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There is an Underwater Acoustics Laboratory somewhere in one of the several U.S. Naval Commands based on the campus of the NASA John C. Stennis Space Center in coastal Mississippi.  Google your way to NASA/SSC, and try to establish telephone contact with the Education Outreach folks first.  Some of the work done in the lab is highly classified to the extreme (anti-submarine and naval mine warfare research, et cetera), so using the education folks as intermediaries would constitute good protocol.  I know a couple of those dudes from back in my 'Salad Days', and I am certain they will have some answers for you if anyone can just get them to talk about their research work.

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Both data compression and audio are big topics, so be prepared to do a lot of reading . Incidentally, what type of degree is this topic for? I'm just asking so I can frame the discussion in a way that's useful for you.

Something to watch, by the way, is that lots of normal words have specialised meanings in each field (and in the computing world, different meanings in different sub-fields).

To most audio engineers, "compression" is used to refer to dynamic range compression, the thing that makes TV advertisements sound louder than programmes.

Compression in computing generally refers to data compression, but there are different sub-fields of this. There are general-purpose lossless statistical compressors, special-purpose lossy compressors for special kinds of source data (e.g. video and audio), and in the mathematics of information theory much more elaborate kinds of thing (as in the works of Gregory Chaitin).

Now, we can talk a bit about data compression of audio (e.g. the fact it's best done by concentrating on the frequency domain, which involves some fun maths), or in the specific case of MP3 the use of psychoaucoustics. MP3-compressed data is analysed in the frequency domain to remove frequencies present in the original sound but that the human auditory system doesn't perceive, so it produces quite a different resulting output signal.

However, rather than that what the original proposal speaks to is an intuition that sounds related to communication are going to be more "complex" than other sounds. That's an interesting notion, but it's one that is actually quite hard to establish.

When we talk about information in signals, there are two main kinds. There is the structure of the signal itself, which is "information" of one kind. Then, there is the communication content that is being carried by the signal, which is what most people would think of as the "information".

The communication content of sounds are carried largely by modulating them. The sounds we produce via the physical processes in the larynx are complex mathematically to begin with, but much of the communication content is then applied as an extra layer over the top of that by the mouth, tounge, and lips.

Similarly, with the sounds of "boat noise", one might think the sound of a screw propellor is simple. But, it's not. There is the basic "beat" of the screw turning modulated by doppler effects based on your relative angle to it, the chaotic swirling of the turbulent water it produces, and then all kinds of "information" carried on top of it (the pistons of a diesel engine producing tiny variations in the rate that the screw turns, for example).

Now, the basic approach your supervisor has suggested is something that does more-or-less work in computing, but often in counterintuitive ways, and not for the reasons you might think.

For instance, plain English text communication is less random than much other data computers deal with, because the format we've encoded printed text in - the roman character set, and english spelling - actually contains a lot of redundancy. This redundancy helps people understand each other and communicate successfully, but it means that the mathematical information content - the "complexity", so to speak - is actually unusually low.

The end result of all this is that the initial hypothesis, which is that sound representing intelligent communication is more "complex" than other sound, is based on some slightly suspect anthropocentric reasoning. The physical processes that produce the sound around us are wonderfully rich and complicated, and carry in them all kinds of information about the physical processes that produce them (ask a seismologist what they can determine from the wiggling of a seismograph, that being very-low-frequency sound).

The communication content of the sounds humans (or dolphins) make is really a very tiny amount of additional variation on top of that, and my intuition is that whether you end up with a detectable result of any kind is largely going to be determined by subtle biases in methodology.