No input symbol should occur more frequently than 1-1/e

Consider any discrete memoryless channel (DMC) with arbitrarily but finite input and output alphabets X , Y respectively. Then, for any capacity achieving input distribution all symbols occur less frequently than 1 − 1 e . That is, max x∈X P (x) < 1− 1 e where P ∗(x) is a capacity achieving input distribution. Also, we provide sufficient conditions for which a discrete distribution can be a capacity achieving input distribution for some DMC channel. Lastly, we show that there is no similar restriction on the capacity achieving output distribution. Index Terms Channel Capacity, Discrete Memoryless Channels (DMC).