Error Exponents of Expander Codes

Error exponents of expander codes

On expander codes

Expander codes count among the numerous applications of expander graphs. The term was first coined by Sipser and Spielman when they showed how expander graphs can be used to devise error-correcting codes with large blocklengths that can correct efficiently a constant fraction of errors. This approach has since proved to be a fertile avenue of research that provides insight both into modern iter...

Low-Density Parity-Check Codes: Constructions and Bounds

Low-density parity-check (LDPC) codes were introduced in 1962, but were almost forgotten. The introduction of turbo-codes in 1993 was a real breakthrough in communication theory and practice, due to their practical effectiveness. Subsequently, the connections between LDPC and turbo codes were considered, and it was shown that the latter can be described in the framework of LDPC codes. In recent...

Expander-like Codes based on Finite Projective Geometry

We present a novel error correcting code and decoding algorithm which have construction similar to expander codes. The code is based on a bipartite graph derived from the subsumption relations of finite projective geometry, and ReedSolomon codes as component codes. We use a modified version of well-known Zemor’s decoding algorithm for expander codes, for decoding our codes. By derivation of geo...

Expander Codes

We present a new class of asymptotically good, linear error-correcting codes based upon expander graphs. These codes have linear time sequential decoding algorithms , logarithmic time parallel decoding algorithms with a linear number of processors, and are simple to understand. We present both randomized and explicit constructions for some of these codes. Experimental results demonstrate the ex...