Deep Learning-Based Decoding for Constrained Sequence Codes

Abstract

Constrained sequence (CS) codes, including fixedlength CS codes and variable-length CS codes, have been widely used in modern wireless communication and data storage systems. Sequences encoded with constrained sequence codes satisfy constraints imposed by the physical channel to enable efficient and reliable transmission of coded symbols. In this paper, we propose using deep learning approaches to decode fixed-length and variable-length CS codes. Traditional encoding and decoding of fixed-length CS codes rely on look-up tables (LUTs), which is prone to errors that occur during transmission. We introduce fixed-length constrained sequence decoding based on multiple layer perception (MLP) networks and convolutional neural networks (CNNs), and demonstrate that we are able to achieve low bit error rates that are close to maximum a posteriori probability (MAP) decoding as well as improve the system throughput. Further, implementation of capacity-achieving fixedlength codes, where the complexity is prohibitively high with LUT decoding, becomes practical with deep learning-based decoding. We then consider CNN-aided decoding of variable-length CS codes. Different from conventional decoding where the received sequence is processed bit-by-bit, we propose using CNNs to perform one-shot batch-processing of variable-length CS codes such that an entire batch is decoded at once, which improves the system throughput. Moreover, since the CNNs can exploit global information with batch-processing instead of only making use of local information as in conventional bit-by-bit processing, the error rates can be reduced. We present simulation results that show excellent performance with both fixed-length and variable-length CS codes that are used in the frontiers of wireless communication systems.

Long-Short Term Memory-Based Application on Adaptive Cross-Platform Decoder for Bit Patterned Magnetic Recording

“…The data cleansing for three header readings accumulated a readback set of 6 × 8,192 and was standardized to a single compatible header of 5 × 8,192. The pre-processing data was determined by the expected value of mean standard derivation (MSD) between two nearby tracks, as follows: (10) where � , _1 is the mean value of signal level between the upper track (a k ) and the lower track (a k+1 ), and � 2 is the variance of the mean value between a k and a k+1 .…”

Construction of Multi-State Capacity-Approaching Variable-Length Constrained Sequence Codes With State-Independent Decoding

“…Note that the encoding and decoding processes are instantaneous with the words in this table. To compare, note that a widely used (1,3) RLL code is the Modified Frequency Modulation (MFM) code with η = 91% [1]. For more examples refer to [24]- [29] and [34, Chapter 6.4].…”

“…Example 9: (DC-free N = 6 code) Consider the construction of an n-step minimal set for the DC-free N = 6 constraint. Using (11), we obtain the range of n as [3,5]. Selecting all states as principal states, the minimal set for the 3-step FSM is shown in Table 16.…”

Synchronization of Variable-Length Constrained Sequence Codes

“…Since Shannon's 1948 paper [5], the design of CS codes has been an active research area where efficient CS codes that satisfy a great variety of constraints have been proposed. Although most CS codes in the literature are fixed-length codes [1]- [4], [6]- [16], recent advances show that variable-length CS codes have the potential to achieve higher code rates with simpler codebooks [17]- [26]. Since CS codes typically do not have strong error-correction capabilities, decoding of CS codes may result in error propagation.…”