## Graduated Seminar Mobile Communications and Coding

Lecturer (assistant) | |
---|---|

Number | 820085453 |

Type | Seminar |

Duration | 3 SWS |

Term | Sommersemester 2019 |

Language of instruction | German |

Position within curricula | See TUMonline |

Dates | See TUMonline |

### Dates

### Course criteria & registration

### Description

### Links

# Organizational Matter

The preliminary meeting will be on Thursday, April 25, 2019 at 3PM in room N2408. Please note that only students which participate in this meeting can be considered for this seminar! The final number of participants will be limited by the number of available topics and if there are too many students, those with earlier registration will be given prioriy.

Below is a list of available topics. Please pick **four** of them and send your choice including priorities to Tasnad Kernetzky latest until Wednesday, April 24, 2019 23:59. The topics will be assigned by the first come, first served principle.

# Available Topics

## Nonlinearity Mitigation in WDM Systems: Models, Strategies and Achievable Rates (Javier Garcia)

The capacity of the nonlinear optical fiber channel, modeled by the Nonlinear Schrödinger Equation (NLSE) is not yet known in closed form. Several simplified models have been developed in the literature. These models admit an information-theoretic analysis, but they are based on assumptions that do not hold in all practical cases. Some of these models are summarized in [1]. The student's task is to review these models and explain their strengths and limitations.

### References

- [1] Secondini, Marco et al. “Nonlinearity Mitigation in WDM Systems: Models, Strategies, and Achievable Rates.” arXiv e-print abs/1811.08942 (2018): arxiv.org/abs/1811.08942

### Prerequisites

- Information theory

## An Overview on Machine Learning Techniques for Optical Networks (Ginni Khanna)

Machine learning has become a new "hot" research topic in almost all fields of research and of course optics doesn't want to feel left behind. This seminar would require the student to read and give a general review of various scenarios in optics and the related machine learning techniques.

### References

- [1] Francesco Musumeci et. al, "An Overview on Application of Machine Learning Techniques in Optical Networks"

### Prerequisites

- Curious to learn about ML techniques
- Optical communications

## An Overview on Simplified Successive Cancellation Decoding of Polar Codes (Peihong Yuan)

Polar codes are a class of error-correction codes introduced by Arıkan in [1]. They can provably achieve channel capacity on a memoryless channel when the code length tends to infinity by successive cancellation (SC) decoding with complexity O(NlogN). The full search can be completed in 2N−2 time-steps [2]. The task of the student is to compare different simplified SC decoders in [2-4].

### References

- [1] E. Arıkan, “Channel polarization: A method for constructing capacity- achieving codes for symmetric binary-input memoryless channels,” IEEE Trans. Inf. Theory, vol. 55, no. 7, pp. 3051–3073, July 2009.

- [2] C. Leroux, A Raymond, G. Sarkis, and W. Gross, “A semi-parallel successive-cancellation decoder for polar codes,” IEEE Trans. Signal Process., vol. 61, no. 2, pp. 289–299, January 2013.

- [3] A. Alamdar-Yazdi and F. R. Kschischang, “A simplified successive- cancellation decoder for polar codes,” IEEE Commun. Lett., vol. 15, no. 12, pp. 1378–1380, December 2011.

- [4] G. Sarkis, P. Giard, A. Vardy, C. Thibeault, and W. Gross, “Fast polar decoders: Algorithm and implementation,” IEEE J. Sel. Areas Commun., vol. 32, no. 5, pp. 946–957, May 2014.

### Prerequisites

- Basic Information Theory

## Bit Flipping Algorithms for LDPC Codes (Emna Ben Yacoub)

A bit flipping (BF) algorithm is a decoding algo rithm for low density parity check codes (LDPC) that can be efficiently implemented by electronic circuits. BF algorithms for decoding LDPC codes have been investigated extensively and numerous variants of BF algorithms, such as the two-bit BF [1] the weighted BF algorithm [2], the modified weighted BF algorithm [3], and other variants [4],[5] have been proposed. The student's task is to review these approaches.

### References

- [1] D. V. Nguyen, M. W. Marcellin, and B. Vasic, “Two-bit bit flipping decoding of LDPC codes,” in Proc. IEEE Int. Symp. Inform. Theory, St. Petersburg, Russia, Jul. 31–Aug. 5 2011, pp. 1995–1999.

- [2] Y. Kou, S. Lin, and M. P. C Fossorier, “Low-density parity-check codes based on finite geometries: a rediscovery and new results, "IEEE Trans.Inf. Theory, pp. 2711–2736, vol. 47, Nov. 2001.

- [3] J. Zhang, and M. P. C. Fossorier, “A modified weighted bit-flipping decoding of low-density parity-check codes, "IEEE Commun. Lett.,pp.165-167, vol. 8, Mar. 2004.

- [4] M. Jiang, C. Zhao, Z. Shi, and Y. Chen, “An improvement on the modified weighted bit flipping decoding algorithm for LDPC codes, "IEEE Commun. Lett., vol. 9, no. 9, pp. 814-816, 2005.

- [5] F. Guo and H. Henzo, “Reliability ratio based weighted bit-flipping decoding for low-density parity-check codes, "IEEE Electron. Lett.,vol.40, no. 21, pp. 1356-1358, 2004

### Prerequisites

- Channel Codes for Iterative Decoding

## Belief Propagation Decoding of Polar Codes (Thomas Wiegart)

Polar codes [1] are capacity achieving codes with a successive cancellation decoder. Their finite-length performance is, however, relatively bad. Several approaches to improve the performance have been presented, such as list decoding and CRC-aided list decoding, which come with the cost of increased complexity. An other approach is to interpret the polar code as factor graph and perform belief propagation (BP) decoding [2]. BP is a well established iterative decoding procedure (known e.g. from LDPC codes) which usually allows efficient and parallel decoding. The student's task is to understand polar codes and the idea of belief propagation (BP) decoding for polar codes. Furthermore, the student should summarize recend advances in BP decoding (such as [3],[4]).

### References

### Prerequisites

- Channel Codes for Iterative Decoding

## Conditional Density Estimation with Neural Networks: Best Practices and Benchmarks (Marcin Pikus)

Given a set of empirical observations, conditional density estimation aims to capture the statistical relationship between a conditional variable x and a dependent variable y by modeling their conditional probability p(y|x). The problem often arises in engineering, machine learning and finance. The paper [1] develops best practices for conditional density estimation for finance applications, however the approach can be used in a wide range of problems. [1] develops an approach based on neural networks, grounded on mathematical insights and empirical evaluations.

### References

- [2] relevant references of [1]

### Prerequisites

- Machine Learning

## Insertions/Deletions-Correcting Codes (Lorenz Welter)

Error-correcting codes like a Hamming-Code or Reed-Solomon-Code are widely know for the usage to correct bit-errors (1->0, 0->1) or bit-erasures (0,1->E). However in digital communication and data storage systems also the insertion and deletion of bits is a typical error. For instance these can be caused through timing defects or packet-loss. Consequently there need to be code constructions capable of correcting these kind of errors. The student's task is to understand the insertion/deletion-scenario and review proposed techniques for coping with such errors.

### References

- [1] N. J. A. Sloane, "On single-deletion-correcting codes", Proc. Codes Designs, pp. 273-291, 2001.

- [2] G. Tenengolts, "Nonbinary codes, correcting single deletion or insertion (Corresp.)," in IEEE Transactions on Information Theory, vol. 30, no. 5, pp. 766-769, September 1984.

- [3] C. Schoeny, A. Wachter-Zeh, R. Gabrys and E. Yaakobi, "Codes Correcting a Burst of Deletions or Insertions," in IEEE Transactions on Information Theory, vol. 63, no. 4, pp. 1971-1985, April 2017.

- [4] V. I. Levenshtein, "Asymptotically optimum binary codes with correction for losses of one or two adjacent bits", Syst. Theory Res., vol. 19, pp. 298-304, 1970.

- [5] A. S. J. Helberg and H. C. Ferreira, "On multiple insertion/deletion correcting codes," in IEEE Transactions on Information Theory, vol. 48, no. 1, pp. 305-308, Jan. 2002.

### Prerequisites

- Channel Coding
- Recommended: Coding Theory for Storage and Networks

## Modified Nonlinear Inverse Synthesis for Optical Transmission Systems with Lumped and Distributed Amplification Schemes (Benedikt Leible)

In an attempt to improve achievable rates of optical communication systems in the high input power regime, modulation via the nonlinear Fourier transform (NFT) has attracted some attention in recent years. Since the NFT was conceived for the deterministic lossless nonlinear Schrödinger equation (NLSE), the fiber loss present in realistic optical communication systems degrades the achievable data rates for NFT aided communication systems. To mitigate the negative effects of attenuation on the nonlinear spectra during propagation, a path loss average (PLA) approach was proposed in [1] and [2] for lumped EDFA and distributed Raman amplification respectively. The students task is to first get familiar (again) with the models for distributed Raman amplification [3, 4] and lumped EDFA amplification and get an overview of why the NFT is thought of as promising in the context of optical transmission systems, by reading the respective sections in [5] (Please note that it is not necessary to fully understand all the intricacies regarding the NFT in [5], since it would be too much for the scope of this seminar). Finally both PLA approaches should be reviewed thoroughly, using references [1] and [2]. References [1] Le, Son Thai et al. “Nonlinear Inverse Synthesis Technique for Optical Links with Lumped Amplification.” [2] Le, Son Thai et al. "Modified Nonlinear Inverse Synthesis for Optical Links with Distributed Raman Amplification" [3] Bromage, Jake. "Raman Amplification for Fiber Communications Systems." [4] Muga, Nelson J., et al. "ASE Noise Simulation in Raman Amplification Systems." [5] Yousefi, Mansoor I., and Frank R. Kschischang. "Information Transmission Using the Nonlinear Fourier Transform, Part I: Mathematical Tools." Prerequisites Optical Communication Systems Nonlinear Optics

## Decoding of Interleaved Codes (Hedongliang Liu)

Interleaving is a coding method to deal with burst errors (many errors happen suddenly). For a known code, such as Reed-Solomon (RS) codes, the decoding of interleaved RS (IRS) codes is well-studied in [1, 2] and the decoding radius is beyond half of minimum distance of the corresponding RS code. A general method for decoding any interleaved codes is proposed in [3]. The student’s task is to understand how the decoding of interleaved RS codes and the general decoding method [3] work and summarize the constraints of two decoding methods.

### References

- [1] A. Wachter-Zeh, A. Zeh, and M. Bossert, “Decoding Interleaved Reed–Solomon Codes Beyond Their Joint Error-Correcting Capability,” Designs, Codes and Cryptography, vol. 71, no. 2, pp. 261–281, 2014.

- [2] G. Schmidt, V. R. Sidorenko, and M. Bossert, “Collaborative Decoding of Interleaved Reed–Solomon Codes and Concatenated Code Designs,” IEEE Trans. Inf. Theory, vol. 55, no. 7, pp. 2991–3012, 2009.

- [3] J. J. Metzner and E. J. Kapturowski, “A General Decoding Technique Applicable to Replicated File Disagreement Location and Concatenated Code Decoding,” IEEE Trans. Inf. Theory, vol. 36, no. 4, pp. 911–917, 1990.

- [4] R. M. Roth, “Introduction to Coding Theory”. Cambridge University Press, 2006. (Chapter 6) (Reference of decoding of RS codes, on which decoding of IRS codes is based on)

### Prerequisites

- Channel Coding (Recommend to take the lecture "Coding Theory for Storage and Networks")

## Security proofs of QKD protocols. (Roberto Ferrara)

Quantum Key Distribution (QKD) exploits the transmission of quantum states to communicate a classical shared key that is provably secure from the any eavesdropper. While QKD does exploit quantum communication and measurements, these are normally used only to obtain a raw classical key and a bound on the information of the eavesdropper, then classical information theory is used to extract the perfect key where the security of the key can be proven thanks to the quantum assumptions. 1) and 2) provide security proofs for broad but specific classes of QKD protocols. The goal is to understand the steps and structure of the QKD protocols and explain their security proofs.

### References

### Prerequisites

- Information theory
- Algorithms in Quantum Theory
- Recommended: Quantum Information Theory (LTI)

## Quantum Repeaters. (Roberto Ferrara)

Quantum information cannot be amplified, only error corrected. At the same time there exists a duality between quantum states and channels, and entangled states can be used to communicate quantum information using only local quantum operations and classical communication (with no quantum communication happening beyond the sharing of the entangled states). The most extreme example are maximally entangled states, which can be used to implement identity quantum channels using what is known as quantum teleportation.Since amplification is impossible, quantum repeater stations are necessary to overcome noise in long distance communications. These repeater stations then help communicate quantum information by performing the error correction, or by distilling maximally entangled states used in teleportation. The goal is to understand and report on a quantum repeater protocol. The student can choose between the original proposal 1), or one of the newest proposal 2).

### References

### Prerequisites

- Algorithms in Quantum Theory
- Recommended: Quantum Information Theory (LTI)

## Lattice-based and/or code-based cryptography (Georg Maringer)

Currently a substantial amount of research is conducted in fields required for manufacturing large scale quantum computers. It is not clear when the first researchers will be able to produce a computer with a sufficient amount of qubits, such that established cryptographic schemes get insecure. However once potential attackers obtain access to such a device most of the established public-key cryptography becomes insecure as it relies on problems like integer factorization or the discrete logarithm problem. Therefore, cryptographers try to create algorithms based on other classes of mathematical problems which are considered hard even if the attackers have access to large scale quantum computers. One promising family of those algorithms is based on problems on high-dimensional lattices. Another one is algorithms based on hard problems in coding theory. The student's task is to understand algorithms and concepts within the family of lattice-based/code-based cryptography.

### References

- [1] J. Hoffstein, J. Pipher, and J. H. Silverman. An Introduction to Mathematical Cryptography. Springer, 2008.

- [2] V. Lyuabashevsky, Chris Peikert, and Oded Regev. On Ideal Lattices and Learning with Errors Over Rings. Journal of the ACM, vol. 60, article no. 43, 2013.

- [3] Robert J. McEliece. A public-key cryptosystem based on algebraic coding theory. Deep Space Network Progress Report, pp. 114-116, 1978.

- [4] Wachter-Zeh, Antonia, Sven Puchinger, and Julian Renner. "Repairing the Faure-Loidreau Public-Key Cryptosystem." 2018 IEEE International Symposium on Information Theory (ISIT). IEEE, 2018.

## Advances in Locally Repairable Codes (Lukas Holzbaur)

Locally repairable codes (LRC) are codes developed for distributed data storage, that allow for the repair of a small number of nodes from few other nodes and have attracted a lot of attention in recent years. Many constructions have since been introduced that achieve the Singlton-like bound [1,2] on the distance given. A class of LRCs that are subcodes of Reed-Solomon codes, which is popular due to it's flexibility and small required field size, was introduced by Tamo et al. in [3]. The students task is to understand the construction of [3] and compare it to other optimal constructions, such as those given in [4,5,6], with special attention to the required field size and whether the code is contained in a supercode from a well-known class.

### References

- [1] Gopalan, P., Huang, C., Simitci, H., & Yekhanin, S. (2012). On the Locality of Codeword Symbols. IEEE Transactions on Information Theory, 58(11), 6925–6934.

- [2] Kamath, G. M., Prakash, N., Lalitha, V., & Kumar, P. V. (2013). Codes with local regeneration. In 2013 IEEE International Symposium on Information Theory (pp. 1606–1610). IEEE.

- [3] Tamo, I., & Barg, A. (2014). A Family of Optimal Locally Recoverable Codes. IEEE Trans. Inf. Theory, 60(8), 4661–4676.

- [4] Tamo, I., Papailiopoulos, D. S., & Dimakis, A. G. (2013). Optimal locally repairable codes and connections to matroid theory. IEEE International Symposium on Information Theory - Proceedings, (July), 1814–1818.

- [5] Chen, Bin et al. “Constructions of Optimal Cyclic (r, δ) Locally Repairable Codes.” IEEE Trans. Information Theory 64 (2018): 2499-2511.

- [6] N. Silberstein, A. S. Rawat, O. O. Koyluoglu and S. Vishwanath, "Optimal locally repairable codes via rank-metric codes," 2013 IEEE International Symposium on Information Theory, Istanbul, 2013, pp. 1819-1823.

### Prerequisites

- Channel Coding

## Photonic-aided analog-to-digital converter (ADC) enabled by synchronized frequency combs (Yizhao Jia)

Optical frequency combs (OFC), have very recently revolutionized fields of metrology, spectroscopy and optical communications, and are potential candidates to be used in photonic-aided ADC. Photonic-aided ADC aims at the acquisition of broadband signals with a high effective number of bits (ENOB) when compared to conventional ADC. The student's task is to understand the principle and review proposed techniques for photonic-aided ADC.

### References

- [1] N. Fontaine et al., “Real-time full-field arbitrary optical waveform measurement,” Nature Photon., vol. 4, no. 4, pp. 248–254, Feb. 2010.

- [2] George C. Valley, "Photonic analog-to-digital converters," Opt. Express 15, 1955-1982 (2007)

- [3] Han, Y. & Jalali, B. Photonic time-stretched analog-to-digital converter: fundamental concepts and practical considerations. J. Lightwave Technol. 21, 3085–3103 (2003).

- [4] "Optical frequency comb technology for ultra-broadband radio-frequency photonics". Laser and Photonics Reviews. 8: 368–393. May 2017.

### Prerequisites

- ADC Theory
- Coherent Optical Communication Systems

## Trellis Shaping (Fabian Steiner)

Trellis Shaping was invented by Forney in [1] and provides a coded modulation setup based on trellis coded modulation (TCM) that is able to achieve a shaping gain. The student is asked to review that scheme, and implement a small example by him/herself. Time permitting, further comparisons to state-of-the-art scheme should be done.

### References

### Prerequisites

- Information Theory
- Channel Coding
- Codes for Iterative Decoding

## Coding with feedback (Patrick Schulte)

"Feedback does not increase capacity" is a well known result from information theory. Since this is an asymptotic result, things may look different in the finite length regime. Here it is really helpful to send extra redundancy if decoding failed. The question is: how much? Richard Wesel and his group have progressed in this question and give insights and algorithms on how to solve this Problem[1,2]. It is the students task not only to present the topic and the results but also to implement the algorithms for deeper understanding. Furthermore, some assumptions should be checked and maybe counterexamples can be found.

### References

## Reed-Muller Codes Achieve Capacity on Erasure Channels (Mustafa Coskun)

Recently, it has been shown that a class of codes with sufficient symmetry, including the Reed-Muller (RM) codes, achieve capacity over erasure channels. The student needs to understand the ingredients of the proof, i.e., area theorem, symmetry of codes, etc. and implement a recently introduced decoding algorithm for RM codes.

### References

## Probabilistic Shaping of Parity Bits (Diego Lentner)

Communication channels often have non-uniform capacity-achieving input distributions, which has been the main motivation for probabilistic shaping (PS). Many different PS schemes have been proposed in literature, see, e.g., the literature review in [1, Sec. II]. Probabilistic amplitude shaping (PAS) [1] uses distribution matching (DM) to map information bits to shaped bits, which are then systematically encoded to append uniformly distributed parity bits. However, there are important cases where optimal transmission requires shaped parities [2, Remark 3], examples include intensity modulation [3] and on-off-keying (OOK). A time-sharing based shaping scheme (sparse-dense-transmission) for OOK was presented in [4], while an implementation for polar codes is shown in [5]. In [6], PAS is extended by probabilistic parity shaping (PPS) to match arbitrary input distributions with systematic encoding. The student will review the literature on probabilistic shaping, understand why many channels require shaped parity bits, compare the different approaches to probabilistic shaping of parity bits, and point out the challenges and limitations of the different approaches.

### References

- [1] G. Böcherer, F. Steiner, and P. Schulte, “Bandwidth efficient and rate-matched low-density parity-check coded modulation,” IEEE Trans.Commun., vol. 63, no. 12, pp. 4651–4665, Dec. 2015

- [2] G. Böcherer, P. Schulte, and F. Steiner, “Probabilistic Shaping and Forward Error Correction for Fiber-Optic Communication Systems,” J.Lightw. Technol., vol. 37, no. 2, pp. 230–244, Jan. 2019.

- [3] T. A. Eriksson, M. Chagnon, F. Buchali, K. Schuh, S. ten Brink, and L. Schmalen, “56 Gbaud probabilistically shaped PAM8 for data center interconnects,” in Proc. Eur. Conf. Optical Commun. (ECOC), 2017.

- [4] A. Git, B. Matuz, and F. Steiner, “Protograph-Based LDPC Code Designfor Probabilistic Shaping with On-Off Keying,” in Proc. Ann. Conf. Inf.Sci. Syst. (CISS), Mar. 2019.

- [5] T. Wiegart, F. Steiner, and P. Yuan, “Shaped On-Off-Keying Using Polar Codes,” Mar. 2019, in preparation.

- [6] G. Böcherer, D. Lentner, A. Cirino, F. Steiner, “Probabilistic Parity Shaping for Linear Codes,” Feb. 2019. Available: arxiv.org/abs/1902.10648

### Prerequisites

- Information Theory
- Channel Coding

## Code-Based Signature Scheme (Thomas Jerkovits)

McEliece is one of the oldest known public key cryptosys tems. Though it was less widely studied than RSA, it is remark able that all known attac ks are still exponen tial. It is widely believed that code-based cryptosystems like McEliece do not allow practical digital signatures. The student should read the paper listed below and understand how the proposed code-based signature scheme works and point out the difficulties of code-based signature schemes.

### References

- [1] Courtois N.T., Finiasz M., Sendrier N. (2001) How to Achieve a McEliece-Based Digital Signature Scheme. In: Boyd C. (eds) Advances in Cryptology — ASIACRYPT 2001. ASIACRYPT 2001. Lecture Notes in Computer Science, vol 2248. Springer, Berlin, Heidelberg ( www.iacr.org/archive/asiacrypt2001/22480158.pdf)

### Prerequisites

- Channel Coding

## Code-Based Encryption (Julian Renner)

Assuming an attack of a sufficiently large quantum computer, several classical public-key algorithms based on factoring large integers and the discrete logarithm problem become insecure since computationally intensive mathematical problems become easy-to-solve. Thus, the National Insitute of Standards and Technology (NIST) started the Post-Quantum Cryptography Standardization. The student should understand the cryptosystem based on MDPC codes [1] and determine its applications in the NIST proposals.

### References

- [1] R. Misoczki, J.-P. Tillich, N. Sendrier, P. Barreto New McEliece variants from Moderate Density Parity-Check codes (https://ieeexplore.ieee.org/document/6620590)

### Prerequisites

- Basic Knowledge in Channel Coding

## Non-square constellations (Delcho Donev)

Investigation of non-square constellations [1]. Bit-error rates for such constellations for transmissions over the AWGN channel.

### References

- [1] M. Abdelazis and T. A. Gulliver, "Triangular Constellations for Adaptive Modulation" (https://ieeexplore.ieee.org/document/8067494)

### Prerequisites

- Digital Communications 1 and 2

## Codes for partially stuck-at memory cells (Haider Al Kim)

The dominance of the non-volatile memories and PCMs (phase change memories) as memory solutions for a variety of applications has brought attention to the pros and cons of these types of memories. The obvious pros of these memories are their huge capacity plus the ability to introduce the technologies of multi-levels. These causes significantly reduce their cost. On the other hand, their cons are the issues related to their reliability which opens the door for new suggested coding and signal processing theorems. The memory cells are stuck-at a state where each cell can have two possible levels, either 0 or 1 (generally speaking) [1]. Different levels of PCM cells (q-ary cells) have multi-level states [2]. "Stuck" means that the cell's charge is trapped in the cell, so that, it cannot change its status to re-write again. The trapped scenario might happen due to the defect in a cell or due to the erasing and re-writing on this cell. Since that is the scenario, the only way to store new information without reducing the lifetimes of these memories is by increasing their trapped levels. That means the level of the cell will be at least 1 and the cell can have a state 1 or more [3]. In other words, to solve this, we need to find a codeword that matches the states of the partially stuck at cells. We can also correct additional random errors occurring during the storing and retrieving process. The student task is to investigate the current constructions for masking partially-stuck-at memory cells and to propose new construction based on similar code families.

### References

- [1] C. Heegard, “Partitioned linear block codes for computer memory with ‘stuck-at’ defects,” IEEE Trans. Inf. Theory, vol. 29, no. 6, pp. 831–842, Nov. 1983.

- [2] G. W. Burr et al., “Phase change memory technology,” J. Vac. Sci.Technol. B, vol. 28, no. 2, pp. 223–262, 2010.

- [3] A.Wachter-Zeh and E. Yaakobi, “Codes for Partially Stuck-At Memory Cells,” IEEE Transactions on Information Theory, vol. 62, no. 2, pp. 639–654, February 2016.

### Prerequisites

- Channel Coding

## Codes for DNA-based data storage (Andreas Lenz)

DNA based data storage is a novel technology, where digital information is stored in synthetic DNA molecules. The recent advance in DNA sequencing methods and decrease in sequencing costs have paved the way for storage methods based on DNA. The natural stability of DNA molecules, (the genetic information from fossils is maintained over tens of thousands of years) motivate their use for long-term archival storage. Furthermore, because the information is stored on molecular levels, such storage systems have extremely high data densities. Recent experiments report data densities of 2 PB/gram, which corresponds to the capacity of a thousand conventional hard disk drives in one gram of DNA. The students task will be to understand important aspects of DNA-based data storage and review recent experiments to compare them in terms of efficiency and employed coding schemes.

### References

- [1] Organick, L., Ang, S. D., Chen, Y.-J., Lopez, R., Yekhanin, S., Makarychev, K., … Strauss, K. (2018). Random access in large-scale DNA data storage. Nature Biotechnology, 36(3).

- [2] Yazdi, S. M. H. T., Kiah, H. M., Garcia-Ruiz, E., Ma, J., Zhao, H., & Milenkovic, O. (2015). DNA-Based Storage: Trends and Methods. IEEE Transactions on Molecular, Biological and Multi-Scale Communications, 1(3), 230–248.

## Power Efficiency in Coherent Fiber-Optical Transmission Systems (Daniel Plabst)

In the 5th generation of wireless communication systems (5G), hardware complexity and power efficiency is one of the main challenges in the design of new base stations. In order to make those systems viable, inexpensive and simple hardware components need to be deployed. The use of low-resolution analog-to-digital converters (ADCs) in the radio-frequency-chain of those base stations provides effective means to curtail hardware complexity and power consumption of the overall system [1]. Naturally, a trade-off between low-end components, costly digital signal processor (DSP) routines and system performance needs to be found. Similar observations can be made in coherent fiber-optical communication systems. Whereas coherent communication systems make superior use of the spectral resources, the traditional use of high-speed ADCs and DSPs on the receiver side presents a bottleneck. The student should comprehend the power consumption behavior of various building blocks of a coherent fiber-optical communication system, be able to identify bottlenecks and describe the trade-off between power efficiency and system performance [2-5].

### References

- [1] Mollén, Christopher. On Massive MIMO Base Stations with Low-End Hardware. Vol. 1756. Linköping University Electronic Press, 2016.
- [2] Perin, Jose Krause. "Spectrally and Power Efficient Optical Communication Systems." arXiv preprint arXiv:1806.01945 (2018). [Only selected chapters]
- [3] Lundberg, Lars. “Aspects of Power Consumption in Coherent Fiber-Optical Communication Systems.” (2017). [Only selected chapters]
- [4] Lundberg, Lars, Peter A. Andrekson, and Magnus Karlsson. "Power consumption analysis of hybrid EDFA/Raman amplifiers in long-haul transmission systems." Journal of Lightwave Technology 35.11 (2017): 2132-2142.
- [5] Kupfer, Theodor, et al. "Optimizing power consumption of a coherent dsp for metro and data center interconnects." Optical Fiber Communication Conference. Optical Society of America, 2017.

### Prerequisites

- Fiber-optical communication systems

## Hybrid ARQ Schemes Based on Polar Codes (Tobias Prinz)

Polar codes [1] are capacity achieving codes that have been chosen for the control channel in the new 5G standard. Hybrid ARQ (HARQ) schemes combine forward error correction and automatic repeat request (ARQ). The students task will be to understand the concept of HARQ and polar codes. Then, different schemes that realize HARQ schemes based on polar codes should be described and compared. A good starting point for that might be [2].

### References

### Prerequisites

- Channel Coding

## Phase Matching in Optical Waveguides (Tasnad Kernetzky)

The nonlinear interaction of light with matter - in form of the Four-wave mixing effect - can be utilized for e.g. wavelength conversion or optical phase conjugation. To achieve high conversion efficiency, energy conservation and phase matching need to be fulfilled. The student's task is to compare different phase matching techniques developed through the last 5 decades.

### References

- [1] D. Dimitropoulos et al., "Phase-matching and nonlinear optical processes in silicon waveguides."

- [2] R. H. Stolen et al., "Phase-matched three-wave mixing in silica fiber optical waveguides."

- [3] G. Rademacher et al., “Investigation of Intermodal Four-Wave Mixing for Nonlinear Signal Processing in Few-Mode Fibers."

### Prerequisites

- Good knowledge of Maxwell's equations
- Optical Communication Systems
- Nonlinear optics
- Four-Wave Mixing