Performance Analysis of Binary Chirp Decoding

Binary Chirp (BC) codebooks consist of ${N^{\left( {{{\log }_2}N + 3} \right)/2}}$ lines in ${\mathbb{C}^N}$, equivalent up to overall phase rotations. Exploiting the underlying algebraic structure, the BCs allow suboptimal decoders with complexity N(logN)
²
, based on autocorrelations between the received signal and its permuted versions. We analyze the performance of these decoders in additive white Gaussian noise channels, providing lower bounds of decoding error probability, which are tight in the limits of low and high signal-to-noise ratio. Due to the autocorrelation nature of the receiver, the error probability becomes a function of order statistics of χ
²
-distributed random variables. Our results can be used when dimensioning communication systems where BCs are used as component codes.