Autocorrelation and Spectrum Analysis for Variable Symbol Length Communications with Feedback

Variable-length feedback codes can provide advantages over fixed-length feedback or non-feedback codes. This letter focuses on uncoded variable-symbol-length feedback communication and analyzes the autocorrelation and spectrum of the signal. We provide a mathematical expression for the autocorrelation that can be evaluated numerically. We then numerically evaluate the autocorrelation and spectrum for the variable-symbol-length signal in a feedback-based communication system that attains a target reliability for every symbol by adapting the symbol length to the noise realization. The analysis and numerical results show that the spectrum changes with SNR when the average symbol length is fixed, and approaches the fixed-length scheme at high SNR.