A Novel Application of LDPC-Based Decoder for WiMAX Dual-mode Inner Encoder

본 논문에서는 OFDM 시스템에서 고속 처리와 성능 향상을 위한 LDPC 코드 기반 결정 궤환 등화기(Decision Feedback Equalizer: DFE)를 제안한다. LDPC 코드는 우수한 오류 정정 능력과 Shannon의 채널 용량에 근접하는 성능을 갖는다. 그러나, 많은 parity 검사 행렬과 반복 횟수를 가진다는 단점이 있다. 제안된 시스템에서는 판정된 신호와 복호기 사이의 신호의 MSE(Mean Square Error)를 등화기로 피드백한다. 이러한 방법을 사용하면 추정된 채널 응답을 보정해 주기 때문에 성능을 향상시킬 수 있다. 또한, 동일한 성능에서 피드백이 포함되지 않은 시스템보다 낮은 반복 횟수를 갖기 때문에 시스템의 복잡도를 줄일 수 있다. 시뮬레이션을 통해 다중 경로 채널에서 CFO(Carrier Frequency Offset)와 위상 잡음이 고려된 OFDM 시스템의 성능을 평가하여 제안 시스템의 우수성을 보인다. In this paper, we propose a decision feedback equalizer based on LDPC(Low Density Parity Check) code for the fast processing and performance improvement in OFDM system. LDPC code has good error correcting capability and its performance approaches the Shannon capacity limit. However, it has longer parity check matrix and needs more iteration numbers. In our proposed system, MSE(Mean Square Error) of signal between decision device and decoder is fed back to equalizer. This proposed system can improve BER performance because it corrects estimated channel response more accurately. In addition, the proposed system can reduce complexity because it has a lower number of iterations than system without feedback at the same performance. Simulation results evaluate and show the performance of OFDM system with the CFO and phase noise in multipath channel.

With the improvement of integration degree, more and more systems that originally implemented on PCB board are integrated into one chip, becoming a SOC (system on a chip). Also with the increasing demand for programmable performance, the use of multi microprocessors structure in SOC designs is becoming much more popular. For the complex real-time systems such as HDTV decoder, it is generally easier with multiple CPUs to provide instant response time and meet the demand of real-time and function complexity. In this paper, based on introduction of the HDTV SOC architecture we designed, a communication and control scheme between master-slave mode dual-processors in the SOC is proposed, as well as a shared memory control method among multi IP function modules in the SOC.

In this paper, we evaluate the performances of the Reed–Solomon (RS) and low density parity check (LDPC) codes in order to propose an efficient coding system for the outer code in high density optical recording channels. Hard decision decoding (HDD) RS code, iterative soft decision decoding (SDD) RS code or LDPC code is used as the outer code and LDPC code is used as the inner code. We compare the bit error rate (BER) performance of each coding system for various code rates, code lengths and burst errors. Simulation results show that the LDPC code has a better BER performance than the HDD RS and iterative SDD RS codes as the outer code in high density optical channels. Therefore, the LDPC code could be more attractive as the outer code than the RS code in high density optical channels.

Low Density Parity Check (LDPC) codes have been widely used in communications systems due to their high error correction capabilities. Recently these codes are also investigated for being exploited in high performance storage systems, especially when Non-Volatile Memory (NVM) technologies are used. The main drawback of using LDPC codes in storage systems with a high number of parallel channels is the increased hardware complexity and cost, especially when variable rate codes are used. In this work, we present an architecture of a NVM-based storage system that dynamically adapts the LDPC's rate to the aging conditions of the storage device in order to maximize its lifetime capacity while keeping low its hardware complexity. In order to decrease the system's complexity we propose a PCIe-based architecture that uses a pool of LDPC decoders shared by all NVM channels and we study its effect on the system's lifetime capacity and the achievable I/O data rate.

Low-density parity-check (LDPC) codes are commonly used in communication systems to improve the system performance, but LDPC codes takes too long for decoding, making communication inefficient and unsuitable for short-frame data transmission methods. In underwater acoustic channels, spread-spectrum communication becomes an effective way to realize long-distance communication. This paper combines short-block LDPC codes with a direct sequence spread spectrum and soft spread spectrum in underwater acoustic communication, addressing the problem of the inapplicability of conventional LDPC codes. The applicability of the proposed method in this paper is verified through simulation tests and pool experiments. The results indicate that the proposed communication system achieves lower bit error rates compared to the classical coding methods used in underwater acoustic spread-spectrum communication systems under the same channel conditions.

Cooperative diversity or user cooperation achieves the diversity gain without adding physical antennas to the users or mobile stations. The users work in cooperative fashion using their single antennas to create a virtual transmit diversity, called relay diversity or cooperative diversity. The diversity gain achieved by cooperative diversity can be further improved using error correction codes. Low-density parity-check (LDPC) codes are linear block codes with good error correction capabilities. We present a novel approach using extended LDPC codes to increase the diversity gain in cooperative diversity. We also compare the extended LDPC codes with punctured LDPC codes in cooperative diversity and show that extended LDPC codes have lesser complexity than punctured LDPC codes in cooperative diversity.

Low Density Parity Check (LDPC) codes are considered to be used in many future communication systems. We will show in this work how the performance of a communication system is influenced when different bit to symbol mapping schemes of a higher order modulation (e.g.: 16-QAM) are combined with LDPC coding. To evaluate and optimize bit-to-symbol mapping methods, a modified version of density evolution is proposed. In addition, simulation results are shown which justify the use of density evolution as a method for qualitative analysis of different symbol mapping schemes in conjunction with LDPC coding. We propose novel mapping methods and show performance results in combination with LDPC coding.

In this paper, LDPC codes and OFDM technologies are studied, and combines LDPC and OFDM to simulate and verify the performance. The encoding of LDPC and logarithmic domain BP decoding algorithm and the principle of OFDM are introduced. Through MATLAB, the simulation of OFDM-LDPC system in different channel, different code length, different iteration times, LDPC and OFDM-LDPC in the same conditions are compared. Through simulation analysis, we can know that the performance of OFDM-LDPC system will improve with the increase of the code length. When the SNR is small, the number of iterations has little effect on the performance of OFDM-LDPC system. When the SNR is large, the performance of the system will be improved with the increase of the number of iterations. The performance of OFDM-LDPC codes is better than that of LDPC codes. The performance of OFDM-LDPC code is better than LDPC code in multipath Rayleigh fading channel.

Free space Optical (FSO) communication systems are severely laid down with the weather situations. Atmospheric turbulence is one of the essential facts that degrade the overall performance of a FSO system even under smooth sky circumstance. Coding is one of the techniques that may be applied to improve the overall performance of a communication system. Moreover, it's miles very crucial to apply proper coding approach to enhance the performance. This paper affords an analytical method to evaluate the overall performance of LDPC and STBC coded FSO communication system under the impact of strong atmospheric turbulence. Evaluation is done to find the expressions for the output photodetector current and signal to noise power ratio. The average bit error rate is evaluated numerically thinking about gamma-gamma distributions for the atmospheric turbulence. Analytical results show that for similar type of system configuration in FSO, STBC provides better performances than LDPC code.

In this paper, we construct binary spatially coupled (SC) low-density parity-check (LDPC) codes based on Euclidean geometry (EG) LDPC codes for storage applications, where high error correction capability, extremely low uncorrectable bit error rate (UBER), and low decoding complexity are required. We propose a systematic way to construct the families of SC LDPC codes from $(m,2^{s})$ EG LDPC codes, which are termed EG-SC LDPC codes. In the construction method, we propose a 2-D edge-spreading process to construct the base matrix of EG-SC LDPC codes, which consists of matrix unwrapping and periodically time-varying of a protograph. A lower bound on the rank of the parity-check matrix of an EG-SC LDPC code is derived. We evaluate the error rate performance of the constructed EG-SC LDPC codes by using a weighted bit-flipping decoding algorithm for its low decoding complexity. Numerical results show that the UBER performance of the constructed EG-SC LDPC codes is superior to that of their EG LDPC code counterparts, and show no error floor compared with the constructed protograph SC LDPC codes and regular LDPC codes.

Hybrid low-density parity-check (LDPC) decoding combines conventional Belief-Propagation (BP) algorithm with stochastic decoding to achieve high performance and low complexity simultaneously. However, lossy and inefficient stochastic-to-binary (S2B) conversion brings extra performance degradation and decoding latency. In this paper, a bit-serial stochastic updating based hybrid decoding (BSSU-HD) is proposed, which employs fully correlated stochastic (FCS) check nodes (CNs) and probability tracers assisted variable nodes (VNs) to accomplish accurate and efficient S2B conversion. Two strategies, including random source selection and tracing speed switching, are proposed to further improve performance and convergence. A BSSU LDPC decoder for IEEE 802.3an is designed in a 65-nm CMOS process, which occupies 4.6 mm <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$^2$</tex-math> </inline-formula> silicon area and achieves a throughput of 200.8 Gb/s at <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$E_b/N_0 = 4.4$</tex-math> </inline-formula> dB with 500 MHz clock frequency from a 1.2 V supply voltage. The power and energy efficiency are 2.933 W and 14.61 pJ/bit, respectively. To the best of our known, it achieves the best decoding performance, the highest throughput and hardware efficiency among state-of-the-art IEEE 802.3an LDPC decoders. We also verify that the BSSU-HD can achieve better performance for multi-rate 5th generation (5G) New Ratio (NR) LDPC codes than conventional algorithm, which greatly extends the application of the stochastic decoding.

The increasing demand for high-density and high-speed digital optical recording systems has made the development of advanced coding and signal processing techniques for fast and reliable data recovery increasingly important. In recent years, the parity-check (PC)-code-based reception technique has been widely studied for magnetic recording systems, and it is projected to be highly promising for high-density optical recording. The PC code is an inner error correction code (ECC), which can detect dominant short error events of the system, using only a few parity bits. This reduces the loss in error correction capability of the outer ECC due to random short errors and results in a simple and efficient solution to improve the overall performance. This thesis is dedicated to the design and analysis of PCcode- based recording systems to achieve higher recording capacity with low implementation complexity, for high-density blue laser disc systems. In particular, most of the key components of the PC-code-based optical recording system have been designed and optimized for different recording densities, and different proportions of white noise and media noise. During the development of advanced coding and detection techniques, it becomes necessary to investigate the system’s performance with different coding schemes and recording densities. In Chapter 2 of the thesis, we propose a generalized Braat-Hopkins model for optical recording channels, which provides a fair basis for the performance comparison of detection schemes over different coding schemes and recording densities, for channels with additive, white Gaussian noise (AWGN) and media noise. Various basic issues associated with the PC-code-based systems are investigated in Chapter 3. These include bounds for bit error rates and error event probabilities, the dominant error events at channel detector output, different PC codes, simple and efficient post-processors, the impact of error events that are split across data block boundaries and the corresponding remedy, as well as the effects of code rates and recording densities. Simulation results show that a 4-bit PC code achieves the best performance. The corresponding bit error rates (BERs) are very close to the performance bounds, at both nominal and high densities. Constrained codes, which serve as a key component in the read-write channel of data storage systems, are desired to have a high code rate with low-complexity encoder/decoder. In Chapter 4, we investigate the design of certain capacity-approaching constrained codes for optical recording systems. In particular, we derive analytically the relationship between the number of encoder states and the maximum size of these codes. We identify the minimum number of encoder states that maximizes the code rate, for any desired codeword length. The design of constrained PC codes is key to the development of PCcode- based systems, and the systematic design of efficient constrained PC codes remains a challenging problem. In Chapter 5, we propose a general and systematic code design technique for constructing capacity-approaching constrained PC codes, which can detect any type of error events of the system, with the minimum code rate loss. Compared to the rate 2/3 code without parity, the newly designed constrained 4-bit PC code achieves a performance gain of 2 dB at nominal density, and 1.5 dB at high density, at BER = 10-5. As the dominant noise for high-density optical recording systems, media noise severely degrades the performance of channel detectors and postprocessors that are designed for AWGN. In Chapter 6, we propose two novel modifications to the bit detector to combat media noise. We further develop a data-dependent post-processing scheme for error correction. Compared to the system designed without considering media noise and without PC codes, the overall performance gain of the developed scheme can be more than 11 dB at high media noise levels. In data storage systems, the ECC failure rate (EFR) serves as the ultimate measure of the data recovery performance. In Chapter 7, we develop semi-analytical approaches for estimating the EFR, and analyze EFRs for the developed PC-code-based systems, for the cases without and with interleaving. Our analysis shows that with the optimum interleaving degrees, compared to the rate 9/13 code without parity, the 2-bit PC code achieves a gain of around 0.5 dB, and the 4-bit PC code gains 0.6 dB, at high record ing density and EFR = 10-16. The thesis concludes in Chapter 8 with some suggestions for further work.

The average bit error rate (ABER) performance of low-density parity-check (LDPC)-coded orthogonal frequency-division multiplexing (OFDM) free-space optical communication system with K-ary quadrature amplitude modulation (QAM) and phase shift keying (PSK) modulation schemes is investigated over the composite Málaga fading channel with atmospheric attenuation and pointing errors considered. The probability density function and cumulative distribution function regarding the aggregated channel model are derived with the help of the generalized Gauss-Laguerre quadrature rule, the analytical ABER expressions for both QAM and PSK OFDM systems are then obtained. On the basis of them, the ABER performance is analyzed with different turbulence strengths, weather conditions, normalized beam width, normalized jitter, and specifically, different values of Málaga distribution parameter ρ. Monte Carlo simulation is offered to confirm the correctness of the proposed ABER models. Moreover, LDPC codes are added into the simulation to enhance system performance. The result shows that, for the same turbulence, weather, and pointing error conditions, whether the LDPC codes are taken into account or not, the ABER performance of 16-QAM OFDM system is better than that of 16-PSK OFDM system over the Málaga fading channel, and the ABER result decreases with higher ρ for both modulation schemes. Furthermore, the LDPC coding can significantly improve the system performance over this aggregated fading channel for these two modulation schemes, and a lower LDPC code rate can obtain a better ABER performance. This work is beneficial for free-space optical system design.

A modified joint source-channel decoding (JSCD) algorithm based on low-density parity-check (LDPC) codes and hidden Markov estimation has been presented and extended to applying over Rayleigh fading channels. The proposed algorithm utilizes the source residual redundancy lack of any priori information of the source parameters, and the modifications employ the self-checking and convergence mechanisms of LDPC codes in adjusting the error probability of the hidden Markov model (HMM). To show the validation of the proposed JSCD methods, we also give a framework for the density evolution analysis for JSCD. Simulation results show that the joint decoding scheme on Rayleigh fading channels greatly reduces the number of iterations and improves the system performance more than 0.7 dB. Moreover, the modified JSCD algorithm leads to the joint decoder to converge at least 10% faster than the unmodified method without any degradation in the decoding performance

Given an all-one base matrix of size $M \times N$ , a closed path of different lengths can be formed by starting at an arbitrary element and moving horizontally and vertically alternatively before terminating at the same “starting” element. When the closed-path length is small, say 4 or 6, the total number of combinations can be evaluated easily. When the length increases, the computation becomes non-trivial. In this paper, a novel method is proposed to evaluate the number of closed paths of different lengths in an all-one base matrix. Theoretical results up to closed paths of length 10 have been derived and are verified by the exhaustive search method. Based on the theoretical work, results for closed paths of length larger than 10 can be further derived. Note that each of such closed paths may give rise to one or more cycles in a low-density parity-check (LDPC) code when the LDPC code is constructed by replacing each “1” in the base matrix with a circulant permutation matrix or a random permutation matrix. Since LPDC codes with short cycles are known to give unsatisfactory error correction capability, the results in this paper can be used to estimate the amount of effort required to evaluate the number of potential cycles of an LDPC code or to optimize the code.