Reliable Bits Research Articles

Hamming Distance Optimized Underwater Acoustic OTFS-IM Systems.

The orthogonal time frequency space (OTFS) modulation technique can provide reliable communication in time-varying channels. Due to the dispersive characteristics of underwater acoustic channels, this paper proposes an OTFS-IM underwater acoustic communication system based on Hamming distance optimization to reduce the impact of dispersion in underwater acoustic communication. Firstly, the OTFS-IM underwater acoustic communication system is introduced, which introduces index modulation into the Delay-Doppler (DD) domain to make the OTFS system have stronger anti-Delay-Doppler capability. In contrast, since there is index sequence redundancy in a specific index combination, a Hamming distance optimization model is used to eliminate the redundant combination in the specific index combination sequence and further improve the bit error rate performance of the system. In addition, the Hamming distance optimized OTFS-IM underwater acoustic communication system is verified by simulation analysis. The results show that the proposed Hamming distance optimized OTFS-IM can achieve more reliable bit error rate performance.

Bit-complexity of classical solutions of linear evolutionary systems of partial differential equations

We study the bit-complexity intrinsic to solving the initial-value and (several types of) boundary-value problems for linear evolutionary systems of partial differential equations (PDEs), based on the Computable Analysis approach. Our algorithms are guaranteed to compute classical solutions to such problems approximately up to error 1/2n, so that n corresponds to the number of reliable bits of the output; bit-cost is measured with respect to n. Computational Complexity Theory allows us to prove in a rigorous sense that PDEs with constant coefficients are algorithmically ‘easier’ than general ones. Indeed, solutions to the latter are shown (under natural assumptions) computable using a polynomial number of memory bits, and we prove that the complexity class PSPACE is in general optimal; while the case of constant coefficients can be solved in #P—also essentially optimally so: the Heat Equation ‘requires’ #P1. Our algorithms raise difference schemes to exponential powers, efficiently: we compute any desired entry of such a power in #P, provided that the underlying exponential-sized matrices are circulant of constant bandwidth. Exponentially powering modular two-band circulant matrices is established even feasible in P; and under additional conditions, also the solution to certain linear PDEs becomes polynomial time computable.

Improving the data reliability of phase modulated holographic storage using a reliable bit aware low-density parity-check code.

Phase modulated holographic storage offers superior storage capacity and a longer life span compared with other storage technologies. However, its application is limited by its high raw bit error rate. We aimed to introduce low-density parity-check (LDPC) codes for data protection in phase modulated holographic storage systems. However, traditional LDPC codes can not fully exploit data error characteristics, causing inaccurate initial log-likelihood ratio (LLR) information, which degrades decoding performance, thus limiting the improvement degree of data reliability in phase modulated holographic storage. Therefore, we propose a reliable bit aware LDPC optimization method (RaLDPC) that analyzes and employs phase demodulation characteristics to obtain reliable bits. More accurate initial LLR weights are assigned to these reliable bits. Hence, the optimized initial LLR can reflect the reliability of the demodulated data more accurately. Experimental results show that RaLDPC can reduce the bit error rate by an average of 38.89% compared with the traditional LDPC code, improving the data reliability of phase modulated holographic storage.

A fast method for blindly identifying Reed‐Solomon codes based on matrix analysis

For the identification of Reed-Solomon (RS) codes, the existing methods need to test the possible codeword length and the primitive polynomials exhaustively. Exhaustive search leads to high computational complexity. To overcome this limitation and fulfill the requirement in practice, a fast blind identification method is proposed. Different with most methods, our identification method is discussed in Galois Field of 2. First, by using Gaussian elimination, the bit matrix is transformed to the simplest upper triangular form. If the assumed codeword length is right, the matrix is of deficient rank, and the parameters of an RS code can be estimated according to the rank. The null space of the matrix, defined as the equivalent binary parity check matrix, can also be obtained from the simplification result. Then, a candidate set of primitive polynomials is constructed according to the estimated codeword length. By using the matrix null space, the correctness of a candidate primitive polynomial is tested through matrix analysis. Finally, by combining the estimated parameters, the generator polynomial of an RS code is identified. To decrease the bit errors in the matrix, soft-decision data is used to select reliable bits. Experimental results show the effectiveness and robustness of our method.

Geometric Constellation Shaping for Concatenated Two-Level Multi-Level Codes

This paper studies a learning approach to geometric shaping (GS) for concatenated two-level multi-level codes (MLC). Unlike standard bit-interleaved coded modulation (BICM), the proposed MLC protects only the least reliable bits (LRBs) by an inner code, and thereby efficiently reduces complexity associated with inner soft-decision (SD) decoding compared to the BICM without performance degradation. We propose a new loss function for training a geometric constellation shape in the proposed MLC, leading to maximization of the achievable rate. More specifically, considering the different coding structures for the most reliable bits (MRBs) and the LRBs, the proposed loss function combines two different functions: the union bound on a bit error rate (BER) for the MRBs and the generalized mutual information (GMI) for the LRBs. We demonstrate by simulations of wavelength division multiplexing (WDM) optical fiber systems that the proposed loss function offers a performance gain over the conventional cross entropy-based loss function. Furthermore, it is demonstrated that the proposed MLC with GS outperforms the conventional BICM with GS in terms of a transmission distance, even with significantly lower SD decoding complexity.

Fast Iterative Soft-Output List Decoding of Polar Codes

Iterative detection and decoding (IDD) enjoys a higher capacity than separate detection and decoding (SDD). However, IDD requires both the detector and the decoder to support soft input and soft output. Considering the standard channel codes in 5G communication systems, the preferred decoder for polar codes, the successive cancellation list (SCL) decoder, outputs only hard decisions on the side of codeword. Yet, current soft-output polar decoders, such as belief propagation (BP) and soft cancellation (SCAN), are much inferior to the SCL decoders in terms of error correction performance. To this end, we propose a soft-output list (SOL) decoder in this paper, which considers both hypotheses of 0 and 1 for unreliable bits and keeps the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a-priori</i> likelihoods for reliable bits, so that it can provide soft output and satisfactory error-rate performance at the same time. Exploiting the property of special nodes, the resulting FastSOL decoder can directly return soft messages from these nodes, thus speeding up the decoding. The error-rate performance of the FastSOL decoder enhances as the number of iterations increases in the non-IDD setup. The proposed FastSOL decoder can also be applied in the IDD system. Concatenated with a maximum <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a-posteriori</i> detector in ten IDD loops, our decoder with a list size of eight exhibits over 1 dB gain compared to using the SCAN decoder for polar codes with length 256 and half rate, which also outperforms the state-of-the-art soft list decoder by 0.12 dB in the same settings with a higher computational complexity, but comparable decoding latency.

A Soft-Aided Staircase Decoder Using Three-Level Channel Reliabilities

The soft-aided bit-marking (SABM) algorithm is based on the idea of marking bits as highly reliable bits (HRBs), highly unreliable bits (HUBs), and uncertain bits to improve the performance of hard-decision (HD) decoders. The HRBs and HUBs are used to assist the HD decoders to prevent miscorrections and to decode those originally uncorrectable cases via bit flipping (BF), respectively. In this paper, an improved SABM algorithm (called iSABM) is proposed for staircase codes (SCCs). Similar to the SABM, iSABM marks bits with the help of channel reliabilities, i.e., using the absolute values of the log-likelihood ratios. The improvements offered by iSABM include: (i) HUBs being classified using a reliability threshold, (ii) BF randomly selecting HUBs, and (iii) soft-aided decoding over multiple SCC blocks. The decoding complexity of iSABM is comparable of that of SABM. This is due to the fact that on the one hand no sorting is required (lower complexity) because of the use of a threshold for HUBs, while on the other hand multiple SCC blocks use soft information (higher complexity). Additional gains of up to 0.53 dB with respect to SABM and 0.91 dB with respect to standard SCC decoding at a bit error rate of $10^{-6}$ are reported. Furthermore, it is shown that using 1-bit reliability marking, i.e., only having HRBs and HUBs, only causes a gain penalty of up to 0.25 dB with a significantly reduced memory requirement.

Performance Analysis of Underwater Acoustic Communications in Barrow Strait

The Arctic Ocean and its various shallow passages are rapidly changing due to global warming. The development of a large-scale wireless network that collects and distributes oceanographic data remotely would be an extremely valuable asset to researchers. This concept, however, is completely dependent upon the ability to acoustically transmit digital information under water over long ranges, which is not currently available. In this work, we investigate the performance of four transceivers that are based on frequency-hopping binary frequency-shift keying and multilevel phase-shift keying (M-PSK) signaling in the 300 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$-$</tex-math></inline-formula> 400-Hz acoustic band. The transceivers use low-rate coding that provides bit rates from 1.8 to 13.3 b/s (bits per second). Their bit error rates are computed based on real data recorded in Barrow Strait (NU). During the 2019 experimental activities, the transmitter was towed by a supporting vessel at an average speed of 4 kn. The receiver, a vertical hydrophone array, was at distance between 14 and 33 km. Additionally, the received signals experienced extended multipath propagation and strong in-band impulsive interferences. For a single-hydrophone receiver, our postprocessing analysis shows reliable bit rates up to 6.7 b/s. When processing uses the array and performs multichannel decision feedback equalization (DFE), the maximum designed rate, i.e., 13.3 b/s, is confirmed. Further analysis reveals that the experimental links could support higher data rates. Our results demonstrate that 2-PSK signaling combined with single-channel DFE and 4-PSK signaling combined with multichannel DFE could reliably achieve 100 and 200 b/s, respectively.

Enhanced BP decoding schemes of polar codes

In this paper, two decoding schemes for polar codes based on the belief propagation (BP) algorithm are proposed. The basic idea of the proposed schemes, called “interleaved BP” (I-BP) and “multiple-candidates BP” (M-BP), is to construct multiple candidates with different reliability values from the received signal and to decode each candidate by a BP decoder. Then, the output of the BP decoder that meets the stopping criterion or the maximum likelihood (ML) rule is chosen as the decoded data. Simulation results show that both the proposed polar decoders outperform the one based only on a single conventional BP decoder. In conjunction with each of the proposed schemes, a feedback structure is also proposed to achieve more performance gain. The proposed feedback structure takes as input the output of each BP decoder, and enhances the a posteriori information of reliable bits and flips unreliable bits. Then, the processed information is fed back into its corresponding decoder. Simulation results show that the performance gain of the proposed schemes with this feedback, compared to the ones without the feedback, may be as large as 1 dB at a frame-error rate 10 − 2 on frequency selective channels and 2 dB at a frame-error rate of 0.07 on doubly selective channels.

Limited-Search Chase Decoding Algorithm for LDPC Coded Underwater Acoustic Multiuser Channels

In this paper, we propose a low-complexity soft-input/soft-output (SISO) Chase multiuser detector that has a polynomial computational complexity in terms of the number of the least reliable bit positions for low-density parity-check (LDPC) coded code-division multiple-access (CDMA) systems, which is a potentially competitive technology for underwater acoustic networks (UWAN). Simulation results over highly correlated channels show that the proposed detector can afford searching over a larger number of the least reliable bit positions and achieve better bit-error-rate (BER) performance as compared with the Chase-II detector at much lower complexity.

Fast Frequency Sweep Analysis of Passive Miniature RF Circuits Based on Analytic Extension of Eigenvalues

The construction of polar codes with code length $n=2^m$ involves $m$ layers of polar transforms. In this paper, we observe that after each layer of polar transforms, one can swap certain pairs of adjacent bits to accelerate the polarization process. More precisely, if the previous bit is more reliable than its next bit under the successive decoder, then switching the decoding order of these two adjacent bits will make the reliable bit even more reliable and the noisy bit even noisier. Based on this observation, we propose a new family of codes called the Adjacent-Bits-Swapped (ABS) polar codes. We add a permutation layer after each polar transform layer in the construction of the ABS polar codes. In order to choose which pairs of adjacent bits to swap in the permutation layers, we rely on a new polar transform that combines two independent channels with $4$-ary inputs. This new polar transform allows us to track the evolution of every pair of adjacent bits through different layers of polar transforms, and it also plays an essential role in the Successive Cancellation List (SCL) decoder for the ABS polar codes. Extensive simulation results show that ABS polar codes consistently outperform standard polar codes by 0.15dB--0.3dB when we use CRC-aided SCL decoder with list size $32$ for both codes. The implementations of all the algorithms in this paper are available at https://github.com/PlumJelly/ABS-Polar

Perturbed Adaptive Belief Propagation Decoding for High-Density Parity-Check Codes

Algebraic codes such as BCH code are receiving renewed interest as their short block lengths and low/no error floors make them attractive for ultra-reliable low-latency communications (URLLC) in 5G wireless networks. This article aims at enhancing the traditional adaptive belief propagation (ABP) decoding, which is a soft-in-soft-out (SISO) decoding for high-density parity-check (HDPC) algebraic codes, such as Reed-Solomon (RS) codes, Bose-Chaudhuri-Hocquenghem (BCH) codes, and product codes. The key idea of traditional ABP is to sparsify certain columns of the parity-check matrix corresponding to the least reliable bits with small log-likelihood-ratio (LLR) values. This sparsification strategy may not be optimal when some bits have large LLR magnitudes but wrong signs. Motivated by this observation, we propose a Perturbed ABP (P-ABP) to incorporate a small number of unstable bits with large LLRs into the sparsification operation of the parity-check matrix. In addition, we propose to apply partial layered scheduling or hybrid dynamic scheduling to further enhance the performance of P-ABP. Simulation results show that our proposed decoding algorithms lead to improved error correction performances and faster convergence rates than the prior-art ABP variants.

Atmospheric pressure air microplasma current time series for true random bit generation

Generating true random bits of high quality at high data rates is usually viewed as a challenging task. To do so, physical sources of entropy with wide bandwidth are required which are able to provide truly random bits and not pseudorandom bits, as it is the case with deterministic algorithms and chaotic systems. In this work we demonstrate a reliable high-speed true random bit generator (TRBG) device based on the unpredictable electrical current time series of atmospheric pressure air microplasma (APAMP). After binarization of the sampled current time series, no further post-processing was needed in order for the bitstreams to pass all 15 tests of the NIST SP 800-22 statistical test suite. Several configurations of the system have been successfully tested at different sampling rates up to 100 MS/s, and with different inter-electrode distances giving visible/non-visible optical emissions. The cost-effectiveness, simplicity and ease of implementation of the proposed APAMP system compared to others makes it a very promising solution for portable TRBGs.

ROBUST CHANNEL ENCODING FOR MMTC NODE IN 5G (NR)

The paper is focused on robust channel encoding for Massive machine type communication (mMTC) communication in 5G (NR). The performance evaluation of channel encoding is obtained at 5G New Radio (NR) PHY. The results show that reliable bit error rate (BER) against the poor channel condition or random fluctuated channel applied. Channel encoding algorithm as a forward error correction code (FEC) is applied on packet to packet basis to improve the BER performance against inter symbol interference. The concept of adaptation of code rate is valuable to reduce the payload effect and provide optimum solution between BER and throughput. Adaptive code rate selection is based on impact of earlier transmitted packet bit using feedback indicator.

Noise Removal in Embedded Image With Bit Approximation

Stego-images are often contaminated by interchannel noise or active noise attack when communicating on the Web. And it is challenging to restore embedded image from corrupted stego-image. This paper studies a kNN-bit approximation algorithm to remove noises in embedded image. The proposed algorithm distinguishes reliable bits from extracted bits, and estimates pixel values by keeping reliable bits unchanged and correcting unreliable bits. Specifically, the 8th (highest) unreliable bit of a pixel can be approximated with its nearest neighbor pixels. And then, if an unreliable bit locates at any one of the 5th-7th bits of a pixel, it is adjusted with two nearest neighbors of the pixel, where the pixel is in-between these two nearest neighbors. Finally, for other unreliable bits, each one is approximated by the maximum and minimum possible values of nearest neighbors of its pixel. We conduct experiments for illustrating the efficiency, and demonstrate that the proposed algorithm can recover the embedded images with good visual quality from corrupted stego-images.

Toward the energy efficiency of multi‐pulse PPM signalling for optical communication

To improve information throughput conventional single-pulse M -ary pulse-position-modulation (PPM) scheme, multi-pulse PPM has been proposed on the optical intensity-modulated and direct-detection channel. Although the multi-pulse M -ary PPM scheme significantly enhances throughput performance, nevertheless, the symbol error rate (SER) increases due to the loss of orthogonality between different pairs of symbols. In this study, the authors first derive the SER performance of general L pulses M -ary PPM scheme under Poisson channel statistic. Moreover, as the green radio is essential in future network, energy efficiency becomes the major concern. Hence, they evaluate L pulses M -ary PPM scheme by the number of reliable bits transmitted per joule of energy consumed. They analyse the trade-off between throughput and power consumption.

A Linear-Complexity Channel-Independent Code Construction Method for List Sphere Polar Decoder

Besides the main decoding methods for polar codes such as successive cancellation (SC) decoding, SC list decoding (SCL), and belief propagation (BP) decoding, list sphere decoding (LSD) is an alternative for short codes regarding its lower complexity. Though the improved LSD (ILSD) can achieve better performance than LSD by a synchronous determination scheme, its performance is still not satisfactory with an inappropriate code construction. Good polar code construction is to pick the K most reliable bits from N bits. However, existing polar construction methods are designed for SC or BP decoders. These construction methods might not be suitable for ILSD, which searches based on the Euclidean distance. In this paper, a linear-complexity channel-independent polar code construction method for ILSD is proposed to improve the performance. Considering the Hamming distance as the reliability for ILSD, the proposed method arranges more frozen bits in the early synchro sets and improves the evaluation of the paths at each decoding level. With linear complexity, this method is channel-independent, which is efficient for offline constructions. Numerical results show the proposed construction with low code rates outperforms the state-of-the-art by 2 dB with ILSD.

An Underwater Acoustic OFDM System Based on NI CompactDAQ and LabVIEW

Recently the orthogonal frequency division multiplexing (OFDM) technique has attracted increasing interests in underwater acoustic (UA) communications. In this paper, we present an OFDM-based UA communication system, which is designed based on the National Instruments LabVIEW software and the CompactDAQ device. Details on both the transmitter and receiver system design are discussed. The performance of this UA OFDM system is verified through recent UA communication experiments performed in a tank, in the Canning River, and in the estuary of the Swan River, Western Australia. Experimental results show that the system achieves a reliable bit error rate performance even with high-order modulation schemes. Compared with conventional field-programmable gate array and digital signal processor based designs, the proposed implementation simplifies the prototype design process and reduces the software development time. The proposed system provides a flexible and reconfigurable prototype for researchers to test and validate the performance of UA communication algorithms in real UA channels.

Machine vision gait-based biometric cryptosystem using a fuzzy commitment scheme

In this paper, a fuzzy commitment scheme is applied with a machine vision gait-based biometric system to enhance system security. The proposed biometric cryptosystem has two phases: enrolment and verification. Each of them comprises three main stages: feature extraction, reliable components extraction, and fuzzy commitment scheme. Gait features are extracted from gait images using local ternary pattern (LTP), and then, the average of one complete gait cycle using the gait energy image (GEl) concept is calculated. The average images are joined using a 2D joint histogram, which is reduced using principal component analysis (PCA) to produce the final feature vector. To enhance the robustness of the system, only highly robust and reliable bits from the feature vector are extracted. Finally, the fuzzy commitment scheme is used to secure feature templates. Bose–Chaudhuri–Hocquenghem codes (BCH) are used for key encoding in the enrolment phase and for decoding in the verification phase. The proposed system is tested using the CMU MoBo and CASIA A databases. The experimental results show that the best error rate for the CMU MoBo database is obtained when using a fast walk for enrolment and verification, where we obtain 0% for the false acceptance rate (FAR) and 0% for the false rejection rate (FRR) for a key length equal to 50 bits. The best error rate for CASIA A dataset is obtained when using the 45-degree direction to the image plane view for enrolment and verification, where we obtain 0% for the false acceptance rate (FAR) and 0% for the false rejection rate (FRR) for a key length equal to 45 bits.

An ant colony optimization aided two-dimensional soft output viterbi algorithm detection scheme for holographic data storage systems

In this paper, we propose an ant colony optimization (ACO) aided two-dimensional (2D) soft output Viterbi algorithm (SOVA) detection scheme for holographic data storage systems. The proposed detection scheme adopts the conventional 2D SOVA detection scheme which has two one-dimensional (1D) SOVA detectors for the horizontal and vertical directions, and employs an ACO detector with a reliability test. The proposed detection scheme operates in two stages. In the first stage, the data is detected by conducting the 2D SOVA detection scheme for the horizontal and vertical directions. In the second stage, the reliability test is taken to detect the less reliable bits in a data page by using the outputs of the horizontal and vertical 1D SOVA detectors from the first stage. If the less reliable bits are detected, the ACO detector is performed to improve the reliability of the unreliable bits. Otherwise, the sum of outputs from the horizontal and vertical 1D SOVA detectors is detected by a threshold detector. The bit error rate performances of the proposed detection scheme are compared to the conventional detection schemes. Simulation results show that the proposed detection scheme performing the ACO detector for only 0.3% of bits has more than 7 dB gains compared to the conventional 2D SOVA detection scheme when the grade of blur is 1.8.