On hard-decision forward error correction with application to high-throughput fiber-optic communications
Doktorsavhandling, 2019

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.

product-like codes

bounded distance decoding

staircase codes.

product codes

hard decision decoding

generalized minimum distance decoding

probabilistic shaping

coded modulation

Achievable information rates

Opponent: Prof. Frank R. Kschischang


Alireza Sheikh

Chalmers, Elektroteknik, Kommunikation, Antenner och Optiska Nätverk

Binary Message Passing Decoding of Product Codes Based on Generalized Minimum Distance Decoding: (Invited Paper)

53rd Annual Conference on Information Sciences and Systems (CISS). Invited paper,; (2019)

Paper i proceeding

Probabilistic Amplitude Shaping with Hard Decision Decoding and Staircase Codes

Journal of Lightwave Technology,; Vol. 36(2018)p. 1689-1697

Artikel i vetenskaplig tidskrift

Achievable Information Rates for Coded Modulation With Hard Decision Decoding for Coherent Fiber-Optic Systems

Journal of Lightwave Technology,; Vol. 35(2017)p. 5069-5078

Artikel i vetenskaplig tidskrift

On Low-Complexity Decoding of Product Codes for High-Throughput Fiber-Optic Systems

IEEE International Symposium on Turbo Codes & Iterative Information Processing (ISTC). Invited paper,; (2019)

Paper i proceeding

Fiber-optic systems play a key role in our everyday's life by providing the Internet backbone. Every time we use social media networks, access a web page, watch Youtube clips, or send an email, fiber-optic links are involved at some point to carry the data. Therefore, the ever increasing number of Internet users as well as the sheer of new applications has been driven by advances in fiber-optic systems. 

Transmission in fiber-optic links is accompanied with noise and several impairments, which in turn distort the received signal. To ensure the quality of the received signal, several impairment compensation methods are required. Even after ideal impairment compensation, the noise introduced, mainly due to the amplifiers, can yield some errors at the received side. Forward error correction (FEC) is used to protect the data from transmission errors.

Optical systems are typically operated at hundreds of Gigabit-per-second, and designing an efficient FEC encoder/decoder operating at such high data rate is a tricky task. FEC based on soft decision decoding (SDD) provides excellent performance at the cost of high decoding complexity and data flow. This makes adapting SDD for high-throughput applications challenging. Hard decision decoding
(HDD) is an appealing alternative due to its associated low decoding data flow.

In this thesis, we are concerned with designing new coding schemes based on HDD which provide an excellent performance-complexity tradeoff. We first study the performance of HDD systems in terms of the so-called achievable information rate. We show that binary codes with HDD are preferable than their nonbinary counterpart. Our result provides a guideline for a system designer to choose the best coding architecture. Then, we propose several coding schemes based on binary codes with limited complexity to improve the performance of the system. The interested reader is referred to page i of the thesis for a technical abstract summarizing the main contributions.







Doktorsavhandlingar vid Chalmers tekniska högskola. Ny serie: 4551



Opponent: Prof. Frank R. Kschischang

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