Constrained codes for digital storage systems are studied. A method for improving signal detection in digital magnetic recording systems is also investigated. The bit stuffing algorithm is a technique for coding constrained sequences by the insertion of bits into an arbitrary data sequence. This approach was previously introduced and applied to the family of $(d, k)$ constraints. Results show that the maximum average rate of the bit stuffing code achieves the Shannon capacity when $k=d+1$ or $k=\infty$, and fails to achieve capacity for all other $(d, k)$ pairs. A modification to the bit stuffing algorithm is proposed that is based on the addition of controlled bit flipping. It is shown that the modified scheme achieves improved average rates over bit stuffing for most $(d, k)$ constraints. All $(d, k)$ constraints for which this scheme produces codes with an average rate equal to the Shannon capacity are determined. A general framework for the construction of $(d, k)$-constrained codes from variable-length source codes is presented. Optimal variable-length codes under the general framework are investigated. The construction of constrained codes from variable-length source codes for encoding unconstrained sequences of independent but biased (as opposed to equiprobable) bits is also considered. It is shown that one can use the Tunstall source coding algorithm to generate optimal codes for a partial class of $(d, k)$ constraints. Bit-stuffing schemes which encode arbitrary inputs into two-dimensional (2-D) constrained arrays are presented. The class of 2-D $(d, \infty)$ constraints as well as the `no isolated bits' constraint are considered. The proposed schemes are based on interleaving biased bits with multiple biases into a 2-D array, while stuffing extra bits when necessary. The performance of the suggested schemes is studied through simulations. A method for joint detection and decoding of coded transmission over magnetic recording channels is considered. The standard framework of turbo equalization is modified to account for the colored noise present in high-density magnetic recording systems. The modified scheme incorporates a noise prediction algorithm, which iteratively and selectively whitens the noise, while utilizing the information produced by the turbo equalization scheme. Simulation results demonstrate the performance improvements obtained by the proposed scheme.

With the massive amount of data produced and stored each year, reliable storage and retrieval of information is more crucial than ever. Robust coding and decoding techniques are critical for correcting errors and maintaining data integrity. Comprising chapters thoughtfully selected from the highly popular Coding and Signal Processing for Magnetic Recording Systems, Advanced Error Control Techniques for Data Storage Systems is a finely focused reference to the state-of-the-art error control and modulation techniques used in storage devices. The book begins with an introduction to error control codes, explaining the theory and basic concepts underlying the codes. Building on these concepts, the discussion turns to modulation codes, paying special attention to run-length limited sequences, followed by maximum transition run (MTR) and spectrum shaping codes. It examines the relationship between constrained codes and error control and correction systems from both code-design and architectural perspectives as well as techniques based on convolution codes. With a focus on increasing data density, the book also explores multi-track systems, soft decision decoding, and iteratively decodable codes such as Low-Density Parity-Check (LDPC) Codes, Turbo codes, and Turbo Product Codes. Advanced Error Control Techniques for Data Storage Systems offers a comprehensive collection of theory and techniques that is ideal for specialists working in the field of data storage systems.

Implementing new architectures and designs for the magnetic recording read channel have been pushed to the limits of modern integrated circuit manufacturing technology. This book reviews advanced coding and signal processing techniques and architectures for magnetic recording systems. Beginning with the basic principles, it examines read/write operations, data organization, head positioning, sensing, timing recovery, data detection, and error correction. It also provides an in-depth treatment of all recording channel subsystems inside a read channel and hard disk drive controller. The final section reviews new trends in coding, particularly emerging codes for recording channels.

The increasing demand for high density storage devices has led to innovative data recording paradigms like optical holographic memories that record and read data in a two-dimensional page-oriented manner. In order to overcome the effects of inter-symbol-interference and noise in holographic channels, sophisticated constrained modulation codes and error correction codes are needed in these systems. This dissertation deals with the information-theoretic and signal processing aspects of holographic storage. On the information-theoretic front, the capacity of two-dimensional runlength-limited channels is analyzed. The construction of two-dimensional runlength-limited codes achieving the capacity lower bounds is discussed. This is a theoretical study on one of the open problems in symbolic dynamics and mathematical physics. The analysis of achievable storage density in holographic channels is useful for building practical systems. In this work, fundamental limits for the achievable volumetric storage density in holographic channels dominated by optical scattering are analyzed for two different recording mechanisms, namely angle multiplexed holography and localized recording. Pixel misregistration is an important signal processing problem in holographic systems. In this dissertation, algorithms for compensating two-dimensional translation and rotational misalignments are discussed and analyzed for Nyquist size apertures with low fill factors. These techniques are applicable for general optical imaging systems.

Constrained Coding and Soft Iterative Decoding is the first work to combine the issues of constrained coding and soft iterative decoding (e.g., turbo and LDPC codes) from a unified point of view. Since constrained coding is widely used in magnetic and optical storage, it is necessary to use some special techniques (modified concatenation scheme or bit insertion) in order to apply soft iterative decoding. Recent breakthroughs in the design and decoding of error-control codes (ECCs) show significant potential for improving the performance of many communications systems. ECCs such as turbo codes and low-density parity check (LDPC) codes can be represented by graphs and decoded by passing probabilistic (a.k.a. `soft') messages along the edges of the graph. This message-passing algorithm yields powerful decoders whose performance can approach the theoretical limits on capacity. This exposition uses `normal graphs,' introduced by Forney, which extend in a natural manner to block diagram representations of the system and provide a simple unified framework for the decoding of ECCs, constrained codes, and channels with memory. Soft iterative decoding is illustrated by the application of turbo codes and LDPC codes to magnetic recording channels. For magnetic and optical storage, an issue arises in the use of constrained coding, which places restrictions on the sequences that can be transmitted through the channel; the use of constrained coding in combination with soft ECC decoders is addressed by the modified concatenation scheme also known as `reverse concatenation.' Moreover, a soft constraint decoder yields additional coding gain from the redundancy in the constraint, which may be of practical interest in the case of optical storage. In addition, this monograph presents several other research results (including the design of sliding-block lossless compression codes, and the decoding of array codes as LDPC codes). Constrained Coding and Soft Iterative Decoding will prove useful to students, researchers and professional engineers who are interested in understanding this new soft iterative decoding paradigm and applying it in communications and storage systems.

Magnetic data storage can be viewed as a data communication system. This is not a sUlprising view, considering that data storage is essentially the transfer of data between different times. The past decade has indeed seen rapidly growing interest in applying improved coding and detection techniques to magnetic data storage, a traditional approach to enhance performance of communication channels. Since its inception in the 1930's, the magnetic recording industry has achieved impressive progress in data capacity. This has been made possible mainly by innovations and advances in heads and media design. However, as the demand for higher storage capacity continues in the modem information era, a need arises to explore other possibilities to help meet the ever-growing demand. Advanced coding and detection are one such possibility, providing an efficient, cost-effective means to increase data capacity. In fact, with the advent of modem Ie technology which has enabled real-time implementation of increasingly complex signal processing algorithms, advanced coding and detection are rapidly becoming a major issue in the development of improved data storage products. While there have been remarkable advances in recent years in the areas of both coding and detection for data storage, this book focuses only on data detection, or the processing of readback waveforms to reproduce stored data, in conjunction with the traditional modulation coding method called run length-limited or (d,k) coding.

The book presents several advances in different research areas related to data storage, from the design of a hierarchical memory subsystem in embedded signal processing systems for data-intensive applications, through data representation in flash memories, data recording and retrieval in conventional optical data storage systems and the more recent holographic systems, to applications in medicine requiring massive image databases.