Error-correction coding for high-density magnetic recording channels.

Finally, a promising algorithm which combines RS decoding algorithm with LDPC decoding algorithm together is investigated, and a reduced-complexity modification has been proposed, which not only improves the decoding performance largely, but also guarantees a good performance in high signal-to-noise ratio (SNR), in which area an error floor is experienced by LDPC codes.The soft-decision RS decoding algorithms and their performance on magnetic recording channels have been researched, and the algorithm implementation and hardware architecture issues have been discussed. Several novel variations of KV algorithm such as soft Chase algorithm, re-encoded Chase algorithm and forward recursive algorithm have been proposed. And the performance of nested codes using RS and LDPC codes as component codes have been investigated for bursty noise magnetic recording channels.Future high density magnetic recoding channels (MRCs) are subject to more noise contamination and intersymbol interference, which make the error-correction codes (ECCs) become more important. Recent research of replacement of current Reed-Solomon (RS)-coded ECC systems with low-density parity-check (LDPC)-coded ECC systems obtains a lot of research attention due to the large decoding gain for LDPC-coded systems with random noise. In this dissertation, systems aim to maintain the RS-coded system using recent proposed soft-decision RS decoding techniques are investigated and the improved performance is presented

Symbol level decoding of Reed-Solomon codes with improved reliability information over fading channels

A thesis submitted to the Faculty of Engineering and the Built Environment, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the degree of Doctor of Philosophy in the School of Electrical and Information Engineering, 2016Reliable and e cient data transmission have been the subject of current research, most especially in realistic channels such as the Rayleigh fading channels. The focus of every new technique is to improve the transmission reliability and to increase the transmission capacity of the communication links for more information to be transmitted. Modulation schemes such as M-ary Quadrature Amplitude Modulation (M-QAM) and Orthogonal Frequency Division Multiplexing (OFDM) were developed to increase the transmission capacity of communication links without additional bandwidth expansion, and to reduce the design complexity of communication systems. On the contrary, due to the varying nature of communication channels, the message transmission reliability is subjected to a couple of factors. These factors include the channel estimation techniques and Forward Error Correction schemes (FEC) used in improving the message reliability. Innumerable channel estimation techniques have been proposed independently, and in combination with di erent FEC schemes in order to improve the message reliability. The emphasis have been to improve the channel estimation performance, bandwidth and power consumption, and the implementation time complexity of the estimation techniques. Of particular interest, FEC schemes such as Reed-Solomon (RS) codes, Turbo codes, Low Density Parity Check (LDPC) codes, Hamming codes, and Permutation codes, are proposed to improve the message transmission reliability of communication links. Turbo and LDPC codes have been used extensively to combat the varying nature of communication channels, most especially in joint iterative channel estimation and decoding receiver structures. In this thesis, attention is focused on using RS codes to improve the message reliability of a communication link because RS codes have good capability of correcting random and burst errors, and are useful in di erent wireless applications. This study concentrates on symbol level soft decision decoding of RS codes. In this regards, a novel symbol level iterative soft decision decoder for RS codes based on parity-check equations is developed. This Parity-check matrix Transformation Algorithm (PTA) is based on the soft reliability information derived from the channel output in order to perform syndrome checks in an iterative process. Performance analysis verify that this developed PTA outperforms the conventional RS hard decision decoding algorithms and the symbol level Koetter and Vardy (KV ) RS soft decision decoding algorithm. In addition, this thesis develops an improved Distance Metric (DM) method of deriving reliability information over Rayleigh fading channels for combined demodulation with symbol level RS soft decision decoding algorithms. The newly proposed DM method incorporates the channel state information in deriving the soft reliability information over Rayleigh fading channels. Analysis verify that this developed metric enhances the performance of symbol level RS soft decision decoders in comparison with the conventional method. Although, in this thesis, the performance of the developed DM method of deriving soft reliability information over Rayleigh fading channels is only veri ed for symbol level RS soft decision decoders, it is applicable to any symbol level soft decision decoding FEC scheme. Besides, the performance of the all FEC decoding schemes plummet as a result of the Rayleigh fading channels. This engender the development of joint iterative channel estimation and decoding receiver structures in order to improve the message reliability, most especially with Turbo and LDPC codes as the FEC schemes. As such, this thesis develops the rst joint iterative channel estimation and Reed- Solomon decoding receiver structure. Essentially, the joint iterative channel estimation and RS decoding receiver is developed based on the existing symbol level soft decision KV algorithm. Consequently, the joint iterative channel estimation and RS decoding receiver is extended to the developed RS parity-check matrix transformation algorithm. The PTA provides design ease and exibility, and lesser computational time complexity in an iterative receiver structure in comparison with the KV algorithm. Generally, the ndings of this thesis are relevant in improving the message transmission reliability of a communication link with RS codes. For instance, it is pertinent to numerous data transmission technologies such as Digital Audio Broadcasting (DAB), Digital Video Broadcasting (DVB), Digital Subscriber Line (DSL), WiMAX, and long distance satellite communications. Equally, the developed, less computationally intensive, and performance e cient symbol level decoding algorithm for RS codes can be use in consumer technologies like compact disc and digital versatile disc.GS201

A Test Vector Generation Method Based on Symbol Error Probabilities for Low-Complexity Chase Soft-Decision Reed-Solomon Decoding

© 2019 IEEE. Personal use of this material is permitted. Permissíon from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertisíng or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.[EN] This paper presents a low-complexity chase (LCC) decoder for Reed-Solomon (RS) codes, which uses a novel method for the selection of test vectors that is based on the analysis of the symbol error probabilities derived from simulations. Our results show that the same performance as the classical LCC is achieved with a lower number of test vectors. For example, the amount of test vectors is reduced by half and by 1/16 for the RS(255,239) and RS(255,129) codes, respectively. We provide an evidence that the proposed method is suitable for RS codes with different rates and Galois fields. In order to demonstrate that the proposed method results in a reduction of the complexity of the decoder, we also present a hardware architecture for an RS(255,239) decoder that uses 16 test vectors. This decoder achieves a coding gain of 0.56 dB at the frame error rate that is equal to 10(-6) compared with hard-decision decoding, which is higher than that of an eta = 5 LCC. The implementation results in ASIC show that a throughput of 3.6 Gb/s can be reached in a 90-nm process and 29.1XORs are required. The implementation results in Virtex-7 FPGA devices show that the decoder reaches 2.5 Gb/s and requires 5085 LUTs.This work was supported by the Spanish Ministerio de Economia y Competitividad and FEDER under Grant TEC2015-70858-C2-2-R. This paper was recommended by Associate Editor M. Boukadoum.Valls Coquillat, J.; Torres Carot, V.; Canet Subiela, MJ.; García-Herrero, FM. (2019). A Test Vector Generation Method Based on Symbol Error Probabilities for Low-Complexity Chase Soft-Decision Reed-Solomon Decoding. IEEE Transactions on Circuits and Systems I Regular Papers. 66(6):2198-2207. https://doi.org/10.1109/TCSI.2018.2882876S2198220766

Iterative Algebraic Soft-Decision List Decoding of Reed-Solomon Codes

In this paper, we present an iterative soft-decision decoding algorithm for Reed-Solomon codes offering both complexity and performance advantages over previously known decoding algorithms. Our algorithm is a list decoding algorithm which combines two powerful soft decision decoding techniques which were previously regarded in the literature as competitive, namely, the Koetter-Vardy algebraic soft-decision decoding algorithm and belief-propagation based on adaptive parity check matrices, recently proposed by Jiang and Narayanan. Building on the Jiang-Narayanan algorithm, we present a belief-propagation based algorithm with a significant reduction in computational complexity. We introduce the concept of using a belief-propagation based decoder to enhance the soft-input information prior to decoding with an algebraic soft-decision decoder. Our algorithm can also be viewed as an interpolation multiplicity assignment scheme for algebraic soft-decision decoding of Reed-Solomon codes.Comment: Submitted to IEEE for publication in Jan 200

An Iteratively Decodable Tensor Product Code with Application to Data Storage

The error pattern correcting code (EPCC) can be constructed to provide a syndrome decoding table targeting the dominant error events of an inter-symbol interference channel at the output of the Viterbi detector. For the size of the syndrome table to be manageable and the list of possible error events to be reasonable in size, the codeword length of EPCC needs to be short enough. However, the rate of such a short length code will be too low for hard drive applications. To accommodate the required large redundancy, it is possible to record only a highly compressed function of the parity bits of EPCC's tensor product with a symbol correcting code. In this paper, we show that the proposed tensor error-pattern correcting code (T-EPCC) is linear time encodable and also devise a low-complexity soft iterative decoding algorithm for EPCC's tensor product with q-ary LDPC (T-EPCC-qLDPC). Simulation results show that T-EPCC-qLDPC achieves almost similar performance to single-level qLDPC with a 1/2 KB sector at 50% reduction in decoding complexity. Moreover, 1 KB T-EPCC-qLDPC surpasses the performance of 1/2 KB single-level qLDPC at the same decoder complexity.Comment: Hakim Alhussien, Jaekyun Moon, "An Iteratively Decodable Tensor Product Code with Application to Data Storage

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