Iterative Soft Input Soft Output Decoding of Reed-Solomon Codes by Adapting the Parity Check Matrix

An iterative algorithm is presented for soft-input-soft-output (SISO) decoding of Reed-Solomon (RS) codes. The proposed iterative algorithm uses the sum product algorithm (SPA) in conjunction with a binary parity check matrix of the RS code. The novelty is in reducing a submatrix of the binary parity check matrix that corresponds to less reliable bits to a sparse nature before the SPA is applied at each iteration. The proposed algorithm can be geometrically interpreted as a two-stage gradient descent with an adaptive potential function. This adaptive procedure is crucial to the convergence behavior of the gradient descent algorithm and, therefore, significantly improves the performance. Simulation results show that the proposed decoding algorithm and its variations provide significant gain over hard decision decoding (HDD) and compare favorably with other popular soft decision decoding methods.Comment: 10 pages, 10 figures, final version accepted by IEEE Trans. on Information Theor

Segmented GRAND: Combining Sub-patterns in Near-ML Order

The recently introduced maximum-likelihood (ML) decoding scheme called guessing random additive noise decoding (GRAND) has demonstrated a remarkably low time complexity in high signal-to-noise ratio (SNR) regimes. However, the complexity is not as low at low SNR regimes and low code rates. To mitigate this concern, we propose a scheme for a near-ML variant of GRAND called ordered reliability bits GRAND (or ORBGRAND), which divides codewords into segments based on the properties of the underlying code, generates sub-patterns for each segment consistent with the syndrome (thus reducing the number of inconsistent error patterns generated), and combines them in a near-ML order using two-level integer partitions of logistic weight. The numerical evaluation demonstrates that the proposed scheme, called segmented ORBGRAND, significantly reduces the average number of queries at any SNR regime. Moreover, the segmented ORBGRAND with abandonment also improves the error correction performance

Distributed video coding for wireless video sensor networks: a review of the state-of-the-art architectures

Distributed video coding (DVC) is a relatively new video coding architecture originated from two fundamental theorems namely, Slepian–Wolf and Wyner–Ziv. Recent research developments have made DVC attractive for applications in the emerging domain of wireless video sensor networks (WVSNs). This paper reviews the state-of-the-art DVC architectures with a focus on understanding their opportunities and gaps in addressing the operational requirements and application needs of WVSNs

Improving Short-Length LDPC Codes with a CRC and Iterative Ordered Statistic Decoding

We present a CRC-aided decodingscheme of LDPC codes that can outperform the underlying LDPC code underordered statistic decoding (OSD). In this scheme, the CRC is usedjointly with the LDPC code to construct a candidate list, insteadof conventionally being regarded as a detection code to prunethe list generated by the LDPC code alone. As an example weconsider a (128,64) 5G LDPC code with BP decoding, which we canoutperform by 2dB using a (128,72) LDPC code in combinationwith a 8-bit CRC under OSD order of 3. The CRC-aided decoding scheme also achieves a better performance than the conventional one where CRC is used to prune the list. A manageable complexity can be achievedwith iterative reliability based OSD, which is demonstrated toperform well with a small OSD order

Distributed Turbo Product Coding Techniques Over Cooperative Communication Systems

In this dissertation, we propose a coded cooperative communications framework based on Distributed Turbo Product Code (DTPC). The system uses linear block Extended Bose-Chaudhuri-Hochquenghem (EBCH) codes as component codes. The source broadcasts the EBCH coded frames to the destination and nearby relays. Each relay constructs a product code by arranging the corrected bit sequences in rows and re-encoding them vertically using EBCH as component codes to obtain an Incremental Redundancy (IR) for source\u27s data. Under this frame, we have investigated a number of interesting and important issues. First, to obtain, independent vertical parities from each relay in the same code space, we propose circular interleaving of the decoded EBCH rows before reencoding vertically. We propose and derive a novel soft information relay for the DTPC over cooperative network based on EBCH component codes. The relay generates Log-Likelihood Ratio (LLR) values for the decoded rows are used to construct a product code by re-encoding the matrix along the columns using a novel soft block encoding technique to obtain soft parity bits with different reliabilities that can be used as soft IR for source\u27s data which is forwarded to the destination. To minimize the overall decoding errors, we propose a power allocation method for the distributed encoded system when the channel attenuations for the direct and relay channels are known. We compare the performance of our proposed power allocation method with the fixed power assignments for DTPC system. We also develop a power optimization algorithm to check the validity of our proposed power allocation algorithm. Results for the power allocation and the power optimization prove on the potency of our proposed power allocation criterion and show the maximum possible attainable performance from the DTPC cooperative system. Finally, we propose new joint distributed Space-Time Block Code (STBC)-DTPC by generating the vertical parity on the relay and transmitting it to the destination using STBC on the source and relay. We tested our proposed system in a fast fading environment on the three channels connecting the three nodes in the cooperative network

Application of wavelets and artificial neural network for indoor optical wireless communication systems

Abstract This study investigates the use of error control code, discrete wavelet transform (DWT) and artificial neural network (ANN) to improve the link performance of an indoor optical wireless communication in a physical channel. The key constraints that barricade the realization of unlimited bandwidth in optical wavelengths are the eye-safety issue, the ambient light interference and the multipath induced intersymbol interference (ISI). Eye-safety limits the maximum average transmitted optical power. The rational solution is to use power efficient modulation techniques. Further reduction in transmitted power can be achieved using error control coding. A mathematical analysis of retransmission scheme is investigated for variable length modulation techniques and verified using computer simulations. Though the retransmission scheme is simple to implement, the shortfall in terms of reduced throughput will limit higher code gain. Due to practical limitation, the block code cannot be applied to the variable length modulation techniques and hence the convolutional code is the only possible option. The upper bound for slot error probability of the convolutional coded dual header pulse interval modulation (DH-PIM) and digital pulse interval modulation (DPIM) schemes are calculated and verified using simulations. The power penalty due to fluorescent light interference (FL I) is very high in indoor optical channel making the optical link practically infeasible. A denoising method based on a DWT to remove the FLI from the received signal is devised. The received signal is first decomposed into different DWT levels; the FLI is then removed from the signal before reconstructing the signal. A significant reduction in the power penalty is observed using DWT. Comparative study of DWT based denoising scheme with that of the high pass filter (HPF) show that DWT not only can match the best performance obtain using a HPF, but also offers a reduced complexity and design simplicity. The high power penalty due to multipath induced ISI makes a diffuse optical link practically infeasible at higher data rates. An ANN based linear and DF architectures are investigated to compensation the ISI. Unlike the unequalized cases, the equalized schemes don‘t show infinite power penalty and a significant performance improvement is observed for all modulation schemes. The comparative studies substantiate that ANN based equalizers match the performance of the traditional equalizers for all channel conditions with a reduced training data sequence. The study of the combined effect of the FLI and ISI shows that DWT-ANN based receiver perform equally well in the present of both interference. Adaptive decoding of error control code can offer flexibility of selecting the best possible encoder in a given environment. A suboptimal ?soft‘ sliding block convolutional decoder based on the ANN and a 1/2 rate convolutional code with a constraint length is investigated. Results show that the ANN decoder can match the performance of optimal Viterbi decoder for hard decision decoding but with slightly inferior performance compared to soft decision decoding. This provides a foundation for further investigation of the ANN decoder for convolutional code with higher constraint length values. Finally, the proposed DWT-ANN receiver is practically realized in digital signal processing (DSP) board. The output from the DSP board is compared with the computer simulations and found that the difference is marginal. However, the difference in results doesn‘t affect the overall error probability and identical error probability is obtained for DSP output and computer simulations

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