On hard-decision forward error correction with application to high-throughput fiber-optic communications

Abstract: The advent of the Internet not only changed the communication methods significantly, but also the life-style of the human beings. The number of Internet users has grown exponentially in the last decade, and the number of users exceeded 3.4 billion in 2016. Fiber links serve as the Internet backbone, hence, the fast grow of the Internet network and the sheer of new applications is highly driven by advances in optical communications. The emergence of coherent optical systems has led to a more efficient use of the available spectrum compared to traditional on-off keying transmission, and has made it possible to increase the supported data rates. To achieve high spectral efficiencies and improve the transmission reach, coding in combination with a higher order modulation, a scheme known as coded modulation (CM), has become indispensable in fiber-optic communications. In the recent years, graph-based codes such as low-density parity-check codes and soft decision decoding (SDD) have been adopted for long-haul coherent optical systems. SDD yields very high net coding gains but at the expense of a relatively high decoding complexity, which brings implementation challenges at very high data rates. Hard decision decoding (HDD) is an appealing alternative that reduces the decoding complexity. This motivates the focus of this thesis on forward error correction (FEC) with HDD for high-throughput, low power fiber-optic communications. In this thesis, we start by studying the performance bounds of HDD. In particular, we derive achievable information rates (AIRs) for CM with HDD for both bit-wise and symbol-wise decoding, and show that bit-wise HDD yields significantly higher AIRs. We also design nonbinary staircase codes using density evolution. Finite length simulation results of binary and nonbinary staircase codes corroborate the conclusions arising from the AIR analysis, i.e., for HDD binary codes are preferable. Then, we consider probabilistic shaping. In particular, we extend the probabilistic amplitude shaping (PAS) scheme recently introduced by Böcherer et al. to HDD based on staircase codes. Finally, we focus on new decoding algorithms for product-like codes to close the gap between HDD and SDD, while keeping the decoding complexity low. In particular, we propose three novel decoding algorithms for product-like codes based on assisting the HDD with some level of soft information. The proposed algorithms provide a clear performance-complexity tradeoff. In particular, we show that up to roughly half of the gap between SDD and HDD can be closed with limited complexity increase with respect to HDD.