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We present a linear program for the one-way version of the partition bound(denoted $\mathsf{prt}^1_\varepsilon(f)$). We show that it characterizesone-way randomized communication complexity $\mathsf{R}_\varepsilon^1(f)$ withshared randomness of every partial function$f:\mathcal{X}\times\mathcal{Y}\to\mathcal{Z}$, i.e., for$\delta,\varepsilon\in(0,1/2)$, $\mathsf{R}_\varepsilon^1(f) \geq\log\mathsf{prt}_\varepsilon^1(f)$ and $\mathsf{R}_{\varepsilon+\delta}^1(f)\leq \log\mathsf{prt}_\varepsilon^1(f) + \log\log(1/\delta)$. This improvesupon the characterization of $\mathsf{R}_\varepsilon^1(f)$ in terms of therectangle bound (due to Jain and Klauck, 2010) by reducing the additive$O(\log(1/\delta))$-term to $\log\log(1/\delta)$.

A note on the partition bound for one-way classical communication complexity