Naturally organic matter is critical. However, in saline/sodic soils, acquiring and developing organic matter is very difficult. High heat, salt saturation and water evaporation mineralize organic matter fiber and break down the materials quickly....sometimes within weeks.

Here is what CSU says:

http://www.ext.colostate.edu/pubs/crops/00504.html

Working with saline tolerant crops comes first. It is the #1 option. This might help:

http://www.ussl.ars.usda.gov/pls/caliche/SALTT42C