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## Über dieses Buch

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.

## Inhaltsverzeichnis

### Chapter 1. Introduction

Abstract
The principles involved in soft iterative decoding are illustrated by a few simple examples in Section 1. A brief summary of digital communications and potential applications is given in Sections 2 and 3, followed by an overview of the chapters in this book in Section 4. A guide to notation and symbols is provided in Section 5.
John L. Fan

### Chapter 2. Message-Passing Algorithm

Abstract
This chapter introduces a framework for understanding probabilistic decoding, and applies it to the decoding of low-density parity check (LDPC) codes. Section 1. sets up the preliminaries for soft iterative decoding. Section 2. explains the message-passing algorithm using normal graphs. Section 3. presents some basic nodes and modules. Section 4. introduces LPDC codes and discusses their decoding algorithm.
John L. Fan

### Chapter 3. Forward-Backward Algorithm

Abstract
Using the framework of the message-passing algorithm, Section 1. introduces the forward-backward algorithm (FBA) for decoding on trellises, in which messages flow in both directions along a linear graph. This algorithm can be used for the decoding of channels with memory and convolutional codes. Section 2. describes some common configurations for turbo decoding.
John L. Fan

### Chapter 4. Application to Magnetic Storage

Abstract
To understand how soft iterative decoding can be applied to communications, we study disk drives, where the high rate of innovation makes it a likely candidate for the early adoption of advanced coding techniques. In particular, unlike communications systems that are based on standards, each hard disk drive can use its own proprietary coding scheme.
John L. Fan

### Chapter 5. Constrained Coding for Hard Decoders

Abstract
In this chapter, constrained coding is considered in the context of a hard-decision decoder for the error-control code (ECC), such as for a Reed-Solomon code. Section 1. introduces constrained coding. Section 2. describes the problem of error-propagation that occurs when a constrained code is concatenated with an error-control code, and addresses it with a modified concatenation scheme. Section 3. considers lossless compression, a technique for improving modified concatenation. Section 4. provides some examples in magnetic recording. This material has appeared in [FC98] and [FMR00].
John L. Fan

### Chapter 6. Constrained Coding for Soft Decoders

Abstract
The art of soft iterative decoding is putting together the various decoders that make up the system, and then iteratively passing messages amongst them. This chapter puts together constrained coding from Chapter 5 with the ECC and channel decoders from Chapters 2 and 3. Section 1. discusses the construction of modulation codes to make soft information available after demodulation. The key result is presented in Section 2., which considers configurations for combined constraint and ECC decoding, such as modified concatenation. For constrained systems, Section 3. then uses the forward-backward algorithm on the trellis of the constraint graph to decode the sequence for additional coding gain. Finally, Section 4. looks at some theoretical aspects of combining ECC and modulation coding. Some of this material has appeared in [FCi99].
John L. Fan

### Chapter 7. Array Codes as LDPC Codes

Abstract
An area of great interest for LDPC codes is the use of structured constructions rather than random constructions. These include graph theoretic approaches, such as the constructions by Margulis [Mar82] and Tanner [Tan00]. Ramanujan graphs are considered by Rosenthal and Vontobel [RV00] and finite geometries are used by Kou, Lin and Fos-sorier [KLF00]. The regular structure can be used to guarantee distance properties, improve cycle characteristics or simplify the implementation.
John L. Fan

### Chapter 8. Other Topics

Abstract
We close with some topics related to the application of soft iterative decoding techniques to communications.
John L. Fan

### Backmatter

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