Statistical Mechanics of Low-Density Parity Check Error-Correcting Codes over Galois Fields

Details Statistical Mechanics of Low-Density Parity Check Error-Correcting Codes over Galois Fields Statistical Mechanics of Low-Density Parity Check Error-Correcting Codes over Galois Fields

2000-10-05

arxiv.org/abs/cond-mat/0010073v1

Physics

Condensed Matter

Statistical Mechanics

7 pages, 1 figure

Scientific paper

10.1209/epl/i2001-00564-y

A variation of low density parity check (LDPC) error correcting codes defined over Galois fields ($GF(q)$) is investigated using statistical physics. A code of this type is characterised by a sparse random parity check matrix composed of $C$ nonzero elements per column. We examine the dependence of the code performance on the value of $q$, for finite and infinite $C$ values, both in terms of the thermodynamical transition point and the practical decoding phase characterised by the existence of a unique (ferromagnetic) solution. We find different $q$-dependencies in the cases of C=2 and $C \ge 3$; the analytical solutions are in agreement with simulation results, providing a quantitative measure to the improvement in performance obtained using non-binary alphabets.

Affiliated with

Also associated with

No associations

Rating

Statistical Mechanics of Low-Density Parity Check Error-Correcting Codes over Galois Fields does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Statistical Mechanics of Low-Density Parity Check Error-Correcting Codes over Galois Fields, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Statistical Mechanics of Low-Density Parity Check Error-Correcting Codes over Galois Fields will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-493709