Chirp Reconstruction Algorithm for Generalized Second-Order Reed-Muller Frames

Abstract

We consider low-complexity decoding of generalized second-order Reed-Muller frames. Second-order Reed-Muller frames are highly non-coherent, highly-structured, sets of $2^{m_{-}}$ dimensional complex vectors with fourth root-of-unity alphabet, that come by design with a low-complexity chirp reconstruction algorithm (ChirpRA). In this paper, we extend ChirpRA to expanded frames in 2m-dimension with same alphabet, and we also generalized it to Reed-Muller frames in other dimensions constructed from different alphabets.