Upper and Lower Bounds on the Minimum Distance of Expander Codes

Abstract

The minimum distance of expander codes over GF(q) is studied. A new upper bound on the minimum distance of expander codes is derived. The bound is shown to lie under the Varshamov-Gilbert (VG) bound while q >= 32. Lower bounds on the minimum distance of some families of expander codes are obtained. A lower bound on the minimum distance of low-density parity-check (LDPC) codes with a Reed--Solomon constituent code over GF(q) is obtained. The bound is shown to be very close to the VG bound and to lie above the upper bound for expander codes.

arXiv comment5 pages, 1 figure, IEEE International Symposium on Information Theory 2011 (ISIT 2011), Saint Petersburg, Russia, to appear