Weaknesses of Margulis and Ramanujan-Margulis Low-Density Parity-Check Codes
David Mackay, Michael S. Postol · Electronic Notes in Theoretical Computer Science · 2003
We report weaknesses in two algebraic constructions of low-density parity-check codes based on expander graphs. The Margulis construction gives a code with near-codewords, which cause problems for the sum-product decoder; The Ramanujan-Margulis construction gives a code with low-weight codewords, which produce an error-floor.