## Hauptseminar Digitale Kommunikationssysteme

Vortragende/r (Mitwirkende/r) | |
---|---|

Nummer | 220085453 |

Art | Seminar |

Umfang | 3 SWS |

Semester | Wintersemester 2019/20 |

Unterrichtssprache | Deutsch |

Stellung in Studienplänen | Siehe TUMonline |

Termine | Siehe TUMonline |

### Termine

### Teilnahmekriterien & Anmeldung

### Lernziele

### Beschreibung

### Lehr- und Lernmethoden

### Studien-, Prüfungsleistung

### Links

## Organizational Matter

The preliminary meeting will be on Thursday, October 17, 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 Tobias Prinz latest until Thursday, October 17, 2019 23:59. The topics will be assigned by the first come, first served principle.

## Available Topics

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

In an attempt to improve achievable rates for 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 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. However a basic understanding of the NFT is required and a short introduction into the topic should be given in the paper/talk.). Finally both PLA approaches should be reviewed/explained 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

### 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

- [1] https://arxiv.org/abs/0807.3917
- [2] https://pdfs.semanticscholar.org/a9ed/49203bffe7b124984a5874fba0940103d8ab.pdf
- [3] https://arxiv.org/abs/1712.08538
- [4] https://arxiv.org/abs/1806.10503

#### Prerequisites

- Channel Codes for Iterative Decoding

### Burst-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 to cope with one special scenario, the burst deletion case. Here the channel deletes only consecutive bits, i.e. a burst.

#### References

- [1] L. Cheng, T. G. Swart, H. C. Ferreira and K. A. S. Abdel-Ghaffar, "Codes for correcting three or more adjacent deletions or insertions," 2014 IEEE International Symposium on Information Theory, Honolulu, HI, 2014, pp. 1246-1250.
- [2] 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.
- [3] 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.
- [4] N. J. A. Sloane, "On single-deletion-correcting codes", Proc. Codes Designs, pp. 273-291, 2001.
- [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 to take the lecture "Coding Theory for Storage and Networks")

### 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 Singleton-like bound [1,2] on the distance. 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]. One important part of this code construction are so-called "good polynomials", which are polynomials of a given degree that evaluate to a constant on given sets of evaluation points.

The students task is to understand the construction of [3] and investigate the construction and properties of such good polynomials.

#### 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.

#### 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 (Trellis Shaping)

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
- Channel Codes for Iterative Decoding

### Code-Based Signature Scheme (Thomas Jerkovits)

McEliece is one of the oldest known public key cryptosystems. Though it was less widely studied than RSA, it is remarkable that all known attacks are still exponential. 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

#### Prerequisites

- Basic Knowledge in Channel Coding

### Bounds on Minimum Distance and Cardinality for Partially Stuck Memory Cells with Error Correction (Haider Al Kim)

Code constructions for masking $u$ partially stuck memory cells with $q$ levels and correcting additional random errors have been presented. However, it is necessary to derive bounds to understand how good these constructions actually are. It is possible to use code families that have generator matrix with all-ones vector to have upper bounds (necessary conditions). On the other hand, we can consider a sufficient condition ( Gilbert–Varshamov Bound) to show the existence of codes with certain parameters ($n$, $k$, $d$, and $q$) that can not only correct certain errors but also meet partially stuck cell constraints.

The student task is to understand the current constructions for masking partially-stuck-at memory cells with error correction and then to derive a general bound on the minimum distance and the cardinality with the constrains where the code construction has partially stuck cells.

#### 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
- (Recommend to take the lecture "Coding Theory for Storage and Networks (Chapter 1 only)")

### Belief Propagation Decoding of CRC-Polar Concatenated Codes (Tobias Prinz)

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]. However, BP decoding cannot be used with outer CRC-codes directly which leads to a significant loss compared to CRC-aided list decoding.

In [3,4,5], methods with belief propagation decoding that include outer CRC-codes are presented. The students task is to summarize these methods and compare them to state-of-the-art CRC-aided list decoding.

#### References

- [1] https://arxiv.org/abs/0807.3917
- [2] https://pdfs.semanticscholar.org/a9ed/49203bffe7b124984a5874fba0940103d8ab.pdf
- [3] J. Guo, M. Qin, A. Guillén i Fàbregas and P. H. Siegel, "Enhanced belief propagation decoding of polar codes through concatenation," 2014 IEEE International Symposium on Information Theory, Honolulu, HI, 2014, pp. 2987-2991.
- [4] https://arxiv.org/abs/1801.04299
- [5] https://arxiv.org/abs/1811.00124

#### Prerequisites

- Channel Coding
- Channel Codes for Iterative Decoding

### Learning to Flip Successive Cancellation Decoding of Polar Codes (Peihong Yuan)

Polar codes achieve the capacity of binary-input discrete memoryless channels asymptotically in the block length under successive cancellation (SC) decoding. Polar codes have been adopted for the control channel in 5G enhanced mobile broadband (eMBB).

Due to the serial nature of SC decoding, an erroneous bit decision can be caused by the channel noise or previous erroneous bit estimates. The main idea of SC flip decoding [1, 2] is trying to correct the first erroneous bit decision by sequentially flipping the unreliable decisions.

The optimal flipping strategy is considered difficult due to lack of an analytical solution. Alternatively, (deep) learning aided SC flip algorithm are investigated in [3, 4].

The task of the student is to understand the algorithms to find the flip positions.

#### References

- [1] O. Afisiadis, A. Balatsoukas-Stimming, and A. Burg, “A low-complexity improved successive cancellation decoder for polar codes,” in Proc. 48th Asilomar Conf. Signals, Systems and Computers, pp. 2116-2120, 2014.
- [2] L. Chandesris, V. Savin, and D. Declercq, “Dynamic-SCFlip Decoding of Polar Codes,” IEEE Trans. Commun., vol. 66, no. 6, pp. 2333-2345, Jun., 2018.
- [3] X. Wang, et al. "Learning to Flip Successive Cancellation Decoding of Polar Codes with LSTM Networks." arXiv preprint arXiv:1902.08394 (2019).
- [4] N. Doan, et al. "Neural Dynamic Successive Cancellation Flip Decoding of Polar Codes." arXiv preprint arXiv:1907.11563 (2019).

### Accuracy of the Split-Step Fourier Method for Wideband Optical Communication Systems (Daniel Plabst)

The propagation of pulses on the optical fiber is modelled by the Nonlinear Schrödinger Equation (NLSE). Since an analytical solution for the NLSE does not exist in the general case, reliable numerical techniques are necessary to estimate the evolution of the optical pulse along the fiber. A simple and efficient tool for solving the NLSE numerically is the Split-Step Fourier Method (SSFM) [1,2].

The SSFM divides the propagation distance into small increments and approximates the propagation within each increment. Unavoidably, numerical estimation errors are introduced, which can be mitigated by reducing the step size and therefore increasing the simulation complexity. In [3] the authors investigate the behavior of the SSFM accuracy versus the step size and aim at finding guidelines for efficient yet accurate numerical simulations. The authors choose a perturbation analysis of the SSFM error and argue that at practical accuracies, the well-known arguments of the Baker-Campbell-Hausdorff (BCH) [1,3] formula may not hold.

The student should understand how both the symmetric and asymmetric SSFM [1] are derived from the NLSE and what the BCH formula implies for both methods. Finally, the key ideas of [3] should be understood and compared to state-of-the-art usages of the SSFM.

#### References

- [1] Agrawal, G. P. "Nonlinear fiber optics 5th ed." (2012): pp. 51.
- [2] Schneider, Thomas. "Nonlinear optics in telecommunications". Springer Science & Business Media, 2004, pp. 139.
- [3] S. Musetti, P. Serena and A. Bononi, "On the Accuracy of Split-Step Fourier Simulations for Wideband Nonlinear Optical Communications," in Journal of Lightwave Technology, vol. 36, no. 23, pp. 5669-5677, Dec.1, 2018.

#### Prerequisites

- Optical Communication Systems

### Insertion and Deletion Correction Using Convolutional Codes (Andreas Lenz)

Due to recent advances in modern storage technologies, such as DNA-based data storage and racetrack memories, the investigation of insertion and deletion (synchronization) errors has gained significant attention in the last years. This is because insertion and deletions errors are one of the limiting factors of such storage systems.

Since the information about the position of the received bits is not certain under the presence of insertion and deletion errors, it is required to design codes that can handle this uncertainty. One way is to use convolutional codes [1] and adapt the Viterbi decoder to be able to handle insertions and deletions. The advantage hereby is that the Viterbi can be used to simultaneously correct synchronization and also conventional symbol substitution errors.

The task of the student will be to investigate convolutional codes for insertions and deletions and, if time allows, implement the Viterbi decoder.

#### References

- [1] Mohamed F. Mansour and Ahmed H.Tewfik, "Convolutional Decoding in the Presence of Synchronization Errors", in IEEE Journal on Selected Areas in Communications, vol. 28, no. 2, pp. 218-227, 2010

#### Prerequisites

- Channel Coding

### Array Codes with Locality (Lia Liu)

Locality has been increasingly studied for coded distributed storage systems (DSS), since we want to keep the communication cost small when some erroneous nodes (e.g., erased, updated) need to be repaired via contacting other nodes. Large-scale DSS can be represented as arrays, where the entries represents the memory cells. Different components codes in [1-4] are considered to construct array codes. Each of them has certain strength and weakness while coping with different error models.

The student’s task is to understand the code constructions introduced in [1-4] and compare the schemes in terms of code rate, error/erasure correction capability, field size, etc.

#### References

- [1] M. Blaum, and S. Hetzler, “Array Codes with Local Properties.” Preprint: arxiv.org/abs/1906.11731
- [2] H. Liu, L. Holzbaur, and A. Wachter-Zeh. “Locality in Crisscross Error Correction.” XVI International Workshop on Algebraic and Combinatorial Coding Theory (ACCT), 2018. arxiv: arxiv.org/abs/1806.07496
- [3] S. Kadhe, S. Rouayheb, I. Duursma, and A. Sprintson. “Codes With Locality in the Rank and Subspace Metrics.” IEEE Transactions on Information Theory 65 (2017): 5454-5468. arxiv: arxiv.org/abs/1707.05944
- [4] N. Silberstein, T. Etzion, and M. Schwartz. “Locality and Availability of Array Codes Constructed from Subspaces.” 2017 IEEE International Symposium on Information Theory (ISIT), 2017. arxiv: arxiv.org/abs/1701.07501v3

#### Prerequisites

- Channel Coding