On the capacity of binary input symmetric q-ary output channels with synchronization errors

In this paper, we develop several lower bounds on the capacity of binary input symmetric q-ary output channels with synchronization errors, e.g., substitution/erasure channels with synchronization errors. More precisely, we show that if a channel with synchronization errors can be decomposed into a cascade of two independent channels where only the first one suffers from synchronization errors, a lower bound on its capacity related to the capacity of the one with only synchronization errors can be given. We present several examples with the new approach and demonstrate that for certain channels, e.g., deletion/substitution channel, it is possible to derive tighter capacity lower bounds than the existing ones.