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Random codes: minimum distances and error exponents

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2 Author(s)

Minimum distances, distance distributions, and error exponents on a binary-symmetric channel (BSC) are given for typical codes from Shannon's random code ensemble and for typical codes from a random linear code ensemble. A typical random code of length N and rate R is shown to have minimum distance NδGV(2R), where δGV(R) is the Gilbert-Varshamov (GV) relative distance at rate R, whereas a typical linear code (TLC) has minimum distance NδGV(R). Consequently, a TLC has a better error exponent on a BSC at low rates, namely, the expurgated error exponent.

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Information Theory, IEEE Transactions on  (Volume:48 ,  Issue: 9 )