Modified Decoding for Low Density Parity Check Codes over Power Line Channels

Turbo codes are attractive compared with Low Density Parity Check (LDPC) codes for Forward Error Correction (FEC) applications mainly due to their superior performance, especially at low Signal-to-Noise Ratio (SNR) such as are common in Powerline channels. For example, IEEE 1901-FFT PHY used the Turbo coding scheme defined in the HomePlug AV standards. However, patent fees are usually required for each turbo-code enabled manufactured device. The objective of this paper is to examine whether unlicensed LDPC codes, with optimized choices of block lengths, could be a viable alternative for future Powerline Communications (PLC) applications. The paper shows that the performance of the LDPC codes can approximate that of the Turbo codes with higher block lengths, on channels with typical and realistic PLC characteristics. The paper also shows that the additional complexity associated with this increase in block length can be mitigated by the use of Quasi-Cyclic LDPC (QC-LDPC) codes.

We propose a novel concatenated coding scheme combined Low Density Parity Check(LDPC) code and vertical Bell Labs layered space-time (VBLAST) code to improve the bit error rate (BER) performance for Free-space optical (FSO) communication links with On Off Keying(OOK) modulation. In the scheme, π-rotation encoding and belief-propagation (BP) decoding algorithm are employed in LDPC code, and minimum mean-square error (MMSE) soft-decision decoding algorithm is used for VBLAST code. Moreover, a joint iterative detection and decoding algorithm of VBLAST code and LDPC code is used to improve the overall link performance. At last, the BER of the proposed scheme over lognormal atmospheric turbulent fading channels is analyzed by using Monte Carlo method. The result shows that the BER of the proposed concatenated coding scheme is much improved than that only use VBLAST code scheme.

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.

In this paper, we propose a concatenated code by combining a Recursive Systematic Convolutional (RSC) code with a Low-Density Parity-Check (LDPC) code. The proposed concatenated code is encoded in parallel by an RSC encoder and an LDPC encoder without interleavers between them. When decoding the proposed concatenated code, the information bits are decoded by two decoding algorithms, and soft information is exchanged between the RSC decoder and the LDPC decoder. This allows for the elimination of wrong codewords output by each decoder. The use of an LDPC code allows us to halt the decoding process when the valid codeword is obtained. We evaluate the error rate performance of the proposed concatenated code by computer simulations. We show that the proposed concatenated code does not have a high error floor, and achieves better BLock Error Rate (BLER) performance than either conventional LDPC codes or conventional turbo codes in the high Eb/No region. We also show that since the proposed concatenated code can correct wrong codewords output by each decoder, it achieves better BLER than the regular LDPC code at the same Bit Error Rate (BER).

Highly reliable LDPC coded data transfer in home networks by using Canete’s PLC channel model

Low Density Parity Check (LDPC) codes have capacity-approaching performance over several channels of interest. In practice, for good block-error rate performance, the girth of the Tanner graph of an LDPC code needs to be as high as possible. In theory, to show that block-error rate approaches zero for increasing block-lengths, the girth of the Tanner graph sequence needs to tend to infinity with block-length. To meet these requirements, we construct sequences of large-girth irregular LDPC codes for a given degree-distribution pair (DDP) by applying a general node splitting algorithm on large girth graphs. The obtained Tanner graph meets the required DDP up to a suitable approximation. By optimizing the node-splitting method and using suitable large-girth graphs, we show code constructions with smaller block length for the same girth, when compared to previous constructions. Similar gains in block length are observed in the construction of sequences of large-girth protograph LDPC codes. Simulations, over a binary erasure channel, confirm the gains in block-error rate obtained by the large girth construction.

Big data storage demands larger cluster. The increasing size of the cluster may lead to failures of larger number of nodes. To provide reliable big data storage, replications are not cost-effective and does not provide a robust solution to prevent data loss. Traditional erasure codes applied in the RAID system such as Reed-Solomon (R-S) based solutions have limitations in providing high reliability. This is because higher reliability requires erasure codes with larger size. The computational cost of the R-S codes increase quadratically with the number of failures the R-S codes can tolerate for the same redundancy rate. It has been shown that Low Density Parity Check (LDPC) codes have lower computational cost and repair network traffic compared with R-S based solutions. Unfortunately, there does not exist a construction method for LDPC codes with larger size to control the computational cost and repair traffic. In this paper, a novel method is proposed to construct a family of LDPC codes - expanCodes with expandable sizes. The proposed expanCodes allows the encoding and decoding complexity remain unchanged with the increase of the size of the LDPC codes. As a result, increased reliability can be achieved without additional computation and repair traffic. The proposed expanCodes is integrated with the Hadoop system. Simulations show that more than 29% decrease in terms of encoding and decoding latency compared with R-S based solutions.

Although Power Line Communication (PLC) is not a new technology, its use to support data transmission over low voltage (LV) distribution networks is still the focus of ongoing research. This thesis focuses on the channel modelling and performance evaluation of narrowband (NB) PLC system. First, the channel modelling approaches of PLC are studied. Then, the proposed PLC channel modelling method based on the bottom-up approach for LV narrowband PLC in a frequency band between 9 kHz and 490 kHz is presented. This proposed model employs the transmission and scattering matrix methods to calculate the transfer function of a typical LV PLC network which comprises two common cable types (copper cables and aluminium conductor steel reinforced). Unlike the top-down approaches, this model is scalable as the network complexity increases and can better describe the network behaviour as a function of physical parameters.In addition, the noise characteristics and popular noise reduction techniques of PLC are studied. The major impairment to the PLC is the impulsive noise which is mainly generated by the switching transient in the network. Hence, a new technique is proposed to mitigate the impact of impulsive noise on data transmission over power lines. This proposed technique is an optimal Clipping/Blanking nonlinearity technique which is based on the minimum bit error rate (BER) search. Results obtained from the simulation of this technique demonstrate that performance has been enhanced in the NB-PLC system. The performance of the narrowband PLC system is also evaluated in both physical (PHY) and medium access control (MAC) layers. Since Orthogonal Frequency Division Multiplexing (OFDM) is a suitable modulation scheme for hostile environment of the power line, it is used to evaluate the PHY layer performance. As a result of the PHY layer performance analyses, it is found that the BER performance between neighbouring points in the typical LV PLC network is reasonable, but communication beyond one hop have to rely on upper layer protocols. In the MAC layer performance evaluation of the PLC system, the widely known random access MAC protocol that uses the Carrier Sense Multiple Access with Collision Avoidance (CSMA/CA) will be utilised. The MAC performance evaluation of the PLC system demonstrates a significant packet loss in LV PLC network even with a light traffic condition due to the noisy channel. Furthermore, the goodput declines abruptly once the individual transmission rate is high enough to block the network. In addition, the simulation results show that the channel errors can be reduced by adjusting the MAC parameters to allow the re-transmissions mechanisms to recoup the lost packets.

In this paper, a random Low-Density Parity-Check (LDPC) code is proposed for Noncontiguous Orthogonal Frequency Division Multiplexing (NC-OFDM) Cognitive Radio (CR) systems. Unlike other encoding schemes which achieve a system code rate of only 1/4 when half of the subcarriers are active, the proposed scheme achieves a system code rate of 1/2. The LDPC code is used to enhance the data transmission rate. A new channel model comprised of a binary erasure channel concatenated with an uncorrelated fading channel and an AWGN channel is adopted for NC-OFDM CR systems. Moreover, the adopted channel model is employed with density evolution algorithm to obtain good degree distribution pairs for the LDPC code. Thereafter, a modified shortest-path algorithm is used to construct the parity-check matrix for the LDPC code. Simulation results show that the proposed LDPC code performs well in terms of both error rate and data transmission rate.

Low-density Parity check codes (LDPC) are gaining interest for high data rate application in both terrestrial and spatial communications which requires low bit error rate. This paper proposes an algorithm through which the best parity check matrix is obtained for irregular low density parity check codes, which reduces the Bit Error Rate ,Frame Error Rate and computational complexity. Tanner graph also called a bipartite graph format in an Low Density Parity Check (LDPC) code design contains many short cycles; it will produce a computational complexity in a code design process and it degrades the code performance. To overcome this effect, we proposed an new algorithm which obtains a best final parity check matrix. Throughout the paper we will give the detailed description of an efficient algorithm proposed. The complexity is studied graphically and analytically. Using proposed algorithm, cycles of length four observed in corresponding matrix are removed. Each matrix is evaluated over a noisy Additive White Gaussian Noise (AWGN) channel. Bit Error rate and Frame error rate is calculated. The results are compared with randomly generated best parity check matrix. Simulation results shows that proposed method successfully overcomes the computational complexity and meets the near Shannon limit.

Ultra low bit error rate (BER) is required in high speed communications such as the 100 Gbit/s long haul optic communications. In this paper, a type of simple product codes is proposed using low density parity check (LDPC) codes with very high rate algebraic block codes by exploiting the sparsity of LDPC decoding failure and sparse error distribution in an LDPC frame with errors. Specifically, different with traditional product codes, the information bits are first encoded with very high rate algebraic block codes of low encoding and decoding complexity. Even the block codes correcting a single error using algebraic decoding method can be used. Then, LDPC codes are used as the inner code to obtain a low decoding threshold using iterative decoding. This design scheme can achieve the ultra low bit error rate at relatively low signal-to-noise ratios. The cost of the proposed scheme is the relatively large latency, which is not so critical for the ultra high speed communications.

Both polar code and Low-Density Parity-Check (LDPC) code have been adopted in 3GPP eMBB scenario. Some scholars have proposed a serial concatenation structure combining these two codes. However, the inner code needs to add redundant bits to protect the redundant bits of the outer code in the serial concatenation. In this paper, we propose a parallel concatenation code combining polar code and LDPC code on the AWGN channel, which does not distinguish the inner code from the outer code. In the proposed concatenated structure, the BP algorithm is used to decode polar code, and the output soft information of BP decoder is logarithmically processed before LDPC decoding. According to the simulation results, compared with the serial concatenated code with the same code rate and code length, the parallel concatenated code has better BER(Bit-Error-Rate) performance.

The application of Low Density Parity Check (LDPC) code in the anti-interference systems has drawn an increasing attention, due to its admiring performance which is very close to the theory limit. This paper focuses on a LDPC encoded slow frequency hopping (SFH) communication system with partial-band interference. Firstly, a modified soft- decision algorithm based on the utilization of interference information is proposed, and its performance is compared with some other soft-decision methods. Secondly, with numerical simulation, the influence of code rate, code length and the number of symbols per hops on the performance of the system with partial band noise interference is illustrated and examined in detail. Considering the great influence of hops per symbol on the performance, interleaver should be used and its influence on the performance is further examined by simulation. Finally, some constructive advises for the design of LDPC coded SFH system are given. Simulation results show that, with a reasonable design, the SFH system with LDPC code could achieve a desirable performance.

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.

In communication systems, the transmitted data is corrupted by channel perturbations, such as noise and fading, which affect the reliability of the received data. Error correction codes are employed to mitigate channel perturbations. However, design and implementation of good and efficient error correction codes remains an open problem. In this paper, Low Density Parity Check (LDPC) codes are considered as they provide a reasonable trade-off between computational complexity and reliability. Good LDPC codes should ideally provide low complexity, close to capacity acheivable transmission rate, high coding threshold, and high decoding stability. In this paper, we investigate a joint LDPC code optimization algorithm using Genetic Algorithm (GA) and Linear Programming (LP) to determine the variable nodes and check nodes degrees distributions. EXIT chart analysis and Frame Error Rate (FER) performance are used to validate the proposed method.