Upper and Lower Bounds on the Minimum Distance of Expander Codes

Details Upper and Lower Bounds on the Minimum Distance of Expander Codes Upper and Lower Bounds on the Minimum Distance of Expander Codes

2011-05-31

arxiv.org/abs/1105.6224v1

Computer Science

Information Theory

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

Scientific paper

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.

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