Approaching Non-Asymptotic FEC Limits for GNSS and Beyond

The goal of this SBIR is to advance the state-of-the-art in forward error correction (FEC) coding in the very short block length regime. We seek code designs and decoding algorithms that can approach fundamental, information-theoretic limits for block sizes as short as 50 bits. Very short block length FEC is important in global navigation satellite systems (GNSS) and ultra-reliable low-latency communications (URLLC). Tight bounds on FEC performance in the finite block length regime have been known since 2010. Whereas Shannon’s channel coding theorem hinted at capacity-achieving code construction techniques for very long block lengths, Polyanskiy, et al.’s results for very short block lengths provide no such guidance to the FEC practitioner. As of today, the information theory community understands the fundamental limits on coding in the very short to short block length regime, but we do not yet understand how to best approach those limits. This SBIR aims to close that gap between theory and practice. Our approach leverages two high-performance, low-complexity universal decoding algorithms. One was developed by the proposed Principal Investigator as part of his doctoral work at USC, the other was proposed recently by researchers at MIT. Whereas prior work focused on the application of these algorithms to existing codes (e.g., BCH and polar codes), we will design new codes in Phase I that are optimized for these algorithms, thereby unlocking powerful new families of scalable short and very short codes. In Phase II, we will develop flexible decoding architectures for implementation and demonstration in software-defined radio and user equipment. In Phase III, we will bring our designs to market for GNSS and URLLC applications.