State-of-the-Art and Open Problems

d codes, which are strong candidates for future optical communication systems. We discuss some recent research on this class of codes in the area of optical communications, and summarize some open research problems. I. INTRODUCTION The ever-growing demand in network capacity has made the use of forward error correction (FEC) a must in optical com­ munications. The first FEC code proposals, in the late 1980s and early 1990s, were based on classical algebraic codes, mainly Reed-Solomon (RS) codes, and hard-decision decoding (HDD). RS codes are characterized by a large minimum distance, which allows to support error rates below 10- 15, as required in optical communications. Furthermore, they possess a strong algebraic structure which can be exploited for low­ complexity syndrome-based decoding. However, RS codes perform far away from the Shannon limit at low error rates. The advent of turbo codes and the rediscovery of low­ density parity-check (LDPC) codes, with unprecedented per­ formance close to the Shannon limit, has attracted a significant interest in the optical communications community in the last few years in modern FEC schemes. Turbo and LDPC codes can be decoded with relatively low complexity using soft­ decision decoding (SDD), also referred to as belief propagation (BP) decoding. Today, coding for long-haul optical commu­ nications can be divided into two main active areas. On one hand, code constructions based on algebraic codes, such as turbo product codes, staircase codes (1) and tightly-braided block (TBB) codes (2), decoded using HDD. On the other hand, LDPC codes with SDD. The latter can provide an extra coding gain with respect to HDD schemes, at the expense of an increased decoding