The capacity of the uniform noise rewritable channel with average cost

We present a closed form expression for the capacity of the uniform noise rewritable channel with average write cost and a constraint on the input range. We show the existence of a critical cost κ0 such that for all costs κ ≥ κ0, the capacity/cost tradeoff is given by an offset added to the logarithm of the cost. Assuming κ0 > 1, for 1 ≤ κ < κ0 the capacity/cost tradeoff grows faster than a logarithm.