A. Simple two-pathway retinal circuit model. A stimulus (s) is presented and transmitted to separate ON and OFF pathways, which receive correlated corrupting noises η+ and η-, respectively. The signals are passed through encoding nonlinearities to produce inputs r+ = f+(s+ η+) + ζ+ and r- = f-(-s- η
) + ζ- to retinal ganglion cells; these responses have been further corrupted by correlated noises ζ+ and ζ-. We calculate the optimal shape of the nonlinearities f+(z) and f
(z) as functions of the noise and stimulus distribution parameters. B. The optimal encoding nonlinearities for low pre- and post-nonlinearity noise variance. C. Large noise variances. D. Very large post-nonlinearity noise.