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Table Of Integrals Series And Products

Data Reduction And Error Analysis For The Physical Sciences

This report describes the progress made towards the completion of a specific task on error-correcting coding. The proposed research consisted of investigating the use of modulation block codes as the inner code of a concatenated coding system in order to improve the overall space link communications performance. The study proposed to identify and analyze candidate codes that will complement the performance of the overall coding system which uses the interleaved RS (255,223) code as the outer code.

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Error-correction coding

The power-line communication (PLC) channel causes information-bearing signals to be affected by impulsive noise and the effects of the multipath fading. To mitigate these effects, we propose the employment of non-binary turbo codes, since non-binary error-correcting codes generally promise an enhanced performance in such harsh environments. In this paper, we investigate the performance of non-binary turbo-codes on PLC channels that exhibit frequency selectivity with additive Middleton Class A noise and compare with a comparable binary turbo-coded PLC system. In order to reduce the effect of multipath and impulsive noise, orthogonal frequency-division multiplexing (OFDM) with non-linear receivers (blanking and clipping) have been employed. The system is examined on extremely impulsive channels where the value of the impulsive index (A) is 0.01 and the noise ratio (Γ) is 0.01. The results show that non-binary turbo codes are very robust and achieve a large gain over binary turbo codes on PLC channels.

Non-binary turbo-coded OFDM-PLC system in the presence of impulsive noise

Non-binary low-density parity-check (NB-LDPC) codes show higher error-correcting performance than binary low-density parity-check (LDPC) codes when the codeword length is moderate and/or the channel has bursts of errors. The need for high-speed decoders for future digital communications led to the investigation of optimized NB-LDPC decoding algorithms and efficient implementations that target high throughput and low energy consumption levels. We carried out a comprehensive survey of existing NB-LDPC decoding hardware that targets the optimization of these parameters. Even though existing NB-LDPC decoders are optimized with respect to computational complexity and memory requirements, they still lag behind their binary counterparts in terms of throughput, power and area optimization. This study contributes to an overall understanding of the state-of-the-art on application-specific integrated-circuit (ASIC), field-programmable gate array (FPGA) and graphics processing units (GPU) based systems, and highlights the current challenges that still have to be overcome on the path to more efficient NB-LDPC decoder architectures. 

/pdf/a-survey-on-high-throughput-non-binary-ldpc-decoders-asic-ragex5n4.pdf

A Survey on High-Throughput Non-Binary LDPC Decoders: ASIC, FPGA, and GPU Architectures

In this study, the performance analyses of the proposed turbo-coded orthogonal frequency division multiplexing (T-COFDM) are investigated over the power-line communication with lognormal channel gain based on derived effective complex-valued ratio distributions of the individual and combined noise samples at the zero-forcing equaliser output. The effective noise samples are derived in the presence of Nakagami-m background interference (BI) noise, Middleton class A impulsive noise (MCAIN) and their combination. The performance of the turbo code has been improved by computing the exact log-likelihood ratio using derived distributions, with the derivation of pairwise error probability and the average upper-bounds (AUBs). Moreover, the bit error rate (BER) degradation in the conventional T-COFDM system has been improved by deriving two clipping thresholds to combat the effect of the non-Gaussian noise, the first one has been derived in the presence of the impulsive noise only modelled by MCAIN model and the second one in the presence of combined Nakagami-m BI noise and MCAIN model. Monte Carlo simulations demonstrate the significant BER improvements of the proposed T-COFDM system compared to the improved conventional T-COFDM system with a close agreement to the AUBs derivation and analytical BER expression.

/pdf/performance-evaluation-of-t-cofdm-under-combined-noise-in-4tn0bu3z5o.pdf

Performance evaluation of T-COFDM under combined noise in PLC with log-normal channel gain using exact derived noise distributions

In this study, the performance of irregular low-density parity check (LDPC) coded orthogonal frequency division multiplexing (COFDM) utilising 4096 quadrature amplitude modulation (4096-QAM) is investigated over multipath power-line communication (PLC) channel. The effective complex-valued ratio distributions of the noise samples at the zero-forcing equaliser output considering both frequency-selective multipath PLCs, background and impulsive noise are derived, in addition to the condition for optimum detection of 4096-QAM and the bit error rate (BER). Moreover, the performance of the LDPC decoder is improved by computing the log-likelihood ratios (LLRs) required for soft decoding based on the derived probability density functions. Numerical results obtained using the newly derived LLRs demonstrate a significant performance improvement compared to the conventional receiver that uses blanking impulsive noise mitigation method and LLR computed based on the Gaussian distribution. Furthermore, EXtrinsic Information Transfer chart analysis demonstrates that the proposed approach requires fewer iterations for convergence compared to the conventional receiver. Finally, utilising channel bandwidth of 22.4 MHz, the proposed system offers an improvement of 111 Mbps over the conventional system to reach a maximum data throughput of 256 Mbps for a signal-to-noise ratio of 39 dB and BER of 10
 -5
.

/pdf/low-density-parity-check-coded-orthogonal-frequency-division-2569y9b178.pdf

Low-density parity check coded orthogonal frequency division multiplexing for PLC in non-Gaussian noise using LLRs derived from effective noise probability density functions

This paper presents an improvement to the end-to-end bit error rate (E2E-BER) performance of turbo-coded orthogonal frequency division multiplexing for physical layer network coding (TC-OFDM-PLNC) over power line communication (PLC) channels in the presence of impulsive noise. A novel detection scheme is introduced to transform the transmit signal constellation based on the frequency-domain channel coefficients in order to improve the performance of the turbo decoder at the relay node and end nodes, respectively, on a link-by-link (LBL) basis utilizing newly derived noise probability density functions (PDFs). Moreover, the closed-form expressions of the BER at the relay, end nodes and E2E are derived, in addition to the E2E average BER upper-bound (AUB). Monte Carlo simulation results closely verify the validity of the derived analytical expressions and reveal that the proposed method utilizing exact derived PDFs for impulsive probability α = 10−1 gives coding gains of 4.5 dB and 8.5 dB at P e = 10−4 for the minimum mean square error (MMSE) and the zero forcing (ZF) equalizers, respectively, compared to the conventional TC-OFDM-PLNC system.

Improved performance of TC-OFDM-PLNC for PLCs using exact derived impulsive noise PDFs

In this paper, we propose Irregular Non-Binary Low Density Parity Check (IR-NB-LDPC) codes with Signed Log Fast Fourier Transform (SL-FFT) decoding algorithm to overcome the harsh environment of power-line communication (PLC) channels. Their performance is compared with Irregular Binary LDPC (IR-B-LDPC) codes using the Sum Product algorithm (SPA). The sparse parity check matrix H of both codes are constructed using progressive edge growth (PEG) algorithm with a novel initialization of the apriori log likelihood ratios (LLR) of each decoder to mitigate the highly impulsive noise in PLC channels. Numerical performance results obtained via simulations show that the proposed system at bit error rate of 10−4 achieves a coding gain of more than 21 dB compared to uncoded system and more than 6 dB compared to IR-B-LDPC codes for the same block length in bits and rates, however, this is accomplished with higher decoding complexity.

Non-binary LDPC coded OFDM in impulsive power line channels

Impulsive noise (IN) can significantly degrade the performance of multi-carrier based communication systems. In order to improve the performance of such systems, conventional IN suppression methods have been proposed to process the signal in the time domain. However, attention has recently focused on using methods implemented in the Frequency Domain (FD). In general, the aim of IN frequency domain estimation schemes is to consider noise samples whose amplitudes are below a fixed threshold as Gaussian distributed noise and therefore are blanked (nulled). In contrast to existing work, this paper presents a novel optimal threshold calculation method to improve the IN frequency domain mitigation methods. The system adopt in this paper is the G.fast standard which uses high order QAM constellations over copper channels. The derived optimum threshold is used in an IN compensation method based on the relationship between two parameters, namely, impulsive Index A and the noise ratio Γ. In order to validate the effectiveness of the proposed scheme, its performance is compared with that of the conventional FD mitigation method which uses a fixed threshold. The impact of both the impulsive Index A and the noise ratio Γ on the DMT-based G.fast copper channel is also discussed in detail. Results show that the proposed method considerably outperforms conventional frequency domain IN mitigation schemes.

Ghanim A. Al-Rubaye

Papers

Performance evaluation of T-COFDM under combined noise in PLC with log-normal channel gain using exact derived noise distributions

Low-density parity check coded orthogonal frequency division multiplexing for PLC in non-Gaussian noise using LLRs derived from effective noise probability density functions

Improved performance of TC-OFDM-PLNC for PLCs using exact derived impulsive noise PDFs

Non-binary LDPC coded OFDM in impulsive power line channels

Optimal Threshold Calculation for Improved Impulsive Noise Mitigation in the Frequency Domain