Concatenated Codes Based on the Plotkin Construction and Their Soft-Input Decoding

• Published in: IEEE transactions on communications Vol. 70; no. 5; pp. 2939 - 2950
• Main Authors: Bailon, Daniel Nicolas, Bossert, Martin, Thiers, Johann-Philipp, Freudenberger, Jurgen
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.05.2022; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Channel coding; Codes; Complexity; computational complexity; Concatenated codes; Decoders; Decoding; error correction codes; Matrix converters; Maximum likelihood decoding; Parity check codes; Polar codes; Reed-Muller (RM) codes; Reliability
• ISSN: 0090-6778; 1558-0857
• DOI: 10.1109/TCOMM.2022.3158329

Reed-Muller (RM) codes have recently regained some interest in the context of low latency communications and due to their relation to polar codes. RM codes can be constructed based on the Plotkin construction. In this work, we consider concatenated codes based on the Plotkin construction, where extended Bose-Chaudhuri-Hocquenghem (BCH) codes are used as component codes. This leads to improved code parameters compared to RM codes. Moreover, this construction is more flexible concerning the attainable code rates. Additionally, new soft-input decoding algorithms are proposed that exploit the recursive structure of the concatenation and the cyclic structure of the component codes. First, we consider the decoding of the cyclic component codes and propose a low complexity hybrid ordered statistics decoding algorithm. Next, this algorithm is applied to list decoding of the Plotkin construction. The proposed list decoding approach achieves near-maximum-likelihood performance for codes with medium lengths. The performance is comparable to state-of-the-art decoders, whereas the complexity is reduced.