Low-Complexity Ordered Statistic Decoder for Primitive Rateless Codes

We investigate the performance of primitive rateless (PR) codes and introduce an enhanced ordered statistics decoder (OSD) designed for decoding them. We demonstrate that constructing PR codes using linear Boolean functions simplifies decoding to identifying dual bases over <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\text{G F}\left(2^{k}\right)$</tex>. By leveraging self-dual bases over <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\text{G F}\left(2^{k}\right)$</tex>, the decoding process for high-rate PR codes is simplified, contributing to a reduced complexity OSD algorithm. Through simulations, we establish that high-rate PR codes can achieve block error rates comparable to their BCH counterparts across various signal-to-noise ratios (SNRs) and code rates. The PR code can be tailored to any rate and block length, and the proposed OSD algorithm makes it well-suited for low-latency applications.