Soft-decision Decoding Research Articles

Error Performance Analysis of an Unequal Error Protection System for the JPEG 2000 and H.265 Standards Over Wireless Channels

In this paper an unequal error protection scheme based on Rate-Compatible Punctured Convolutional codes employing Hierarchical PSK modulation is presented. New error bounds are derived and reported for AWGN and flat Rayleigh fading channels. Both soft and hard decision decoding techniques are considered in our analysis. The proposed scheme does not involve increased in complexity of resources and bandwidth expansion either. It is shown that by varying the signal to noise ratio and a specific constellation parameter set, which controls the level of error protection, significant error performance can be achieved over the uniform modulation case. All the established theoretical upper bounds are illustrated with numerical examples and these are also simulated using Matlab Simulink® 2017. Simulation results show that near-13-dB difference is achieved between the first and last priority sub-channels of the UEP communication system. The proposed scheme can find suitable applications in digital video broadcasting and Wireless JPEG2000 as well as H.265 data transmission systems.

Sequencing barcode construction and identification methods based on block error-correction codes.

Multiplexed sequencing relies on specific sample labels, the barcodes, to tag DNA fragments belonging to different samples and to separate the output of the sequencers. However, the barcodes are often corrupted by insertion, deletion and substitution errors introduced during sequencing, which may lead to sample misassignment. In this paper, we propose a barcode construction method, which combines a block error-correction code with a predetermined pseudorandom sequence to generate a base sequence for labeling different samples. Furthermore, to identify the corrupted barcodes for assigning reads to their respective samples, we present a soft decision identification method that consists of inner decoding and outer decoding. The inner decoder establishes the hidden Markov model (HMM) for base insertion/deletion estimation with the pseudorandom sequence, and adapts the forward-backward (FB) algorithm to output the soft information of each bit in the block code. The outer decoder performs soft decision decoding using the soft information to effectively correct multiple errors in the barcodes. Simulation results show that the proposed methods are highly robust to high error rates of insertions, deletions and substitutions in the barcodes. In addition, compared with the inner decoding algorithm of the barcodes based on watermarks, the proposed inner decoding algorithm can greatly reduce the decoding complexity.

Improved Decoding of Linear Block Codes by Concatenated Decoders

The use of decoding algorithms allows us to retrieve information after transmitting it over a noisy communication channel. Soft decision decoding is powerful in concatenation schemes that use two or more levels of decoding. In our case, we make a concatenation between the Hartmann & Rudolph (HR) algorithm as symbol-by-symbol decoder and the chase-2 algorithm that is word-to-word decoding algorithm. In this paper, we propose to combine two decoding algorithms for constructing a new one with more efficiency and less complexity. This work consists firstly to use the HR with a reduced number of codewords of the dual code then the Chase-2 algorithm which exploits the output of PHR. The simulations results and the comparisons made show that the proposed decoding scheme guarantees very good performance with reduced temporal complexity.

Flexible Multilevel Coding with Concatenated Polar-Staircase Codes for M-QAM

In this work, a multilevel coding (MLC) based coded modulation scheme with two degrees of freedom in rate flexibility is proposed and compared with a bit-interleaved coded modulation (BICM) scheme from a performance versus complexity perspective. The proposed MLC scheme is based on a rate flexible inner soft-decision polar code and utilizes an outer hard-decision staircase code structure as in the 400ZR concatenated forward error-correcting code. The performance of the MLC scheme is investigated for a range of inner code lengths, inner decoder list sizes, and signaling with 16 and 64 quadrature amplitude modulation, respectively. The MLC is designed such that a portion of the staircase encoded bits can bypass the inner code. The number of required inner soft-decision decoders can thus be reduced, thereby saving computational complexity. The proposed MLC scheme simultaneously offers up to a 53.7% reduction in the number of inner decoders and up to 0.55 dB of performance improvement when compared with the similar BICM approach.

A Generalized Parity-Check Transformation for Iterative Soft-Decision Decoding of Binary Cyclic Codes

The conventional parity-check matrix transformation algorithm (PTA) requires matrix inversion to transform matrices of maximum distance separable (MDS) codes. However, such matrix transformation is not always guaranteed for the class of non-MDS codes. Hence, the PTA fails for binary cyclic (BC) codes. To overcome this limitation, we developed a generalized parity-check matrix transformation (GPT) algorithm for binary cyclic codes. The GPT avoids the matrix inversion step of the PTA. It permutes the columns of the parity-check matrix based on the reliability information from the channel. Results show a significant bit error rate (BER) performance gain as compared to the existing PTA. It also presents a reasonable BER performance as compared to the other soft-decision (SD) decoding algorithms. In addition, the decoder functions within a practical decoding time complexity, particularly at the message passing stage.

A Robust Transceiver for Narrow-Band Communications in Presence of Carrier Frequency Offset

We address narrow-band communications in presence of large and time-varying carrier frequency offset (CFO) at the receiver. This is a general assumption which includes the condition due to the Doppler effect where the transmitter and/or receiver are moving with a relative time-varying speed. A robust transceiver system is proposed to dynamically estimate and compensate the CFO. The proposed system is particulary attractive for low data-rate communications (e.g., voice service) where the CFO is significantly larger than the data bandwidth. A two-step carrier recovery scheme is developed with large acquisition range and fast frequency tracking. The proposed method provides accurate CFO estimation with affordable complexity. We also devise a robust frame synchronization scheme to provide accurate timing in presence of CFO. Furthermore, non-coherent detection with soft-decision decoding is employed to provide a low-complexity receiver with acceptable sensitivity. The proposed transceiver design is implemented on FPGA and real-time experiments are conducted on a Xilinx ZC706 evaluation base board along with AD-FMCOMMS3 daughterboard. After validating the experiments compared to the simulation results, the design was optimized for implementation on XC7Z020 and further integrated with the analog front-end on a board with smaller footprint.

Progressive Algebraic Soft-Decision Decoding of Reed–Solomon Codes Using Module Minimization

The algebraic soft-decision decoding (ASD) of Reed–Solomon (RS) codes yields a competent decoding performance with a polynomial-time complexity. But its complexity remains high due to the interpolation that generates the interpolation polynomial $Q(x,y)$ . The progressive ASD (PASD) algorithm has been introduced to construct $Q(x,y)$ with a progressively enlarged $y$ -degree, adjusting its error-correction capability and computation to the received information. However, this progressive decoding is realized at the cost of memorizing the intermediate decoding information. To overcome this challenge, this paper proposes a new PASD algorithm which is evolved from the ASD using module minimization (MM) interpolation. Polynomial $Q(x,y)$ can be constructed through the image of the progressively enlarged submodule basis without the need of memorizing the intermediate decoding information, eliminating the memory cost of progressive decoding. The MM interpolation also attributes to a remarkably lower complexity than the original PASD algorithm. Furthermore, a complexity reducing variant is proposed based on assessing the degree of Lagrange interpolation polynomials. We also analyze the complexity of the proposed decoding methods and reveal their channel dependent feature. Our simulation results show their low-complexity and advanced decoding performances.

A Novel Baseband Faster-Than-Nyquist Non-Orthogonal FDM IM/DD System With Block Segmented Soft-Decision Decoder

In this paper, we systematically investigate our recently proposed faster-than-Nyquist non-orthogonal frequency-division multiplexing (FTN-NOFDM) generation technique for intensity modulation/direct detection (IM/DD) optical systems. The proposed scheme is based on modified fractional discrete Fourier transform (mFrDFT), and presents several advantages compared to other existing generation methods. Due to the exemption of guard bands, the proposed scheme achieves higher tolerance to narrow-bandwidth filtering. Besides, without the constraints on compression factor and modulation formats, the proposed system gives better signal flexibility and compatibility to various advanced signal processing techniques. To meet the demand on a large number of FTN-NOFDM subcarriers and high-order modulation formats, we further propose an efficient block segmented soft-decision decoder (BSSDD), which does not need to adjust the signal architecture or sacrifice the spectral efficiency. A 22.24-Gb/s 4-QAM FTN-NOFDM signal with up to 25% bandwidth saving has been successfully implemented over 20-km standard single mode fiber (SSMF) in an IM/DD optical communication system while keeping the bit error ratio (BER) below the hard-decision forward error correction (HD-FEC) limit. For both 4-QAM and 16-QAM FTN-NOFDM systems, the proposed BSSDD achieves better performance than the conventional decoder. All the results indicate that the proposed FTN-NOFDM technique has great potential to be used in high-speed IM/DD optical systems.

Improved MPEG-4 high-efficiency AAC with variable-length soft-decision decoding of the quantized spectral coefficients

MPEG-4 High-Efficiency Advanced Audio Coding (HE-AAC) is designed for low bit rate applications, such as audio streaming in mobile communications. The HE-AAC audio codec offers a better coding efficiency since variable-length codes (VLCs) are adopted. However, HE-AAC has originally been designed for storage and error-free transmission conditions. For the transmission over bit error-prone channels, error propagation is a serious problem for the VLCs. Therefore, a robust HE-AAC decoder is desired, especially for mobile communications. In contrast to traditional hard-decision decoding, utilizing bit-wise channel reliability information, soft-decision (SD) decoding has been known to offer better audio quality. In HE-AAC, the global gain parameter is coded with fixed-length codes (FLCs), while the scale factors and quantized spectral coefficients are coded with VLCs. In this work, we apply FL/SD decoding to the global gain parameter, VL/SD decoding to the parameters scale factors and quantized spectral coefficients. Especially, in order to apply VL/SD decoding to the quantized spectral coefficients, a new modified trellis representation in VL/SD decoding is proposed. An improved HE-AAC performance is clearly observed, with the support of both instrumental measurements and a subjective listening test.

Fast and Scalable Soft Decision Decoding of Linear Block Codes

Ordered statistics-based decoding (OSD), which exhibits a near maximum likelihood decoding performance, suffers from huge computational complexity as the order increases. In this letter, we propose a fast and scalable OSD by considering the OSD as a fast searching problem. In the searching process, if the up-to-date minimum cost value is less than a predicted threshold value, then we can safely skip the search for remaining higher orders. The computational complexity of the proposed algorithm converges quickly to that of order one, regardless of the maximum order. Compared with the probabilistic necessary conditions-based OSD, the proposed algorithm exhibits speed-up gains of a factor of approximately 2,740 (at 3.0dB) for (127,64) BCH codes, with an indistinguishable decoding performance.

Multicarrier DS-CDMA System Under Fast Rician Fading and Partial-Time Partial-Band Jamming

The impact of joint partial-time, partial-band jamming on a multicarrier (MC) asynchronous direct-sequence code-division multiple access (DS-CDMA) system in a fast fading environment is studied in conjunction with two different subcarrier combining and decoding schemes. An easy-to-evaluate upper bound using the Chernoff bound is provided and compared to simulation results. Simulation results suggest that for soft-decision decoding systems, under Rayleigh fading, full-time, full-band jamming is most effective. In contrast to the Rayleigh case, when a sufficiently strong line-of-sight component exists in the channel, the jammer’s optimal strategy of attacking in time or frequency depends on the strength and the type of error correction that the system is deploying for that dimension. For hard-decision decoding systems, in Rayleigh fading, partial-band jamming is recommended. For the coding strategies examined, in Rician fading, the jammer should switch from full-time, partial-band jamming to a strategy that jams a higher percentage of the more heavily protected dimension as the jamming power increases. Furthermore, for AWGN channels, the results from the system show that the jammer should always jam a higher percentage of the more heavily protected dimension.

Error-Correcting WOM Codes: Concatenation and Joint Design

We construct error-correcting write-once memory (WOM) codes that guarantee correction of any specified number of errors in $q$ -level memories. The constructions use suitably designed short $q$ -ary WOM codes and concatenate them with outer error-correcting codes over different alphabets using suitably designed mappings. With a new storage-efficiency measure, we call EC-rate and show that for common error types the codes save redundancy and implementation complexity over straightforward concatenation. In addition to constructions for guaranteed error correction, we extend the error-correcting WOM scheme to binary multi-level coding for random errors, and toward soft-decision decoding provide an efficient way to extract reliability information without using higher-precision readout.

Adaptive Soft Detection for Flash Memory

To provide reliability of flash memory, error-correcting codes are usually used which can be further enhanced by moving on from hard-decision to soft-decision decoders. This requires multiple readings to obtain a reliability measure of the stored data, which is complicated by the fact that a posteriori probability distributions change as the memory ages through retention and wear-out. The existing methods for reading a flash memory either assume knowledge of these distributions or require a large number of readings for accurate estimation. In this letter, we propose a low-complexity algorithm that tracks the soft-decision boundaries and estimates the corresponding log-likelihood ratios (LLRs). It does not require any additional readings and only involves simple calculations using already available variables. The efficacy is verified through the simulations and is shown to provide near-optimal performance.

Deep Learning-Aided Dynamic Read Thresholds Design for Multi-Level-Cell Flash Memories

The practical NAND flash memory suffers from various non-stationary noises that are difficult to be predicted. For example, the data retention noise induced channel offset is unknown during the readback process, and hence severely affects the reliability of data recovery from the memory cell. In this paper, we first propose a novel recurrent neural network (RNN)-based detector to effectively detect the data stored in the multi-level-cell (MLC) flash memory without the prior knowledge of the channel. However, compared with the conventional threshold detector, the proposed RNN detector introduces much longer read latency and more power consumption. To tackle this problem, we further propose an RNN-aided (RNNA) dynamic threshold detector, whose detection thresholds can be derived based on the outputs of the RNN detector. We thus only need to activate the RNN detector periodically when the system is idle. Moreover, to enable soft-decision decoding of error-correction codes, we first show how to obtain more read thresholds based on the hard-decision read thresholds derived from the RNN detector. We then propose integer-based reliability mappings based on the designed read thresholds, which can generate the soft information of the channel. Finally, we propose to apply density evolution (DE) combined with the differential evolution algorithm to optimize the read thresholds for low-density parity-check (LDPC) coded flash memory channels. Computer simulation results demonstrate the effectiveness of our proposed RNNA dynamic read thresholds design, for both the uncoded and LDPC-coded flash memory channels, without any prior knowledge of the channel.

Coding for Visible Light Communication Using Color-Shift Keying Constellations

Color-shift keying (CSK) is a modulation scheme used in visible light communication (VLC) to transmit data by varying the intensity of red, green, and blue LEDs. We study the channel coding for VLC using CSK under constraints of no color shift and no illumination flicker during transmission and design codes over newly introduced symmetric symbol constellations over a triangle intensity plane. One class of codes contains the transmitted sequence based on finite-state machines, and the other is based on the concept of trellis-coded modulation for mitigating color shifts during transmission. The codes have a trellis structure which allows optimal soft-decision decoding using the Viterbi algorithm providing asymptotic coding gain improvements of 1.5 to 3.5 dB with respect to the uncoded transmission while complying with the color shift and flicker constraints.

Novel non‐linear demapper for soft decision decoder of LDPC codes in impulsive noise

Impulsive noises severely degrade the performance of a communication system. This study deals with the performance of the soft decision decoder for low-density parity-check codes over impulsive noise channels. To simplify the calculation of log likelihood ratio (LLR) and cooperate with the soft decision decoder, a new non-linear approximation named inverse demapper of LLR over the impulsive noise is proposed. Without carrying the noise statistics, the inverse demapper performs close to the optimal demapper. In addition, the density evolution is employed to obtain optimal parameters of the inverse demapper. Then, the extrinsic information transfer chart analysis and simulation results are presented to verify the effectiveness of the authors' proposed demapper.

High Speed Soft Decision Decoding of Linear Codes Based on Hash and Syndrome Decoding

High Speed Soft Decision Decoding of Linear Codes Based on Hash and Syndrome Decoding

Low complexity decoding of Reed–Solomon codes over magnetic recording channels

A low complexity soft-decision decoding technique is presented for Reed–Solomon codes, over magnetic recording channels (MRC), by considering symbol and bit reliability, jointly. A symbol detection scheme for burst error scenarios has been put forward for the iterative error-and-erasure decoding algorithm (IEED), which is based on multiple trials, and is a combination of the generalised minimum distance and Chase-2 decoding schemes. In order to decrease complexity, the decoding test patterns are used in a certain order, while the stopping criteria is also discussed. Simulations show that the proposed algorithms can achieve almost the same performance as that of IEED for the additive white Gaussian noise channel and slightly better performance in MRC, but with significantly less complexity.

A Low Error Rate BCH-Based Encoder-Decoder Approach for Electromagnetic Measurement While Drilling System

In practical applications of electromagnetic measurement while drilling (EM-MWD) in the underground coal mine, the signal-to-noise ratio (SNR) of a receiver cannot always meet the requirements of reliable communication conditions due to the earth attenuation, interfering signal from the well site, and so on. Aimed to solve these problems, this paper presents a low error rate Bose–Chaudhuri–Hocquenghem (BCH)-based encoder–decoder technology for EM-MWD. First, this paper studies the relationship among the BCH encoding error performance and the decoding method, the source length, and other factors through simulation; then, we obtain an optimal length of BCH code for EM-MWD through analyzing the bit error performance of hard-decision decoding and soft-decision decoding with different lengths of BCH code. Finally, we compare the proposed algorithm with the conventional binary phase-shift keying (BPSK) approach in the actual environment. The results show that the proposed algorithm can reduce the bit error rate by about ten times at a lower SNR, achieving a reliable communication condition when the SNR of a received signal is reduced. It demonstrates the effectiveness of the proposed BCH encoder and the decoder algorithm based on BPSK for EM-MWD.

수중 레이저 통신에서 LDPC 부호화된 M-레벨 펄스 위치 변조 신호의 연판정 복호 기법

본 논문에서는 수중 레이저 통신에서 적용되는 M진 PPM 변조 방식의 복조 과정에서 연판정 기법을 제안하며, LDPC 부호화 방식과 M진 PPM 변조 방식을 적용하여 연판정 기법과 기존의 경판정 기법의 성능을 비교 분석하는 시뮬레이션을 수행하였다. 시뮬레이션 결과 본 논문에서 제안한 연판정 기법이 기존의 경판정 기법보다 0.2dB ~ 2.2dB의 성능이 향상됨을 확인하였다.