In today’s lecture, we studied the notion of randomized complexity, where the protocols are allowed to use random bits and have a bounded probability of error (over the randomness used by the protocol). In particular, let denote the minimum number of bits exchanged by any protocol for that errs with probability at most . We first saw that any asymptotically binary good code (that can be generated by a deterministic algorithm) implies that . We then saw how using a Reed-Solomon code over an alphabet of size , we can show that (this is a log factor better than the protocol which repeats protocol based on binary codes times).

Next lecture, we’ll go back to our good old tradeoff of rate vs. distance and we’ll prove the Plotkin bound.

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