I recommend that you read up a bit on the paleo/paleolithic diet, I'm not familiar with English language resources on this subject, so here are just two sample hits (Like this one http://paleodietlifestyle.com/ or this one http://altmed.creighton.edu/Paleodiet/Details.html) or a blog intended for diabetes and paleo diet specifically http://paleodiabetic.com/2011/11/06/...for-diabetics/
The idea (very simplified) is that we are genetically most suited to consume foods that have been consumed for many many thousands of years before "civilization" ie. to eat the same way as cavemen. In practical terms, a strict paleo diet completely excludes all grains, dairy and legumes (and of course all processed foods) which leaves lean meats tons of vegetables, some fruit (some fruits are very high in sugars thouhgh) and good fats, so the end result is a low carb (and enjoyable) diet.
It's not necessarily something that has to be followed to the letter IMO, but it's very much worth to explore the research behind it and adapt to this lifestyle somewhat, it seems to work wonders for a lot of people and there's research to support that it very much helps with type 2 diabetes. (eg. http://www.ucsf.edu/news/2010/05/598...leolithic-diet)