On the Practicality of Low-Density Parity-Check Codes

Recent advances in coding theory have produced two classes of codes, turbo codes and low-density parity-check (LDPC) codes, which approach the Shannon limit of channel capacity while admitting efficient implementations of message encoding and decoding in software. Theoretic results about the latter have been shown to apply to the former, hence we examine the evolution of LDPC codes from their origin in Gallager’s 1963 thesis to their current incarnation as tornado codes developed by Luby, Mitzenmacher, Shokrollahi, and Spielman. After considering several analytic approaches to quantifying their performance, we discuss the practicality of LDPC codes, particularly those designed for the erasure channel, when applied to a number of current problems in networking.