Chapter 1 - Introduction

Abstract

Codes on graphs, such as turbo codes and low-density parity-check (LDPC) codes, have revolutionized communications and are becoming standard in many applications. The inherent low complexity of LDPC decoders opens up avenues for their use in different high-speed applications, including optical communications. LDPC codes are linear block codes for which the parity-check matrix has low density of ones. LDPC codes have generated great interest in the coding community, resulting in a better understanding of different aspects of LDPC codes and their decoding process. Moreover, it has been shown that an iterative LDPC decoder based on the sum-product algorithm is able to achieve a performance as close as 0.0045 dB to the Shannon limit. Future Internet traffic growth will require deployment of optical transmission systems with data rates at 100 Gb/s and higher. Dealing with the nonlinear effects and PMD is more manageable, while the aggregate data rate is maintained above 100 Gb/s.