  From the eardrum to the auditory cortex, where acoustic stimuli are decoded,
there are several stages of auditory processing and transmission where
information may potentially get lost. In this paper, we aim at quantifying the
information loss in the human auditory system by using information theoretic
tools.
  To do so, we consider a speech communication model, where words are uttered
and sent through a noisy channel, and then received and processed by a human
listener.
  We define a notion of information loss that is related to the human word
recognition rate. To assess the word recognition rate of humans, we conduct a
closed-vocabulary intelligibility test. We derive upper and lower bounds on the
information loss. Simulations reveal that the bounds are tight and we observe
that the information loss in the human auditory system increases as the signal
to noise ratio (SNR) decreases. Our framework also allows us to study whether
humans are optimal in terms of speech perception in a noisy environment.
Towards that end, we derive optimal classifiers and compare the human and
machine performance in terms of information loss and word recognition rate. We
observe a higher information loss and lower word recognition rate for humans
compared to the optimal classifiers. In fact, depending on the SNR, the machine
classifier may outperform humans by as much as 8 dB. This implies that for the
speech-in-stationary-noise setup considered here, the human auditory system is
sub-optimal for recognizing noisy words.
