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

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.

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.

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.

Power line communication for home networking is a new convenient method. However, power line communication makes degradation because of the impulsive interference generated by electrical appliances. Therefore, it is the first problem we need to be solved. In this paper, we apply LDPC (low density parity check) codes to AWAN (additive white class a noise) channels which is usually used as the model of impulsive noise environment of power line channels. We propose a modification to Log-BP (log domain belief propagation) decoding which is suitable for AWAN channels. At last, we show the BER (bit error rate) performance of the modified Log-BP decoding over AWAN channels by Monte-Carlo simulation.

In this paper, a modified weighted bit-flipping (WBF) algorithm is proposed for finite geometry low-density parity-check (FG-LDPC) codes. The calculation for the flipping function in the new method includes all the elements in sum product algorithm (SPA) instead of the minimum one in most existing methods. Simulation results show that the proposed method exhibits better performance than the best method available in the literature so far. The performances of different algorithms are also considered in random constructed LDPC codes. The reliability ratio based WBF (RRWBF) method performs the best in this kind of codes and the proposed method performs very closely to the RRWBF method. The decoding complexities for both FG-LDPC and random constructed LDPC are also analyzed.

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).

Scheduling strategy is considered an important aspect of belief-propagation (BP) decoding of low-density parity-check (LDPC) codes because it affects the decoder's convergence rate, decoding complexity and error-correction performance. In this paper, we propose two new scheduling strategies for the BP decoding of non-binary LDPC (NB-LDPC) codes. Both the strategies are devised based on the concept of check node reliability and employ a heuristically defined threshold which can adapt to the communication channel variations. As the scheduling strategies only update a subset of the check nodes in each iteration, they result in reduced iteration cost. Furthermore, since the BP performs suboptimally for finite-length LDPC codes, especially for short-length LDPC codes, by enhancing the message propagation over the Tanner Graphs of short-length NB-LDPC codes, the new scheduling strategies can even improve the error-correction performances of BP decoding. Simulation results demonstrate that the new scheduling strategies provide good performance/complexity tradeoffs.

The performance of low-density parity-check (LDPC) codes can be evaluated by using the dual adaptive importance sampling (DAIS) method. To further accelerate the convergence speed of simulation, an improved method is proposed in which the biased distribution is multiplied with an auxiliary biased function. In this proposed method, samples are limited in the restricted region, where most of the events result in decoding failure, by multiplying the original biased distribution of DAIS method by a second bias. This scheme speeds up the convergence of simulation in the restricted region. Compared with the traditional DAIS method, simulation results for two specific LDPC codes verify that this proposed method achieves the significant simulation gain without sacrificing the accuracy.

Low Density Parity Check (LDPC) codes are Shannon-Limit approaching codes. Shannon stated the theoretical bounds for digital data transmission in a given channel capacity with error correction coding. Spread Spectrum also called as CDMA (Code Division Multiple Access) is an efficient way of radio wave communication deployed in commercial broadcasts, ham radios, military communications, police radios, etc. CDMA is a means of signal transmission in which the signal frequency is spread over a very wide bandwidth. Spreading of data is achieved prior to transmission with the help of an independent code called ‘Pseudo Noise Code’ (PN sequences), which is subsequently used in the receiver end to de-spread the signal received in order to recover the signal data. PN sequences based on prime numbers like Legendre & Weil sequences are used in the present work. An impressive part of LDPC lies in its decoding algorithm. Sum-Product Algorithm (SPA) decoding offers the best error performance amongst all the types of decoding techniques of LDPC codes and thus applied here. This paper demonstrates an idea of introducing LDPC codes along with DS-Spread Spectrum technique using Legendre & Weil sequences. In the present work, the encoding and decoding algorithms are applied after spreading of the signal. SPA decoding technique is successfully employed and simulated results are plotted taking an example design to illustrate the concepts discussed above.

In this paper we propose an innovative channel coding scheme called 'Accumulate Repeat Accumulate codes' (ARA). This class of codes can be viewed as serial turbo-like codes, or as a subclass of Low Density Parity Check (LDPC) codes, thus belief propagation can be used for iterative decoding of ARA codes on a graph. The structure of encoder for this class can be viewed as precoded Repeat Accumulate (RA) code or as precoded Irregular Repeat Accumulate (IRA) code, where simply an accumulator is chosen as a precoder. Thus ARA codes have simple, and very fast encoder structure when they representing LDPC codes. Based on density evolution for LDPC codes through some examples for ARA codes, we show that for maximum variable node degree 5 a minimum bit SNR as low as 0.08 dB from channel capacity for rate 1/2 can be achieved as the block size goes to infinity. Thus based on fixed low maximum variable node degree, its threshold outperforms not only the RA and IRA codes but also the best known LDPC codes with the dame maximum node degree. Furthermore by puncturing the accumulators any desired high rate codes close to code rate 1 can be obtained with thresholds that stay close to the channel capacity thresholds uniformly. Iterative decoding simulation results are provided. The ARA codes also have projected graph or protograph representation that allows for high speed decoder implementation.

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.

Effect of channel mismatch on decoding performance of low density parity check (LDPC) codes over binary symmetric channel (BSC) under sum-product algorithm (SPA) is analyzed in this paper. Density evolution is employed in theoretical analysis to get optimal initial value for SPA. Based on the results, a modified SPA algorithm is proposed. When decoding using this modified SPA algorithm, no channel information is needed at the decoder side. This will be of significant value for time-varying channels. Theoretical claims from density evolution are confirmed by extensive simulations. Our simulations show that by fixing the initial value for all channel conditions, decoding performance can be improved. One channel state estimation algorithm is proposed in this paper based on the error detection ability of LDPC codes. Maximum number of iterations taken when decoding a LDPC code can be dynamically adjusted according to the estimated channel state. Further performance improvements can be achieved by using the dynamic iteration number adjusting scheme together with the modified sum-product algorithm.

In this paper, we focus on the Generalized Belief Propagation (GBP) algorithm to solve trapping sets in Low-Density Parity-Check (LDPC) codes. Trapping sets are topological structures in Tanner graphs of LDPC codes that are not correctly decoded by Belief Propagation (BP), leading to exhibit an error-floor in the Bit-Error Rate (BER). Stemming from statistical physics of spin glasses, GBP consists in passing messages between clusters of Tanner graph nodes in another graph called the region-graph. Here, we introduce a specific clustering of nodes, based on a novel local loopfree principle, that breaks trapping sets such that the resulting region-graph is locally loopfree. We then construct a hybrid decoder made of BP and GBP that proves to be a powerful decoder as it clearly improves the BER and defeats the error-floor.

Two new design approaches for constructing Low-Density Parity-Check (LDPC) codes are proposed. One is used to design regular Quasi-Cyclic LDPC (QC-LDPC) codes with girth at least 8. The other is used to design irregular LDPC codes. Both of their parity-check matrices are composed of Circulant Permutation Matrices (CPMs). When iteratively decoded with the Sum-Product Algorithm (SPA), these proposed codes exhibit good performances over the AWGN channel.