# Modulation Decoding Based on K-Means Algorithm for Bit-Patterned Media Recording
###### Abstract  
In bit-patterned media recording (BPMR) systems, the readback signal is affected by neighboring islands that are characterized by intersymbol interference (ISI) and intertrack interference (ITI). Since increasing the areal density encourages the influence of ISI and ITI, it is more difficult to detect the data. Modulation coding can prevent the occurrence of specific data patterns that can cause severe ISI and ITI. In this study, we propose a modulation decoding method based on the K-means algorithm for a BPMR system to improve decoding capabilities. As the K-means algorithm helps understand data patterns and characteristics, the K-means decoder shows the best performance.  
bit-patterned media recording; K-means algorithm; modulation coding +
Footnote †: journal: Applied  
Academic Editor: [PERSON]  
Footnote †: journal: Applied  
Academic Editor: [PERSON]  
Recently, several signal processing schemes with machine learning for communication and data storage system channels have been studied to improve decoding capabilities and system performance. In [11], the equalizer technique based on a multilayer perceptron (MLP) was discussed. The MLP equalizer outperforms the conventional equalizer because the MLP equalizer can solve the linear and nonlinear phenomena of the channels. In [12], the neural-network-based modulation decoding of constrained sequence codes like run-length-limited code and DC-free code was introduced and evaluated in wireless channels. The iterative detection technique with MLP was proposed to decrease the effect of ITI and improve the performance [13]. In [14], a bit-flipping scheme using the K-means algorithm was proposed to flip a sign of data that is predicted to be an error. However, these works using machine learning algorithms were applied to signal detection without modulation decoding.  
Modulation codes are generally used to mitigate ISI which occurs in the data storage systems by imposing constraints. To improve the capability of the modulation decoder, the machine learning algorithm was applied as the decoding algorithm. In [15], the modulation decoding technique using MLP was proposed. However, the MLP, which is a supervised learning technique, requires labeled data and a training process, making it very costly and time-consuming.  
In this paper, we propose a modulation decoding method based on the K-means algorithm for a BPMR system to improve decoding capabilities. The K-means algorithm is an unsupervised learning algorithm which does not require labeled data and training processes and automatically groups data into clusters [16]. To utilize these advantages, we apply the K-means algorithm for the decoding algorithm. The proposed modulation decoding method based on the K-means algorithm can consider the geometrical distance between received codewords used depending on the characteristics or patterns of the received data sequences.  
The rest of this paper is organized as follows. In Section (2), we introduce the BPMR channel model and PRML detector. Section (3) explains the proposed modulation decoding scheme using MLP, and Section (4) contains the simulation and results. Finally, Section (5) concludes the paper.