Low-Complexity Grassmannian Quantization Based on Binary Chirps

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 di- mensions, 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.