Multiple parallel channels are ubiquitous in optical communications, with spatial division multiplexing (separate physical paths) and wavelength division multiplexing (separate optical wavelengths) being the most common forms. Here, we investigate the viability of polarization division multiplexing, the separation of distinct parallel optical communication channels through the polarization properties of light. Two or more linearly polarized optical signals (at different polarization angles) are transmitted through a common medium, filtered using aluminum nanowire optical filters fabricated on-chip, and received using individual silicon photodetectors (one per channel). The entire receiver (including optics) is compatible with standard CMOS fabrication processes. The filter model is based upon an input optical signal formed as the sum of the Stokes vectors for each individual channel, transformed by the Mueller matrix that models the filter proper, resulting in an output optical signal that impinges on each photodiode. The results show that two- and three-channel systems can operate with a fixed-threshold comparator in the receiver circuit, but four-channel systems (and larger) will require channel coding of some form. For example, in the four-channel system, 10 of 16 distinct bit patterns are separable by the receiver. The model supports investigation of the range of variability tolerable in the fabrication of the on-chip polarization filters.