Bounding the capacity of the multinomial channel using KL divergence covering and packing

We examine the capacity for the multinomial channel, a natural extension of the binomial channel. In the multinomial channel setting, the input is a probability distribution over k entries, and the output of the channel is n items sampled independently with the chosen input probability distribution. Applications of this channel include the use of composite DNA, which is a method for expanding the alphabet set used in DNA storage systems in order to improve the information throughput. In this work, we compute non-asymptotic upper and lower bounds for the information rate of the multinomial channel.