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Asymmetric Shaping for Higher-Order Modulation Dirty-Paper Coding using Polar Codes

Description

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Supervisor:

Student

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Decoding for High-Throughput Applications

Description

Implementation and analysis of decoding algorithms for high-throughput applications.

Supervisor:

Student

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Soft-Aided Decoding of Product-Like Codes

Description

Topic for "Hauptseminar Digitale Kommunikationssysteme" (MSEI) (https://www.ei.tum.de/index.php?id=5492) NOT for "Seminar on Topics in Communications Engineering" (MSCE).

Coding for high-throughput applications has become an active research field both in industry and academia. To meet the ever increasing demand for higher data rates, low-complexity algorithms became necessary, being able to handle throughputs in the order of several hundreds of Gigabits per second with low power consumption. This requirement has led to a widespread use of hard-decision decoding (HDD) algorithms for error correction in fiber-optic networks where optimal soft-decision decoding (SDD) has been considered too complex. Such systems usually employ product-like codes, which can be particularly well decoded with HDD.

Only recently, several soft-aided decoding algorithms have been proposed to close the performance gap between HDD and SDD while keeping moderate complexity, e.g., iterative bounded distance decoding with scaled reliability [1], iterative generalized minumum distance decoding with scaled reliability [2], and binary message passing based on generalized minimum distance decoding [3].

The student's task is to understand and discuss the complexity-performance tradeoff of HDD and SDD and the role of the decoder data flow in the tradeoff. Further, the student will summarize the algorithms [1]-[3] and compare them from a performance-complexity perspective. The student will also relate this algorithms to the standard algorithms for HDD and SDD of product-like codes, iterative bounded distance decoding and Chase-Pyndiah decoding [4], respectively. Finally, the student will discuss the soft-aided decoding approach in comparison to other low-complexity decoding approaches in literature such as quantized message passing for low-density parity-check codes [5], [6], and concatenated SDD-HDD architectures [7], [8].

References:

• [1] A. Sheikh, A. Graell i Amat, and G. Liva, “Binary message passing decoding of product-like codes,” IEEE Trans. Commun., vol. 67, no. 12, pp. 8167–8178, Dec. 2019.
• [2] A. Sheikh, A. Graell i Amat, G. Liva, C. Häger, and H. D. Pfister, “On low-complexity decoding of product codes for high-throughput fiber-optic systems,” in Proc. IEEE Int. Symp. on Turbo Codes & Iterative Inf. Proc. (ISTC), Hong Kong, Dec. 2018.
• [3] A. Sheikh, A. Graell i Amat, and G. Liva, “Binary message passing decoding of product codes based on generalized minimum distance decoding,” in Proc. 53rd Annu. Conf. Inf. Sciences and Systems (CISS), Baltimore, MD, Mar. 2019.
• [4] R. Pyndiah, “Near optimum decoding of product codes: Block turbo codes,” IEEE Trans. Commun., vol. 46, no. 8, pp. 1003–1010, Aug. 1998.
• [5] G. Lechner, T. Pedersen, and G. Kramer, “Analysis and Design of Binary Message Passing Decoders,” IEEE Trans. Commun., vol. 60, no. 3, Mar. 2012.
• [6] F. Steiner, E. B. Yacoub, B. Matuz, G. Liva, and A. Graell i Amat, “One and two bit message passing for SC-LDPC codes with higher-order modulation,” J. Lightwave Technol., vol. 37, no. 23, pp. 5914–5925, Dec. 2019.
• [7] M. Barakatain, F. R. Kschischang, “Low-complexity concatenated LDPC-staircase codes,” J. Lightwave Technol., vol. 36, no.12, pp. 2443–2449, Jun. 2018.
• [8] M. Barakatain, D. Lentner, G. Böcherer, F. R. Kschischang, “Performance-Complexity Tradeoffs of Concatenated FEC for Higher-Order Modulation,” J. Lightwave Technol., vol. 38, no. 11, pp. 2944–2953, Jun. 2020.

Prerequisites

Supervisor:

Student

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Protograph-based LDPC Code Design for Finite Number of Iterations

Description

Low-density parity-check (LDPC) codes are usually designed using an extrinsic information transfer (EXIT) analysis to compute the asymptotic iterative decoding threshold for a given code ensemble. The iterative decoding threshold over an additive white Gaussian noise (AWGN) channel is thereby defined as the minimum signal-to-noise ratio (SNR) for which the a posteriori mutual information converges to one as the number of decoding iterations goes to infinity.

For practical applications, however, decoding is often performed using only a small number of iterations. Mulholland et al. investigated a code design for protograph-based LDPC codes where the protograph-based EXIT (PEXIT) analysis [1] is run for the targeted number of decoding iterations only [2]. They showed that for the binary erasure channel (BEC), the obtained iteration-constrained threshold does not match the bit error rate (BER) threshold of finite-length codes.

In this thesis, the student will understand and reproduce the results from [2], apply these tools to the AWGN channel, and compare them to code design tools developed at the institute.

[1] G. Liva and M. Chiani, “Protograph LDPC codes design based on EXIT analysis,” in Proc. IEEE Global Telecommun. Conf. (GLOBECOM), Nov. 2007, pp. 3250–3254.

[2] I. P. Mulholland, E. Paolini, and M. F. Flanagan, “Design of protograph-based LDPC code ensembles with fast convergence properties,” in Proc. Int. ITG Conf. Syst. Commun. Coding (SCC), Feb. 2017, pp. 1–6.

Prerequisites

Supervisor:

Student

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Code construction for quasi-cyclic LDPC codes based on PEG and ACE

Description

Finite length low-density parity-check codes can be constructed based on different approaches. The most obvious approach is a random, unconstrained construction, where the edges in the parity-check matrix are placed based on the desired edge distribution pairs.

In general, this approach leads to suboptimal performance, as the codes have  a lot of small cycles, which deteriorate the belief propagation decoding. To mitigate this, greedy approaches like progressive edge (PEG) have been proposed. PEG can further be complemented by taking the extrinsic cycle degree into accout [2], which also provides an additional measure for the "harmfullness" of a cycle in the Tanner graph.

In this research internship, the student is asked to implement a tool for building finite length QC LDPC codes which uses both PEG and ACE for girth optimization and conditioning.

[1] X.-Y. Hu, E. Eleftheriou, and D. M. Arnold, “Regular and irregular progressive edge-growth Tanner graphs,” IEEE Trans. Inf. Theory, vol. 51, no. 1, pp. 386–398, Jan. 2005.

[2] T. Tian, C. R. Jones, J. D. Villasenor, and R. D. Wesel, “Selective avoidance of cycles in irregular LDPC code construction,” IEEE Trans. Commun., vol. 52, no. 8, pp. 1242–1247, 2004.

Prerequisites

Supervisor:

Student