Bounding the Capacity of the Multinomial Channel Using KL Divergence Covering and Packing

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Jennifer Tang

Published: 2025, Last Modified: 26 Jan 2026ISIT 2025EveryoneRevisionsBibTeXCC BY-SA 4.0
Abstract: 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.