Consider the binary input, ternary output binary erasure channel (BEC) given in Fig. 1.22, where ∆ denotes an erasure and δ is the probability of an erasure. Assume that we use this channel for...

Consider the binary input, ternary output binary erasure channel (BEC) given in Fig. 1.22, where ∆ denotes an erasure and δ is the probability of an erasure. Assume that we use this channel for communication together with maximum-likelihood (ML) decoding. Show that the ML decoding algorithm corrects all erasure patterns whose Hamming weights are less than the minimum distance dmin.

Fig. 1.22