| Summary: | To meet high reliability and low latency requirements in many new applications, such as those in Ultra Reliable Low Latency Communications (URLLC), a universal optimal decoder is desired that can not only be used to select the best short code candidate, but also can adapt itself to channel memory avoiding performance degradation. The Guessing Random Additive Noise Decoding (GRAND) algorithm makes such a decoder possible. Its prevailing research is outlined in Chapter 1.
The well-known Markovian channels are selected for investigation in Chapter 2, leading to the Markov ordered GRAND (GRAND-MO) decoder. By exploring channel statistical properties in its pattern generation, GRAND-MO achieves significant decoding gains with increasing channel memory, eliminating the need of interleavers. The algorithm is extended to high-order modulations by guessing symbol noises, voiding de-mappers and achieving additional decoding gains, especially with the augmented constellation.
Chapter 3 explains the rationale behind the basic version of Ordered Reliability Bits GRAND (ORGRAND), and extends the algorithm to its full version, overcoming the performance limitation in high SNR regions. A number of complexity control techniques ensure the robustness and feasibility of ORBGRAND for practical implementations. Its extension to high-order modulations is justified with additional decoding gain as well as the elimination of complex de-mapping operations.
Armed with both hard and soft detection variants of GRAND, Cyclic Redundancy Check (CRC) codes are evaluated and recognized with excellent performance, beating state-of-art CA-Polar codes. Random Linear Codes (RLCs) are also enabled to be good candidates for their security features. Owing to the advent of GRAND, the two codes, having long been neglected for error correction, become good candidates to URLLC applications, as presented in Chapter 4.
With decoding performance investigated for GRAND variants, their implementations are also studied. Computational complexity analysis is performed for each GRAND variant as well as CRC decoding. Moreover, a number of practical issues are addressed in Chapter 5 to facilitate hardware implementations of GRAND decoders. The investigation of GRAND from performance to implementation demonstrates GRAND's potentiality as a practical solution to URLLC applications.
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