I think work by Erik Hoel in studying causal emergence might bear on this, especially in the role that error correction might play: https://www.mdpi.com/1099-4300/19/5/188

It seems that error correcting channels provide a mechanism for the emergence of agency which must play an important role in consciousness. Another idea which I think is also buried in Hoel’s work, is dealt directly by Christoph Adami :http://rsta.royalsocietypublishing.org/content/374/2063/20150230

I think before we can grapple with the question of consciousness we should first define what we mean by ‘information’. I particularly like Adami’s definition, as data which allows you to “make a prediction better than chance”. Hoel uses the term ‘Effective Information’ which is very similar to Adami’s definition of information. For Hoel this constitutes the critical part of causal emergence.