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

Physical layer forward error correcetion in DVB-S2 networks.

Thesis (M.Sc.Eng.)-University of KwaZulu-Natal, Durban, 2012.The rapid growth of wireless systems has shown little sign of ceasing, due to increased consumer demand for reliable interactive services. A key component of the development has centered on satellite networks, which allows provision of services in scenarios where terrestrial systems are not viable. The Digital Video Broadcasting-Satellite Second Generation (DVB-S2) standard was developed for use in satellite broadcast applications, the foremost being video broadcasting. Inherent to DVB-S2 is a powerful forward error correction (FEC) module, present in both the Physical and Data Link Layer. Improving the error correcting capability of the FEC is a natural advent in improving the quality of service of the protocol. This is more crucial in real time satellite video broadcast where retransmission of data is not viable, due to high latency. The Physical Layer error correcting capability is implemented in the form of a concatenated BCH-LDPC code. The DVB-S2 standard does not define the decoding structure for the receiver system however many powerful decoding systems have been presented in the literature; the Belief Propagation-Chase concatenated decoder being chief amongst them. The decoder utilizes the concept of soft information transfer between the Chase and Belief Propagation (BP) decoders to provide improved error correcting capability above that of the component decoders. The following dissertation is motivated by the physical layer (PL) FEC scheme, focused on the concatenated Chase-BP decoder. The aim is to generate results based on the BP-Chase decoder in a satellite channel as well as improve the error correcting capability. The BP-Chase decoder has shown to be very powerful however the current literature provides performance results only in AWGN channels. The AWGN channel however is not an accurate representation of a land-mobile satellite (LMS) channel; it does not consider the effect of shadowing, which is prevalent in satellite systems. The development of Markov chain models have allowed for better description of the characteristics of the LMS channel. The outcome being the selection of a Ku band LMS channel model. The selected LMS channel model is composed of 3 states, each generating a different degree of shadowing. The PL system has been simulated using the LMS channel and BP-Chase receiver to provide a more accurate representation of performance of a DVB-S2 network. The effect of shadowing has shown to reduce coding performance by approximately 4dB, measured over several code lengths and decoders, when compared with AWGN performance results. The second body of work aims to improve the error correcting capability of the BP-Chase decoder, concentrating on improving the LDPC decoding module performance. The LDPC system is the basis for the powerful error correcting ability of the concatenated scheme. In attempting to improve the LDPC decoder a reciprocal improvement is expected in the overall decoding performance of the concatenated decoder. There have been several schemes presented which improve BP performance. The BP-Ordered statistics decoder (OSD) was selected through a process of literary review; a novel decoding structure is presented incorporating the BP-OSD decoder into the BP-Chase structure. The result of which is the BP-OSD-Chase decoder. The decoder contains two stages of concatenation; the first stage implements the BPOSD algorithm which decodes the LDPC code and the second stage decodes the BCH code using the Chase algorithm. Simulation results of the novel decoder implementation in the DVBS2 PL show a coding gain of 0.45dB and 0.15dB versus the BP and BP-Chase decoders respectively, across both the AWGN and LMS channel

Self-concatenated code design and its application in power-efficient cooperative communications

In this tutorial, we have focused on the design of binary self-concatenated coding schemes with the help of EXtrinsic Information Transfer (EXIT) charts and Union bound analysis. The design methodology of future iteratively decoded self-concatenated aided cooperative communication schemes is presented. In doing so, we will identify the most important milestones in the area of channel coding, concatenated coding schemes and cooperative communication systems till date and suggest future research directions

PARALLEL SUBSPACE SUBCODES OF REED-SOLOMON CODES FOR MAGNETIC RECORDING CHANNELS

Read channel architectures based on a single low-density parity-check (LDPC) code are being considered for the next generation of hard disk drives. However, LDPC-only solutions suffer from the error floor problem, which may compromise reliability, if not handled properly. Concatenated architectures using an LDPC code plus a Reed-Solomon (RS) code lower the error-floor at high signal-to-noise ratio (SNR) at the price of a reduced coding gain and a less sharp waterfall region at lower SNR. This architecture fails to deal with the error floor problem when the number of errors caused by multiple dominant trapping sets is beyond the error correction capability of the outer RS code. The ultimate goal of a sharper waterfall at the low SNR region and a lower error floor at high SNR can be approached by introducing a parallel subspace subcode RS (SSRS) code (PSSRS) to replace the conventional RS code. In this new LDPC+PSSRS system, the PSSRS code can help localize and partially destroy the most dominant trapping sets. With the proposed iterative parallel local decoding algorithm, the LDPC decoder can correct the remaining errors by itself. The contributions of this work are: 1) We propose a PSSRS code with parallel local SSRS structure and a three-level decoding architecture, which enables a trade off between performance and complexity; 2) We propose a new LDPC+PSSRS system with a new iterative parallel local decoding algorithm with a 0.5dB+ gain over the conventional two-level system. Its performance for 4K-byte sectors is close to the multiple LDPC-only architectures for perpendicular magneticxviiirecording channels; 3) We develop a new decoding concept that changes the major role of the RS code from error correcting to a "partial" trapping set destroyer

Advanced channel coding techniques using bit-level soft information

In this dissertation, advanced channel decoding techniques based on bit-level soft information are studied. Two main approaches are proposed: bit-level probabilistic iterative decoding and bit-level algebraic soft-decision (list) decoding (ASD). In the first part of the dissertation, we first study iterative decoding for high density parity check (HDPC) codes. An iterative decoding algorithm, which uses the sum product algorithm (SPA) in conjunction with a binary parity check matrix adapted in each decoding iteration according to the bit-level reliabilities is proposed. In contrast to the common belief that iterative decoding is not suitable for HDPC codes, this bit-level reliability based adaptation procedure is critical to the conver-gence behavior of iterative decoding for HDPC codes and it significantly improves the iterative decoding performance of Reed-Solomon (RS) codes, whose parity check matrices are in general not sparse. We also present another iterative decoding scheme for cyclic codes by randomly shifting the bit-level reliability values in each iteration. The random shift based adaptation can also prevent iterative decoding from getting stuck with a significant complexity reduction compared with the reliability based parity check matrix adaptation and still provides reasonable good performance for short-length cyclic codes. In the second part of the dissertation, we investigate ASD for RS codes using bit-level soft information. In particular, we show that by carefully incorporating bit¬level soft information in the multiplicity assignment and the interpolation step, ASD can significantly outperform conventional hard decision decoding (HDD) for RS codes with a very small amount of complexity, even though the kernel of ASD is operating at the symbol-level. More importantly, the performance of the proposed bit-level ASD can be tightly upper bounded for practical high rate RS codes, which is in general not possible for other popular ASD schemes. Bit-level soft-decision decoding (SDD) serves as an efficient way to exploit the potential gain of many classical codes, and also facilitates the corresponding per-formance analysis. The proposed bit-level SDD schemes are potential and feasible alternatives to conventional symbol-level HDD schemes in many communication sys-tems

Comparison of code rate and transmit diversity in MIMO systems

A thesis submitted in ful lment of the requirements for the degree of Master of Science in the Centre of Excellence in Telecommunications and Software School of Electrical and Information Engineering, March 2016In order to compare low rate error correcting codes to MIMO schemes with transmit diversity, two systems with the same throughput are compared. A VBLAST MIMO system with (15; 5) Reed-Solomon coding is compared to an Alamouti MIMO system with (15; 10) Reed-Solomon coding. The latter is found to perform signi cantly better, indicating that transmit diversity is a more e ective technique for minimising errors than reducing the code rate. The Guruswami-Sudan/Koetter-Vardy soft decision decoding algorithm was implemented to allow decoding beyond the conventional error correcting bound of RS codes and VBLAST was adapted to provide reliability information. Analysis is also performed to nd the optimal code rate when using various MIMO systems.MT201

Perturbed Adaptive Belief Propagation Decoding for High-Density Parity-Check Codes

Algebraic codes such as BCH code are receiving renewed interest as their short block lengths and low/no error floors make them attractive for ultra-reliable low-latency communications (URLLC) in 5G wireless networks. This article aims at enhancing the traditional adaptive belief propagation (ABP) decoding, which is a soft-in-soft-out (SISO) decoding for high-density parity-check (HDPC) algebraic codes, such as Reed-Solomon (RS) codes, Bose-Chaudhuri-Hocquenghem (BCH) codes, and product codes. The key idea of traditional ABP is to sparsify certain columns of the parity-check matrix corresponding to the least reliable bits with small log-likelihood-ratio (LLR) values. This sparsification strategy may not be optimal when some bits have large LLR magnitudes but wrong signs. Motivated by this observation, we propose a Perturbed ABP (P-ABP) to incorporate a small number of unstable bits with large LLRs into the sparsification operation of the parity-check matrix. In addition, we propose to apply partial layered scheduling or hybrid dynamic scheduling to further enhance the performance of P-ABP. Simulation results show that our proposed decoding algorithms lead to improved error correction performances and faster convergence rates than the prior-art ABP variants

A STUDY OF ERASURE CORRECTING CODES

This work focus on erasure codes, particularly those that of high performance, and the related decoding algorithms, especially with low computational complexity. The work is composed of different pieces, but the main components are developed within the following two main themes. Ideas of message passing are applied to solve the erasures after the transmission. Efficient matrix-representation of the belief propagation (BP) decoding algorithm on the BEG is introduced as the recovery algorithm. Gallager's bit-flipping algorithm are further developed into the guess and multi-guess algorithms especially for the application to recover the unsolved erasures after the recovery algorithm. A novel maximum-likelihood decoding algorithm, the In-place algorithm, is proposed with a reduced computational complexity. A further study on the marginal number of correctable erasures by the In-place algoritinn determines a lower bound of the average number of correctable erasures. Following the spirit in search of the most likable codeword based on the received vector, we propose a new branch-evaluation- search-on-the-code-tree (BESOT) algorithm, which is powerful enough to approach the ML performance for all linear block codes. To maximise the recovery capability of the In-place algorithm in network transmissions, we propose the product packetisation structure to reconcile the computational complexity of the In-place algorithm. Combined with the proposed product packetisation structure, the computational complexity is less than the quadratic complexity bound. We then extend this to application of the Rayleigh fading channel to solve the errors and erasures. By concatenating an outer code, such as BCH codes, the product-packetised RS codes have the performance of the hard-decision In-place algorithm significantly better than that of the soft-decision iterative algorithms on optimally designed LDPC codes