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Binary Chirps (BCs) are 2^m dimensional complex vectors employed in deterministic compressed sensing and in random/unsourced multiple access in wireless networks. The vectors are obtained by exponentiating codewords from a 2nd order Reed-Muller code defined over Z4, the ring of integers modulo 4. We doubled the size of the BC codebook, without compromising performance in wireless multiple access.more » « less
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Pllaha, Tefjol; Heikkila, Elias; Calderbank, Robert; Tirkkonen, Olav (, 2022 IEEE Wireless Communications and Networking Conference)We consider autocorrelation-based low-complexity decoders for identifying Binary Chirp codewords from noisy signals in N = 2^m dimensions. The underlying algebraic structure enables dimensionality reduction from N complex to m binary dimensions, which can be used to reduce decoding complexity, when decoding is successively performed in the m binary dimensions. Existing low-complexity decoders suffer from poor performance in scenarios with strong noise. This is problematic especially in a vector quantization scenario, where quantization noise power cannot be controlled in the system. We construct two improvements to existing algorithms; a geometrically inspired algorithm based on successive projections, and an algorithm based on adaptive decoding order selection. When combined with a breadth-first list decoder, these algorithms make it possible to approach the performance of exhaustive search with low complexity.more » « less
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