A Study on Iterative Decoding by Neural Network Detector in SMR System

Abstract

IntroductionWe study the low-density parity-check (LDPC) coding [1] and iterative decoding system, as signal processing for the shingled magnetic recording (SMR) [2] in two-dimensional magnetic recording (TDMR). Previously we have reported waveform equalization using a two-dimensional finite impulse response (TD-FIR) filter [3] and an inter-track interference (ITI) canceler [4] and showed the influence of ITI is reduced. Also, we have proposed a neural network detector (NND) and evaluated the performance of the first decoding by the NND [5]. In this study, the NND iteratively calculates the log-likelihood ratio (LLR) as the decoding reliability using the returned sum-product (SP) decoder [6] output sequence as well as using TD-FIR filter [3] output sequence. Furthermore, we compare the iterative decoding using an NND with a soft-output Viterbi algorithm (SOVA) detector with the signal-dependent noise predictor [7], [8].Read/write systemThe input sequence passes through a 128/130 (0, 16/8) run-length limited (RLL) encoder and a (3, 30)-regular LDPC encoder to be changed into the recording sequence and is recorded on a granular medium model [4] under the specification of 4 Tbit/inch2. In the reading process, the decoding target track and both adjacent tracks are read composed by the array head with three readers at the same time [1], [2], and the different additive white Gaussian noise (AWGN) sequence is added to each waveform as the system noise. The signal-to-noise ratio (SNRS) for the system noise at the reading point is defined as SNRS = 20log10(A/σS) [dB], where A is the positive saturation level of the waveform reproduced from an isolated magnetic transition and σS is the root-mean-square (RMS) value of the system noise in the bandwidth of the channel bit rate fc. A channel bit response including read/write (R/W) process on the intended track is equalized to the partial response class-I (PR1) target by the equalizer composed of three low-pass filters (LPFs) having cut-off frequency xh normalized by the fc and TD-FIR filter with Nt taps, where Nt is the number of taps [3] for a reader. We assume that these parameters are set to xh = 0.4 and Nt = 15. Then, the output waveform from the PR1 channel is iteratively decoded by the turbo equalization performed between an NND and an SP decoder [6]. The SP decoder also iteratively decodes using the constraint of LDPC code until the maximum iteration number isp times. Furthermore, the SP decoder returns the reliability sequence including the parity bits of LDPC code to the NND again. In this way, the turbo equalization for the target track is performed with the maximum iteration number iglobal times. After the given number of iterations in the turbo equalization, the output sequence is obtained by the posterior probability sequence except parity passing through a hard decision unit and the RLL decoder. Then, the bit error rate (BER) is calculated by comparing the input sequence with the output sequence.Neural network detectorFigure 1 shows the block diagram of the turbo equalization. In the figure, D is the delay operator for a bit interval, Nm (m = 1∼3) is the number of elements in the mth layer. We adopt N1 = 30, N2 = 10 and N3 = 1. The NND consists of the neural network, the memory, the selector, and the LLR calculator. The neural network provides outputs for 3-bit patterns in the down-track direction for the TD-FIR filter and the returned SP decoder outputs, and stores the output in the memory. In the training process by back-propagation algorithm, we set the training signal to be “1” for the target bit pattern and “0” for the others, in order to obtain connection weight sets wij(m)(n) between the ith element at the mth layer and the jth (j = 1∼Nm-1) element at the (m - 1)th layer for the nth pattern (n = 1∼8). Furthermore, the LLR calculator provides the logarithmic ratio of the maximum values for the center bit “1” and “0” from the selector.Performance evaluationFigure 2 shows the BER performances for SNRS. The marks of circle and triangle show the performances of the NND and the SOVA detector, respectively. Here, the LLR of the SOVA detector is provided by the metric of the PR1 channel, where the metric is calculated considering the external LLR obtained by the SP decoder output [5]-[7]. The turbo equalization parameters isp and iglobal adopt the optimum values for minimizing the BER in each detector. As can be seen from the figure, the system with the NND improves about 5.5 dB in the required SNR to achieve no-errors compared to the system with the SOVA detector.AcknowledgmentsThis work was supported in part by the Advanced Storage Research Consortium (ASRC). **