In spectrum-sliced wavelength division multiple access (WDMA) optical communication systems, excess noise due to the thermal nature of the broadband source, such as the superfluorescent fiber source (SFS), limits the signal-to-noise ratio (SNR) at the photodetector output. If the statistics of the detected signal are Gaussian, a common assumption, then the bit-error rate (BER) performance of the system is predicted to reach a minimum that cannot be improved by increasing the received optical power. The actual performance, however, depends on the true detection noise statistics. We have measured the statistical distribution of the photoelectric current from a PIN photodiode illuminated by a spectrum-sliced, erbium-doped SFS. The histogram of the measurement data is best described by a negative binomial model for the corresponding photoelectron count with thermal light. Consequently, the BER performance of a spectrum-sliced WDMA system using such a superfluorescent fiber source is not limited by the SNR, a fundamentally different result from that predicted using the Gaussian assumption.