▁called ▁ 0 ▁and ▁ 1 ). ▁( A ▁non - binary ▁channel ▁would ▁be ▁capable ▁of ▁transm itting ▁more ▁than ▁two ▁symbols , ▁possibly ▁even ▁an ▁infinite ▁number ▁of ▁choices .) ▁The ▁channel ▁is ▁not ▁perfect ▁and ▁sometimes ▁the ▁bit ▁gets ▁" er ased "; ▁that ▁is , ▁the ▁bit ▁gets ▁sc ram bled ▁so ▁the ▁receiver ▁has ▁no ▁idea ▁what ▁the ▁bit ▁was . ▁ ▁The ▁B EC ▁is , ▁in ▁a ▁sense , ▁error - free . ▁Un like ▁the ▁binary ▁symmetric ▁channel , ▁when ▁the ▁receiver ▁gets ▁a ▁bit , ▁it ▁is ▁ 1 0 0 % ▁certain ▁that ▁the ▁bit ▁is ▁correct . ▁The ▁only ▁confusion ▁ar ises ▁when ▁the ▁bit ▁is ▁er ased . ▁ ▁This ▁channel ▁is ▁often ▁used ▁by ▁the or ists ▁because ▁it ▁is ▁one ▁of ▁the ▁simplest ▁no isy ▁channels ▁to ▁analyze . ▁Many ▁problems ▁in ▁communication ▁theory ▁can ▁be ▁reduced ▁to ▁a ▁B EC . ▁ ▁Definition ▁ ▁A ▁binary ▁er asure ▁channel ▁with ▁er asure ▁probability ▁ ▁is ▁a ▁channel ▁with ▁binary ▁input , ▁t ern ary ▁output , ▁and ▁probability ▁of ▁er asure ▁. ▁That ▁is , ▁let ▁ ▁be ▁the ▁transm itted ▁random ▁variable ▁with ▁alphabet ▁. ▁Let ▁ ▁be ▁the ▁received ▁variable ▁with ▁alphabet ▁, ▁where ▁ ▁is ▁the ▁er asure ▁symbol . ▁Then , ▁the ▁channel ▁is ▁character ized ▁by ▁the ▁conditional ▁prob abilities ▁ ▁Cap acity ▁of ▁the ▁B EC ▁ ▁The ▁capacity ▁of ▁a ▁B EC ▁is ▁. ▁ ▁Int uit ively ▁ ▁can ▁be