On Low-Complexity Decodable Universally Good Linear Codes

Here we discuss the universal block decoding problem for memoryless systems and focus on figures of merit and linear code constructions that facilitate the analysis and construction of low-complexity decoding algorithms. We discuss the properties of ‘universally good codes’ and how such codes lie on the Gilbert-Varshamov bound. We next speak to analogues of the minimum-distance criterion and develop conditions for universal decoding success. We illustrate that universal decoding over linear codes is NP-complete. From here we consider bipartite graph code constructions and illustrate that with large enough fixed degree, linear codes based on graphs and inner codes that are universally good become universally good aggregately.