Improving LDPC Decoding Performance for 3D TLC NAND Flash by LLR Optimization Scheme for Hard and Soft Decision

Low-density parity-check (LDPC) codes have been widely adopted in NAND flash in recent years to enhance data reliability. There are two types of decoding, hard-decision and soft-decision decoding. However, for the two types, their error correction capability degrades due to inaccurate log-likelihood ratio (LLR) . To improve the LLR accuracy of LDPC decoding, this article proposes LLR optimization schemes, which can be utilized for both hard-decision and soft-decision decoding. First, we build a threshold voltage distribution model for 3D floating gate (FG) triple level cell (TLC) NAND flash. Then, by exploiting the model, we introduce a scheme to quantize LLR during hard-decision and soft-decision decoding. And by amplifying a portion of small LLRs, which is essential in the layer min-sum decoder, more precise LLR can be obtained. For hard-decision decoding, the proposed new modes can significantly improve the decoder’s error correction capability compared with traditional solutions. Soft-decision decoding starts when hard-decision decoding fails. For this part, we study the influence of the reference voltage arrangement of LLR calculation and apply the quantization scheme. The simulation shows that the proposed approach can reduce frame error rate (FER) for several orders of magnitude.

A QR Code-Based Approach to Differentiating the Display of Augmented Reality Content

The augmented reality (AR) system requires markers to recognize and locate virtual objects on the screens of mobile devices. However, both markers and objects must be registered via the online platform in advance. In addition, an AR marker can only pair with a fixed set of virtual objects, limiting the flexibility and immediacy of changing and updating these data. This paper incorporates the quick response barcode (QR code) into the AR system to address these issues. We propose an algorithm with two vital goals, including (1) generating differentiated virtual objects for different target users by using only one QR code as the marker and (2) concealing different private authentication in QR modules by applying the error correction capability. We then demonstrate the proposed approach via a simulation of two practical scenarios, the electronic catalogs for business applications, and differentiated instructional materials for digital learning. This paper contributes to AR and QR code research and practices.

Generalized Concatenated Codes over Gaussian and Eisenstein Integers for Code-Based Cryptography

The code-based McEliece and Niederreiter cryptosystems are promising candidates for post-quantum public-key encryption. Recently, q-ary concatenated codes over Gaussian integers were proposed for the McEliece cryptosystem, together with the one-Mannheim error channel, where the error values are limited to the Mannheim weight one. Due to the limited error values, the codes over Gaussian integers achieve a higher error correction capability than maximum distance separable (MDS) codes with bounded minimum distance decoding. This higher error correction capability improves the work factor regarding decoding attacks based on information-set decoding. The codes also enable a low complexity decoding algorithm for decoding beyond the guaranteed error correction capability. In this work, we extend this coding scheme to codes over Eisenstein integers. These codes have advantages for the Niederreiter system. Additionally, we propose an improved code construction based on generalized concatenated codes. These codes extend to the rate region, where the work factor is beneficial compared to MDS codes. Moreover, generalized concatenated codes are more robust against structural attacks than ordinary concatenated codes.

Performance Investigation of MIMO Based CO-OFDM FSO Communication Link for BPSK, QPSK and 16-QAM under the Influence of Reed Solomon Codes

The MIMO based CO-OFDM FSO communication system is emerging as a promising approach to meet the future bandwidth requirements for seamless communication. The atmosphere being the propagation medium is a major hindrance in wide-scale acceptability of FSO technology. For seamless and error-free transmission and reception of data, a novel concept of MIMO integrated with RS code is proposed in this paper. The system performance of an RS 64 (RS (255,127)) coded MIMO-based CO-OFDM FSO communication link was investigated using BPSK, QPSK and 16-QAM under the combined effects of geometric losses, path losses and atmospheric attenuations at a hitherto un-investigated data rate of 40 Gbps and a link distance of 5 km. The modified gamma-gamma distribution was used for modeling a moderately turbulent channel. With link length varying over a range of 1 to 5 km, error correction was maximum in 16-QAM as compared to BPSK and QPSK, with 150 to 167 corrected errors. In terms of PAPR, PSK was more apt than QAM, but with a compromise in BER. The geometric losses were reduced with link length due to an increase in error correction capability for all three modulation cases, with the least losses occurring in 16-QAM. At the target bit error rate (BER), the signal to noise ratio (SNR) required for BPSK and QPSK was higher by 3.98 dB and 6.14 dB compared to 16-QAM.

On Ordinary Words of Standard Reed–Solomon Codes over Finite Fields

Reed–Solomon codes are widely used to establish a reliable channel to transmit information in digital communication which has a strong error correction capability and a variety of efficient decoding algorithm. Usually we use the maximum likelihood decoding (MLD) algorithm in the decoding process of Reed–Solomon codes. MLD algorithm relies on determining the error distance of received word. Dür, Guruswami, Wan, Li, Hong, Wu, Yue and Zhu et al. got some results on the error distance. For the Reed–Solomon code [Formula: see text], the received word [Formula: see text] is called an ordinary word of [Formula: see text] if the error distance [Formula: see text] with [Formula: see text] being the Lagrange interpolation polynomial of [Formula: see text]. We introduce a new method of studying the ordinary words. In fact, we make use of the result obtained by Y.C. Xu and S.F. Hong on the decomposition of certain polynomials over the finite field to determine all the ordinary words of the standard Reed–Solomon codes over the finite field of [Formula: see text] elements. This completely answers an open problem raised by Li and Wan in [On the subset sum problem over finite fields, Finite Fields Appl. 14 (2008) 911–929].

Blind Recognition of Parameters of Reed Solomon Code from Intercepted Erroneous Codewords

Error correcting codes are designed for reliable transmission of digital information over a noisy channel. Several papers have been published on blind identification of binary FEC codes but papers reported on the identification of non-binary error correcting codes are less. Due to its strong error correction capability, RS (Reed-Solomon) code is being used widely. So technique for blind recognition of RS code is required to analyse intercepted signal as well as for intelligent communication. This paper presents a technique for extraction of parameters of Reed-Solomon code from intercepted demodulated bitstream. The proposed algorithm is very simple and hence it is very practical for hardware implementation. Our approach has been verified using MATLAB simulation.

Deep extended feedback codes

A new Deep Neural Network (DNN)-based error correction encoder architecture for channels with feedback, called Deep Extended Feedback (DEF), is presented in this paper. The encoder in the DEF architecture transmits an information message followed by a sequence of parity symbols which are generated based on the message as well as the observations of the past forward channel outputs sent to the transmitter through a feedback channel. DEF codes generalize Deepcode in several ways: parity symbols are generated based on forward channel output observations over longer time intervals in order to provide better error correction capability; and high-order modulation formats are deployed in the encoder so as to achieve increased spectral efficiency. Performance evaluations show that DEF codes have better performance compared to other DNN-based codes for channels with feedback.

Efficient implementation of error correction codes in modular code

The article develops an efficient implementation of an algorithm for detecting and correcting multivalued residual errors with a fixed number of calculations of the syndrome, regardless of the set of moduli size. Criteria for uniqueness are given that can be met by selecting moduli from a set of primes to satisfy the desired error correction capability. An extended version of the algorithm with an increase in the number of syndromes depending on the number of information moduli is proposed. It is proposed to remove the restriction imposed on the size of redundant moduli. Identifying the location of the error and finding the error vector requires only look-up tables and does not require arithmetic operations. In order to minimize the excess space, an extended algorithm is also proposed in which the number of syndromes and look-up tables increases with the number of information moduli, but the locations of errors can still be identified without requiring iterative computations. By using the approximate method, we have reduced the computational complexity of the algorithm for calculating the syndrome from quadratic to linear-logarithmic, depending on the number of bits in the dynamic range.

Performance of a parallel Hamming coding in short-frame OFDM sensor's network

In this paper, we focus on the most relevant Error Correcting Codes (ECCs): the Hamming code and the Reed-Solomon code in order to meet the trade-off between the low implementation complexity and the high error correction capacity in a short-frame OFDM communication system. Moreover, we discuss and validate via simulations this trade-off between complexity (Hamming is the easiest to code) and error correction capability (Reed-Solomon being the most effective). Therefore, we have to either improve the correction capacity of the Hamming code, or decrease the complexity cost for the Reed-Solomon code. Based on this analysis, we propose a new design of parallel Hamming coding. On the one hand, we validate this new model of parallel Hamming coding with numerical results using MATLAB-Simulink tools and BERTool Application which makes easier the Bit Error Rate (BER) performance simulations. On the other hand, we implement the design of this new model on an FPGA mock-up and we show that this solution of a parallel Hamming encoder/decoder uses a few resources (LUTs) and has a higher capability of correcting when compared to the simple Hamming code.

Dependable Wireless System with Shortened Code Using Distance Information between Integrated Terminals

Since wireless systems allow for easier access to communication paths than wired systems, it is necessary to improve their dependability against cyberterrorists. To make wireless systems more dependable, additional measures at the lower layer are required, in addition to those at the upper layers. Our proposal uses an integrated terminal-like cellular phone which has multiple radio access technologies (RATs) such as cellular, wireless local area network (LAN), Bluetooth, and an ultra-wide band (UWB). We propose to communicate information encoded by shortened code using multiple RATs. Redundancy by RATs and their error correction capability can simultaneously improve wiretap resistance and attack resistance. A codeword of shortened code is obtained by removing a part of a codeword of popular code. A decoder can improve the error correction capability if the removed part is known. By using shortened codes, the dependability can be further enhanced because the error correction capability between the legitimate receiver and the cyberterrorist can make a difference. To do this, it is necessary to securely share the removed part between the sender and receiver. Our proposal is to securely measure the distance between the sender and receiver using UWB and use it as the removed part. It was confirmed that the secrecy capacity is improved.