# RNN-Based Sequence to Sequence Decoder for Run-Length Limited Codes in Visible Light Communication
###### Abstract  
Unmanned aerial vehicles (UAVs) equipped with visible light communication (VLC) technology can simultaneously offer flexible communications and illumination to service ground users. Since a poor UAV working environment increases interference sent to the VLC link, there is a pressing need to further ensure reliable data communications. Run-length limited (RLL) codes are commonly utilized to ensure reliable data transmission and flicker-free perception in VLC technology. Conventional RLL decoding methods depend upon look-up tables, which can be prone to erroneous transmissions. This paper proposes a novel recurrent neural network (RNN)-based decoder for RLL codes that uses sequence to sequence (seq2 seq) models. With a well-trained model, the decoder has a significant performance advantage over the look-up table method, and it can approach the bit error rate of maximum a posteriori (MAP) criterion-based decoding. Moreover, the decoder is use to deal with multiple frames simultaneously, such that the totality of RLL-coded frames can be decoded by only one-shot decoding within one time slot, which is able to enhance the system throughput. This shows our decoder's great potential for practical UAV applications with VLC technology.  
run-length limited codes; seq2 seq model; RNN-based decoding; unmanned aerial vehicles; visible light communication +
Footnote †: journal: Sensors  
20  
codewords from that have never been seen during training. Another study [10] exploited DL techniques to optimize well-known decoding schemes and proposed a DL-aided belief propagation (BP) decoder. They employed non-fully connected neural networks to simulate the regular BP decoding. Since the performance of the BP algorithm is independent of the transmitted codewords, only a single codeword (e.g., the all-zero codeword) needs to be used for training. Realizing that BP decoding contains many multiplications, reference [11] improved the neural network (NN) architecture and achieved similar performance to [10] with lower complexity based on offset min-sum algorithm. As we will show in the rest of our paper, since the used RLL source words are normally fairly short, probably a few tens of bits at most [1, 12, 13], DL techniques fit well with RLL decoding, naturally avoiding the explosive numbers of training set data and weights that occur in ECC decoding. Thus, there is a pressing need to exploit DL techniques for RLL decoding in UAVs with VLC.  
Recurrent neural networks (RNNs) are suitable for processing one-dimensional signals, especially sequence-based tasks with time dependence. Thus, this paper proposes an RNN-based decoder to improve the performance of RLL codes. We use a sequence to sequence (seq2 seq) model with multiple-to-multiple configure (multiple inputs and multiple outputs) to learn the mappings between RLL source words and noisy received signals. We systematically analyze and demonstrate the effectiveness of our proposed decoder for RLL decoding. Our contributions are as follows:  
* We exploited RNN technology for RLL decoding based on seq2 seq models and found that a well-trained seq2 seq model can achieve MAP-based decoding performance, thereby improving the reliability of VLC.
* We show that the proposed decoder has sufficient capacity to handle multiple RLL-coded frames and implement multi-frame parallel decoding with only one-shot decoding, which largely improves the system throughput and reduces parallel decoding complexity.
* We found that the number of frames for parallel decoding impacts the fitting of the decoder due to its restricted learning abilities, and further analyzed the _saturation frame_ of the decoder based on our proposed criterion.  
The remainder of the paper proceeds as follows. Section 2 reviews the model of VLC and the RLL codes. Section 3 proposes the seq2 seq decoder, including its design and the network training approach. Section 4 presents our simulation results, and Section 5 concludes the paper.