High-Rate Fair-Density Parity-Check Codes

Explore the concept of fair-density parity-check (FDPC) codes designed for high-rate applications in this 41-minute lecture by Hessam Mahdavifar from Northeastern University. Learn about the construction of FDPC codes, starting with a base parity-check matrix and using a deterministic combinatorial method. Discover how permuted versions of the base matrix are stacked to create codes with smaller dimensions while maintaining high rates. Examine methods for characterizing and bounding the weight distribution of these new codes, and understand how they are used to derive union-type approximate upper bounds on error probability under Maximum Likelihood decoding. Gain insights into a novel decoding approach combining weighted min-sum message-passing with a progressive list component, known as the MP-PL decoder. Analyze simulation results for various high-rate FDPC codes in moderate-to-large block length regimes, and see how they outperform other state-of-the-art codes in certain parameter ranges while offering lower complexity and latency.