Shannon's Theorems for Channels with Synchronization Errors

A memoryless channel with synchronization errors is defined as a channel in which each input symbol independently of other symbols is transformed into a word of random (including also zero) length, and at the output of the channel the ordinal number of the input symbol from which the given output symbol was obtained is unknown. For such channels Shannon’s theorem on transmission rates for which noise stable coding methods exist, is formulated and proved.