Galligan, Kevin (2024) Universal Error Correction Decoding Algorithms. PhD thesis, National University of Ireland Maynooth.

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Abstract

There is no perfect communication channel, and any communication necessarily involves some level of noise. Attempting to hold a conversation across a crowded room, for instance, will likely result in miscommunication due to background noise. Channel coding, as a field, is concerned with reducing the rate of error in such noisy communication channels. This can be achieved by encoding messages with channel codes, which allow communication errors to be detected and corrected. The study of channel coding was launched in 1948 [78], and it now underlies critical technology such as the Internet, space communications, and storage of digital information [57]. In this thesis, we develop new algorithms and channel coding techniques based on Guessing Random Additive Noise Decoding (GRAND), a recently introduced family of decoders for channel codes. GRAND algorithms, unusually, can decode any channel code of any length that has a moderate amount of redundancy. Assuming that all messages are equally likely, they achieve maximum-likelihood decoding, which is the best possible outcome of decoding a channel code. GRAND challenges several assumptions of traditional channel coding and asserts a new decoding paradigm in which the particular channel code being used doesn't matter, allowing greater flexibility in the design of communication schemes. Given that an upper bound on GRAND's computational complexity increases exponentially with the amount of redundancy in a code, it is impractical to directly decode arbitrary channel codes that have a large amount of redundancy. The goal of this thesis is thus to explore if GRAND can be used to decode such high-redundancy codes, which are suitable for the noisiest channel environments. To that end, we introduce and develop two iterative decoding algorithms, Iterative GRAND (IGRAND) and block turbo decoding with GRAND, for a powerful class of channel codes known as product codes. Product codes are, in general, high-redundancy codes formed from a concatenation of low- to moderateredundancy component codes. The key insight of the algorithms considered here is that GRAND can decode product codes by decoding each of their component codes in turn, circumventing the aforementioned complexity constraint. Soft information indicates the reliability of a received message and is useful for a wide range of applications, including error detection and turbo decoding. In addition to the goal of decoding high-redundancy codes, this thesis also investigates the question of whether it is possible for GRAND decoding to output accurate soft information. We derive probabilistic soft output formulae for GRAND algorithms, evaluate their accuracy, and explore their application to error detection.

Item Type:	Thesis (PhD)
Keywords:	Universal; Error; Correction; Decoding; Algorithms;
Academic Unit:	Faculty of Science and Engineering > Research Institutes > Hamilton Institute
Item ID:	18343
Depositing User:	IR eTheses
Date Deposited:	02 Apr 2024 10:56
URI:
Use Licence:	This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here

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