## Seminar on Topics in Communications Engineering

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

Nummer | 240030134 |

Art | Seminar |

Umfang | 3 SWS |

Semester | Wintersemester 2019/20 |

Unterrichtssprache | Englisch |

Stellung in Studienplänen | Siehe TUMonline |

Termine | Siehe TUMonline |

### Termine

### Teilnahmekriterien & Anmeldung

### Beschreibung

### Lehr- und Lernmethoden

### Links

## Available Topics

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

A bit flipping (BF) algorithm is a decoding algorithm 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

### 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

- [1] https://ieeexplore.ieee.org/abstract/document/8647619
- [2] https://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=8006530

### 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

### Non-square constellations (Delcho Donev)

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

#### References

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

### Deep Learning of the Nonlinear Schrödinger Equation in Fiber-Optic Communications (Javier Garcia)

The Nonlinear Schrödinger Equation (NLSE) is a partial differential equation that governs the optical fiber channel. Digital back-propagation (DBP) is an equalization technique that numerically simulates the Nonlinear Schrödinger Equation (NLSE) in a reversed manner in order to invert the effect of the channel. However, this simulation is computationally expensive and its implementation in real-time systems is challenging. The authors of [1] and [2] propose to exploit the similarity of the structure of DBP with that of a deep neural network in order to design a neural network that is able to equalize the optical fiber channel more efficiently. They claim to achieve similar performance to DBP with reduced computational complexity.

The task of the student is to read Refs. [1] and [2], summarize the proposed solution and compare it to existing equalization methods.

#### References