There is a preconscious reduction of bandwidth (lot's of pruning). The input is transformed, from lots of points in low dimensional spaces to fewer points in a higher dimensional one, and it is hypothesized that consciousness is isomorphic to the integration process that performs that transformation.
That theory has the big advantage of being neither anthropo- nor neurocentric. It can be related to any physical system (biological or otherwise).
Stephen Hawking has been spotted at consciousness conferences recently.
edit: corrected and refined.
Furthermore Kupfmuller,Nørretranders are not alone in this regard:
"We can therefore conclude that the maximal information flow of the process of conscious sensory perception is about 40 bits/second -- many orders of magnitude below that taken in by receptors [nerve endings]."
-- Manfred Zimmermann. "Neurophysiology of Sensory Systems" in Robert F. Schmidt ed., Fundamentals of Sensory Physiology (1986) p.116
"... If we do not act in the way we think we do, the reason is partly to do with the bandwidth of consciousness - its ability to transmit information measured in terms of bits per second. [...] The bandwidth of consciousness is around eighteen bits."
--John N Gray (2002) 
First prize would be evidence for a refutation of the 'consciousness operates at a low information rate' hypothesis, as opposed to conjecture or speculation.
That being said, I didn't read the papers in question, and they may have a valid argument.
However, I don't understand how you can encode in 16 per second the evolution of your current experience out of all the possible states your brain may be in and go to.
There is a lot of compression due to expectations, but I still find it hard to believe that it is so low.
Edit: For serial tasks (say, reading, listening to someone speak), the 16-40 bps range makes some sense, but I don't think that visual experience can be reduced that much.
Edit 2: Take, say, music. You can encode the audible note tones on 6-7 bit. You can easily listen 4 notes chords played 4 times per second. We're already in the 100 bps ball park, and we haven't taken timbre and loudness into account.
This advantage has a downside: the definition is so broad that any large, integrated system can be described as conscious. Of course, you can argue about what counts as "integration" and whether, say, Los Angeles is really a well-integrated system.
The point is that the nature of the experience is isomorphic to the integration process, which is very different from system to system.
That's why IMO, for example, anthropomorphism in AI is a dead end, and the turing test is irrelevant.
If not off, at least, it is greatly reduced, and memory encoding is turned off, anyway. You can even wake up for a few minutes and not remember it.
That is, in slow wave sleep. In REM sleep, you can be conscious, and probably are systematically (dreams) even though you don't always remember it.
"and hence how designers of e-learning materials need to avoid creating cognitive overload."
is totally ridiculous. His conclusion might be true, but unless he wants to posit the number of these consciousness bits expended on parts of e-learning software it doesn't follow from the premise.
By that measure, a two-hour movie can be compressed down to 22.5 kilobytes... :-)
I can't speak for other's but for myself that sort of compression ratio seems at least possible.
Most of the conscious mind is dealing with a highly compressed stream of symbols (compressed abstracted versions of the actual audio-visual stream), and how they relate to one another in time and space.
More concretely, imagine yourself watching a movie in the theatre:
"That actor's accent is a bit off" "Why do her teeth look so bright?" "I forgot who directed this, hmm was it that Swedish guy.. the guy who directed 'Heaven', wait... was he Swedish? Aargh I wish I could go on IMDB now and check"
".. ugh that kid in the front row's phone is distracting"
"The visual style reminds me of this other movie".
"The music is getting ominous, something bad is about to happen."
"Oh crap the main character is screwed, how he is going to escape this trap?"
"I wonder if my gf is enjoying the movie?"
Is this referring to conscious sensations recorded in memory, then maybe I can be warmed up to the idea. Long term memory is definitely spotty, although why can I recall my favorite latest dance track with such precision? The lead, bass, kick, clap and atmospherics themselves must compose more than 16 bits/sec.
What about what is processed by the unconscious, to be remembered later? Like when you didn't notice something at the time, but in the future something sparks your memory to remember it. Does the unconscious (that can become conscious) operate on a separate port with its own bandwidth?
But consciously? I strictly, abhorrently refuse. This music is FLAC, baby.
On the other hand, if it is true, then maybe our brain's compression algorithms are insane. Maybe we process sensations in relation to all our past sensation - I hear only the unique parts of this epic bassline, but the data contains pointers to all the basslines I've heard before, turning my consciousness into a complex amalgam of current and past. Then a two-hour movie in 22.5 kilobytes could make sense.
For an example of the estimation of the conscious bandwidth while listening to music, see the second edit of this comment: http://news.ycombinator.com/item?id=4829147
There are active paradigms to detect it in non-communicating subjects (playing tennis in one's head while in an FMRI, for example), and research is under way to find passive paradigms.
See for example: Preserved feedforward but impaired top-down processes in the vegetative state. http://www.ncbi.nlm.nih.gov/pubmed/21566197 , or this: http://blogs.nature.com/news/2012/10/a-tool-to-quantify-cons...
Quick : Think of that internet song with the Korean guy doing the horsey dancing. Heard it a few times? What's the third verse like?
We're not talking anything like lossless compression : Kind of the opposite.