network (NN) based components. Thus, we partition the encoding graph into smaller sub-blocks and train them individually, closely approaching maximum a posteriori (MAP) performance per sub-block. These blocks are then connected via the remaining conventional belief propagation decoding stage(s). The resulting decoding algorithm is non-iterative and inherently enables a highlevel of parallelization, while showing a competitive bit error rate (BER) performance. We examine the degradation through partitioning and compare the resulting decoder to state-of-theart polar decoders such as successive cancellation list and belief propagation decoding.

Deep Learning-Based Decoding for Constrained Sequence Codes

“…We use the notation h = [h 1 , h 2 , ..., h L ] to represent a network with L hidden layers, where h l denotes the number of neurons in the fully connected layer l, or the number of kernels in the convolutional layer l. In recent works that apply DNNs to decode ECCs, the training set explodes rapidly as the source word length grows. For example, with a rate 0.5 (n = 1024, k = 512) ECC, one epoch consists of 2 512 possibilities of codewords of length 1024, which results in very large complexity and makes it difficult to train and implement DNN-based decoding in practical systems [28], [29], [31], [32]. However, we note that in FL CS decoding, this problem does not exist since CS source words are typically considerably shorter, possibly only up to a few dozen symbols [1], [6]- [17].…”

“…Recently several works have reported the application of DNNs to the decoding of error control codes (ECCs) [28]- [33]. A DNN enables low-latency decoding since it enables one-shot decoding, where the DNN finds its estimate by passing each layer only once [28], [31], [32]. In addition, DNNs can efficiently execute in parallel and be implemented with low-precision data types on a graphical processing unit (GPU), field programmable gate array (FPGA), or application specific integrated circuit (ASIC) [28], [31]- [33], [35].…”

“…However, since the number of candidate codewords becomes extremely large with medium-to-large codeword lengths (i.e., a few hundred to a few thousand bits), direct application of DNNs to ECC decoding becomes difficult because of the explosive number of layers and weights. In [32], DNNs were employed on sub-blocks of the decoder, which were then connected via belief propagation decoding to enable scaling of deep learningbased ECC decoding. In [33], the authors proposed recurrent neural network (RNN)-based decoding for linear codes, which outperforms the standard belief propagation (BP) decoding and significantly reduces the number of parameters compared to BP feed-forward neural networks.…”

MIND: Model Independent Neural Decoder

“…Among future directions, it is worth considering to combine other neural decodes with MIND, such as neural LDPC [29] [30] and Polar [32] decoders. Beyond neural decoder design, MAML can also be applied to Channel Autoencoder [27] design, which deals with designing adaptive encoder and decoder.…”

Low-Complexity LSTM-Assisted Bit-Flipping Algorithm For Successive Cancellation List Polar Decoder

“…Recently, as deep learning (DL) has many revolutionary breakthroughs in the field of computer vision and natural language processing, many researchers have also been dedicated to applying this powerful technique to enhance decoding algorithms [3]- [7]. However, their decoding capacity is still worse than the state-of-the-art CRC-assisted successive cancellation list (CA-SCL) [8]- [10].…”