Tight Capacity Bounds for Discrete Memoryless Channels with Synchronization Errors, Additive Noise, and Large Alphabets

We study the capacity of discrete memoryless channels with synchronization errors and additive noise. We show that with very large alphabets, their capacity can be achieved by i.i.d. input sources, and prove tight lower and upper capacity bounds. An interesting result is that as long as the input sequences are not completely deleted, the capacity of channels with large alphabets corrupted by discrete timing errors is always nonzero even if all the symbols are corrupted.