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Upper and Lower Bounds on the Minimum Distance of Expander Codes

Research paper by Alexey Frolov, Victor Zyablov

Indexed on: 31 May '11Published on: 31 May '11Published in: Computer Science - Information Theory



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.