Run-length Limited Research Articles

Distribution Matching for Dimming Control in Visible-Light Region-of-Interest Signaling

We propose a two-level dimmer based on binary distribution matching where a low-rate signal controls the output probability distribution of a high-rate bit sequence, which can be used in region-of-interest (RoI) signaling applications. To reduce the rate loss of the dimmer, we propose the extended multiset-partition distribution matching (EMPDM) algorithm with a novel binary-tree-structure implementation. In addition, we introduce 4p-EMPDM, a compact version of EMPDM, which has a typical composition (TC) and four leading composition pairs (CPs). The codebook of 4p-EMPDM includes only run-length-aware codewords, which reduces the maximum run-length of the transmitted bit sequence by 4.27 times. Hence, it guarantees flicker mitigation for visible-light RoI signaling systems at 6 kHz without using any run-length limited code (non-RLL). Using experimental data collected from the low-rate RoI signaling prototype, we introduced a threshold range where both intensity and area information of the received training symbols can be exploited to optimize the shaping ratios of the 4p-EMPDM dimmer. Because of the non-RLL feature, the proposed system can support soft-decision forward-error-correction (FEC) decoding to improve reliability. Our system outperforms related systems based on hybrid modulation schemes in terms of spectral efficiency, bit rate, and minimum required optical clock rate.

Adding RLL Properties to Four CCSDS LDPC Codes without Increasing Their Redundancy

This paper presents the construction of Run Length Limited (RLL) Error Control Codes (ECCs) from four Low Density Parity Check (LDPC) Codes specified by Consultative Committee for Space Data Systems (CCSDS). The obtained RLL-ECCs present a practical alternative to the CCSDS codes with pseudo-randomizers. Their advantage is that the maximal runlengths of equal symbols in their codeword sequences are guaranteed, which is not the case if the common approach with pseudo-randomizers is used. The other advantages are that no additional redundancy is introduced into encoded codewords and that the encoding and decoding procedures of the original error control CCSDS codes do not have to be modified in the following cases. In the first case if hard decoding is used and the transmission channel can be modeled as a Binary Symmetric Channel (BSC) or in the second case if soft decoding and coherent Binary Phase Shift Keying (BPSK) modulation is used and the appropriate transmission channel model is an Additive White Gaussian Noise (AWGN) channel.

RNN-Based Sequence to Sequence Decoder for Run-Length Limited Codes in Visible Light Communication.

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 (seq2seq) 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.

Improved DC-Free Run-Length Limited 4B6B Codes for Concatenated Schemes

In this letter, we introduce a class of improved DC-free 4B6B codes in terms of error correction capabilities for a serially concatenated architecture. There are billions of different codebooks that can be derived from the 16 codewords contained in the traditional 4B6B code as per the IEEE 802.15.7 standard for visible light communication (VLC). These codebooks can be classified based on distances properties which determine their error correction performances. The traditional 4B6B code is suitable for hard-decision decoding, however, when a soft decoder is used like in a serially concatenated architecture, that code becomes obsolete. Simulations show that the proposed 4B6B code concatenated with forward error correction (FEC) codes, has better performance compared to state-of-the-art schemes such as the original 4B6B code, the enhanced Miller code, the Manchester code, the 5B10B code and the (0,4) 2/3 RLL code.

Construction and Encoding Algorithm for Maximum Run-Length Limited Single Insertion/Deletion Correcting Code

Maximum run-length limited codes are constraint codes used in communication and data storage systems. Insertion/deletion correcting codes correct insertion or deletion errors caused in transmitted sequences and are used for combating synchronization errors. This paper investigates the maximum run-length limited single insertion/deletion correcting (RLL-SIDC) codes. More precisely, we construct efficiently encodable and decodable RLL-SIDC codes. Moreover, we present its encoding algorithm and show the redundancy of the code.

An improvement of BER using two-dimensional constrained code for array-reader-based magnetic recording

To achieve ultra-high areal densities in future magnetic recording technologies such as bit-patterned magnetic recording (BPMR) systems, each bit-island must be closely moved. However, the reduction of bit island spacing always leads to both inter-symbol interference (ISI) and inter-track interference (ITI), which can degenerate system performance. Previously, a one-dimensional (1D) run-length limited (RLL) code was employed to efficiently avoid the ISI effect, while a two-dimensional (2D) detector is widely utilized to deal with the ITI effect as well. However, its complexity is higher than the traditional 1D detector. Therefore, to avoid the fatal data patterns that lead to severe ITI effect, we first present the application of 1D RLL code to be as the 2D modulation code in the multi-head multi-track BPMR systems. Moreover, we also present the modified 2D Viterbi detector that is designed based on our proposed encoding condition. The numbers of state and branch in the traditional trellis’s structure are properly reduced according to encoding condition, thus it does not only provide a lower complexity but also operate better than the traditional 2D Viterbi detector. Results reveal that our proposed coding scheme and modified 2D Viterbi detector can efficiently protect and cope with the ITI effect.

Zero-Crossing Modulation for Wideband Systems Employing 1-Bit Quantization and Temporal Oversampling: Transceiver Design and Performance Evaluation

Next-generation wireless communications systems are anticipated to utilize the vast amount of available spectrum in the millimeter-wave and sub-terahertz bands above 100 G Hz to meet the ever-increasing demand for higher data rates. However, the analog-to-digital converter (ADC) power consumption is expected to be a major bottleneck if conventional system designs are employed at these frequencies. Instead, shifting the ADC resolution from the amplitude domain to the time domain by employing 1-bit quantization and temporal oversampling w.r.t. the Nyquist rate is expected to be more energy-efficient. Hence, we consider a system employing 1-bit quantization and temporal oversampling at the receiver, which operates on a wideband line-of-sight channel. We present a practical transceiver design for a zero-crossing modulation waveform, which combines faster-than-Nyquist signaling and runlength-limited (RLL) transmit sequences. To this aim, we derive four fixed-length finite-state machine RLL encoders enabling efficient transmit signal construction and soft-demapping at the receiver. Moreover, we propose a soft-output equalizer, which approximates maximum a posteriori RLL symbol detection. We evaluate the system performance in terms of peak-to-average-power ratio, coded block error rate, and a lower bound on the spectral efficiency (SE) w.r.t. a fractional power containment bandwidth. Our numerical results show that SEs of up to 4 bit/s/Hz are achievable with the presented transceiver design.

Synchronization of Variable-Length Constrained Sequence Codes

We study the ability of recently developed variable-length constrained sequence codes to determine codeword boundaries in the received sequence upon initial receipt of the sequence and if errors in the received sequence cause synchronization to be lost. We first investigate construction of these codes based on the finite state machine description of a given constraint, and develop new construction criteria to achieve high synchronization probabilities. Given these criteria, we propose a guided partial extension algorithm to construct variable-length constrained sequence codes with high synchronization probabilities. With this algorithm we construct new codes and determine the number of codewords and coded bits that are needed to recover synchronization once synchronization is lost. We consider a large variety of constraints including the runlength limited (RLL) constraint, the DC-free constraint, the Pearson constraint and constraints for inter-cell interference mitigation in flash memories. Simulation results show that the codes we construct exhibit excellent synchronization properties, often resynchronizing within a few bits.

Resource-Optimized Design of Bit-Shuffle Block Coding for MIMO-VLC

Designing a run-length-limited (RLL) code for a visible light communication (VLC) system requires consideration of several performance factors including hardware overhead, transmission efficiency, and direct current (DC) balance. This paper proposes a novel RLL code called bit-shuffle block codes for high-rate multiple-input multiple-output (MIMO)-VLC systems that can offer excellent constant illumination and transmission efficiency with extensively-optimized hardware resources. Due to the structure of the Omega network, the proposed bit-shuffle block coding method can increase transmission efficiency and significantly reduce hardware overhead. In addition, it can generate codewords dynamically, which guarantees DC balance with multiple LEDs to serve the dual purpose of illumination and communication. Experimental results confirm that the proposed bit-shuffle block coding demonstrate excellent performance in resource optimization, and can be a viable solution for MIMO-VLC applications that can send large volumes data with limited hardware resources.

On Bi-Modal Constrained Coding

Bi-modal (respectively, multi-modal) constrained coding refers to an encoding model whereby a user input block can be mapped to two (respectively, multiple) codewords. In current storage applications, such as optical disks, multi-modal coding allows to achieve DC control, in addition to satisfying the runlength limited (RLL) constraint specified by the recording channel. In this work, a study is initiated on bi-modal fixed-length constrained encoders. Necessary and sufficient conditions are presented for the existence of such encoders for a given constraint. It is also shown that under somewhat stronger conditions, one can guarantee a bi-modal encoder with finite decoding delay.

PR-NN: RNN-Based Detection for Coded Partial-Response Channels

In this paper, we investigate the use of recurrent neural network (RNN)-based detection of magnetic recording channels with inter-symbol interference (ISI). We refer to the proposed detection method, which is intended for recording channels with partial-response equalization, as Partial-Response Neural Network (PR-NN). We train bi-directional gated recurrent units (bi-GRUs) to recover the ISI channel inputs from noisy channel output sequences and evaluate the network performance when applied to continuous, streaming data. The computational complexity of PR-NN during the evaluation process is comparable to that of a Viterbi detector. The recording system on which the experiments were conducted uses a rate-2/3, (1,7) runlength-limited (RLL) code with an E <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> PR4 partial-response channel target. Experimental results with ideal PR signals show that the performance of PR-NN detection approaches that of Viterbi detection in additive white gaussian noise (AWGN). Moreover, the PR-NN detector outperforms Viterbi detection and achieves the performance of Noise-Predictive Maximum Likelihood (NPML) detection in additive colored noise (ACN) at different channel densities. A PR-NN detector trained with both AWGN and ACN maintains the performance observed under separate training. Similarly, when trained with ACN corresponding to two different channel densities, PR-NN maintains its performance at both densities. Experiments confirm that this robustness is consistent over a wide range of signal-to-noise ratios (SNRs). Finally, PR-NN displays robust performance when applied to a more realistic magnetic recording channel with MMSE-equalized Lorentzian signals.

Code design for run-length control in visible light communication

Run-length limited (RLL) codes can facilitate reliable data transmission and provide flicker-free illumination in visible light communication (VLC) systems. We propose novel high-rate RLL codes, which can improve error performance and mitigate flicker. Two RLL coding schemes are developed by designing the finite-state machine to further enhance the coding gain by improving the minimum Hamming distance and using the state-splitting method to realize small state numbers. In our RLL code design, the construction of the codeword set is critical. This codeword set is designed considering the set-partitioning algorithm criterion. The flicker control and minimum Hamming distance of the various proposed RLL codes are described in detail, and the flicker performances of different codes are compared based on histograms. Simulations are conducted to evaluate the proposed RLL codes in on-off keying modulation VLC systems. Simulation results demonstrate that the proposed RLL codes achieve superior error performance to the existing RLL codes.

Hardware Architectures of Visible Light Communication Transmitter and Receiver for Beacon-based Indoor Positioning Systems

High-speed applications of Visible Light Communications have been presented recently in which response times of photodiode-based VLC receivers are critical points. Typical VLC receiver routines, such as soft-decoding of run-length limited (RLL) codes and FEC codes was purely processed on embedded firmware, and potentially cause bottleneck at the receiver. To speed up the performance of receivers, ASIC-based VLC receiver could be the solution. Unfortunately, recent works on soft-decoding of RLL and FEC have shown that they are bulky and time-consuming computations. This causes hardware implementation of VLC receivers becomes heavy and unrealistic. In this paper, we introduce a compact Polar-code-based VLC receivers. in which flicker mitigation of the system can be guaranteed even without RLL codes. In particular, we utilized the centralized bit-probability distribution of a pre-scrambler and a Polar encoder to create a non-RLL flicker mitigation solution. At the receiver, a 3-bit soft-decision filter was implemented to analyze signals received from the VLC channel to extract log-likelihood ratio (LLR) values and feed them to the Polar decoder. Therefore, the proposed receiver could exploit the soft-decoding of the Polar decoder to improve the error-correction performance of the system. Due to the non-RLL characteristic, the receiver has a preeminent code-rate and a reduced complexity compared with RLL-based receivers. We present the proposed VLC receiver along with a novel very-large-scale integration (VLSI) architecture, and a synthesis of our design using FPGA/ASIC synthesis tools.

Efficient Channel Coding for Dimmable Visible Light Communications System

Visible light communication (VLC) offers wireless communication within short-range based on wavelength converters and light-emitting diode (LED). In the VLC system, conventional forward error correction (FEC) codes are not guaranteed to provide flicker mitigation and dimming support. Consequently, modified coding schemes are introduced for reliable VLC. These methods require complicated coding structures, use of lookup tables, and the addition of large redundancy, resulting to increased computational complexity and low transmission efficiency. In this article, we propose a coding scheme that is flicker-free and enhances the transmission efficiency for VLC systems. The proposed scheme is based on polar codes (PC) and Knuth balancing code with enhanced prefix coding technique. The results show that the proposed algorithm exhibits improved transmission efficiency compared to the PC without and with run-length limited code, for dimming values 75% (or 25%) and 87.5% (or 12.5%). Also, the proposed scheme presents a significant bit error rate (BER) performance gain compared to the schemes in literature. The proposed scheme is flicker-free, provides a simple encoding structure, does not utilize lookup tables, generates minimal number of redundancies for energy efficiency. Thus, the approach is flexible, and it is more suitable for real-time VLC systems.

Are Run-Length Limited Codes Suitable for Simultaneous Energy and Information Transfer?

Run-length limited (RLL) codes are a well-studied class of constrained codes having application in diverse areas, such as optical and magnetic data recording systems, DNA-based storage, and visible light communication. RLL codes have also been proposed for the emerging area of simultaneous energy and information transfer, where the receiver uses the received signal for decoding information as well as for harvesting energy to run its circuitry. In this paper, we show that RLL codes are not the best codes for simultaneous energy and information transfer, in terms of the maximum number of codewords which avoid energy outage, i.e., outage-constrained capacity. Specifically, we show that sliding window constrained (SWC) codes and sub-block energy constrained (SEC) codes have significantly higher outage-constrained capacities than RLL codes for moderate to large energy buffer sizes.

Variable- and Fixed-Length Balanced Runlength-Limited Codes Based on a Knuth-Like Balancing Method

A novel Knuth-like balancing method for runlength-limited words is presented, which forms the basis of new variable- and fixed-length balanced runlength-limited codes that improve on the code rate as compared to balanced runlength-limited codes based on Knuth’s original balancing procedure developed by Immink et al. While Knuth’s original balancing procedure, as incorporated by Immink et al. , requires the inversion of each bit one at a time, our balancing procedure only inverts the runs as a whole one at a time. The advantage of this approach is that the number of possible inversion points, which needs to be encoded by a redundancy-contributing prefix/suffix, is reduced, thereby allowing a better code rate to be achieved. Furthermore, this balancing method also allows for runlength violating markers which improve, in a number of respects, on the optimal such markers based on Knuth’s original balancing method.

New Run-Length Limited Codes in On–Off Keying Visible Light Communication Systems

Run-length limited (RLL) codes can facilitate reliable data transmission and provide flicker-free illumination in on-off keying-modulated visible light communication (VLC) systems. This letter proposes new RLL codes that can decrease error and achieve desirable brightness levels with high throughput. The flicker control and free distance of the proposed rate 2/3 RLL codes are extensively described. Extensive simulations evaluated the proposed RLL codes in forward error correction (FEC)-uncoded and FEC-coded VLC systems, demonstrating that the proposed RLL codes offer superior error performance when compared with rate 1/2 Miller and enhanced Miller codes.

Feedback Capacity and Coding for the $(0,k)$ -RLL Input-Constrained BEC

The input-constrained binary erasure channel (BEC) with strictly causal feedback is studied. The channel input sequence must satisfy the $(0,k)$ -runlength limited (RLL) constraint, i.e., no more than $k$ consecutive ‘0’s are allowed. The feedback capacity of this channel is derived for all $k\geq 1$ , and is given by $C^{\mathrm {fb}}_{(0,k)}(\varepsilon ) = \max \frac {\overline {\varepsilon }H_{2}(\delta _{0})+\sum _{i=1}^{k-1}\left ({\overline {\varepsilon }^{i+1}H_{2}(\delta _{i})\prod _{m=0}^{i-1}\delta _{m}}\right )}{1+\sum _{i=0}^{k-1}\left ({\overline {\varepsilon }^{i+1} \prod _{m=0}^{i}\delta _{m}}\right )}$ , where $\varepsilon $ is the erasure probability, $\overline {\varepsilon }=1-\varepsilon $ and $H_{2}(\cdot )$ is the binary entropy function. The maximization is only over $\delta _{k-1}$ , while the parameters $\delta _{i}$ for $i\leq k-2$ are straightforward functions of $\delta _{k-1}$ . The lower bound is obtained by constructing a simple coding for all $k\geq 1$ . It is shown that the feedback capacity can be achieved using zero-error, variable length coding. For the converse, an upper bound on the non-causal setting, where the erasure is available to the encoder just prior to the transmission, is derived. This upper bound coincides with the lower bound and concludes the search for both the feedback capacity and the non-causal capacity. As a result, non-causal knowledge of the erasures at the encoder does not increase the feedback capacity for the $(0,k)$ -RLL input-constrained BEC. This property does not hold in general: the $(2,\infty )$ -RLL input-constrained BEC, where every ‘1’ is followed by at least two ‘0’s, is used to show that the feedback capacity can be strictly smaller than the non-causal capacity.

MIMO Codes for Uniform Illumination Across Space and Time in VLC With Dimming Control

Indoor visible light communications (VLC) require simultaneous illumination and communication. Hence, uniformity in the illumination is a key consideration for user comfort and data transfer in the VLC systems. Several run-length limited codes have been proposed in the literature which mitigate flicker for single input and single output VLC systems. Recently, codes have been proposed for multiple input multiple output (MIMO) VLC systems. However, uniform illumination along with dimming control has not been considered for MIMO VLC systems. Hence, in this paper, we propose codes with generalized algorithms for encoding and decoding that maintain consistency in the illumination across space and time and achieve the desired dimming level. We present the expressions for code rate, run-length, and Hamming distance for the proposed codes. Through Monte Carlo simulations, we compare the codeword error rate (CER) performance of the proposed codes with zero-forcing, minimum mean square error, and maximum likelihood based detectors for various number of transmit and receive antennas. We also compare the mutual information of the proposed codes for various number of transmit and receive antennas. The numerical results show that the proposed codes exhibit good performance while satisfying the design criteria.

Mutually Uncorrelated Codes for DNA Storage

Mutually uncorrelated ( MU ) codes are a class of codes in which no proper prefix of one codeword is a suffix of another codeword. These codes were originally studied for synchronization purposes and recently, Yazdi et al. showed their applicability to enable random access in DNA storage. In this paper,we follow the research of Yazdi et al. and study MU codes along with their extensions to correct errors and balanced codes. We first review a well-known construction of MU codes and study the asymptotic behavior of its cardinality. This task is accomplished by studying a special class of run-length limited codes that impose the longest run of zeros to be at most some function of the codewords length. We also present an efficient algorithm for this class of constrained codes and show how to use this analysis for MU codes. Next, we extend the results on the run-length limited codes in order to study $(d_{h},d_{m})$ -MU codes that impose a minimum Hamming distance of $d_{h}$ between different codewords and $d_{m}$ between prefixes and suffixes. In particular, we show an efficient construction of these codes with nearly optimal redundancy. We also provide similar results for the edit distance and balanced MU codes. Last, we draw connections to the problems of comma-free and prefix synchronized codes.