On lossy compression of binary matrices

We consider lossy compression of random binary matrices under distortion constraints that strive to preserve the structure of the matrix. Specifically, we assume that matrix elements are statistically independent (but not necessarily identically distributed), and that the worst case row/column average distortion is to be controlled. We discuss a natural notion of matrix types termed (R, c)-type, and provide various results concerning its probability and cardinality, as well as a “Sanov-type” result, in the spirit of the method-of-types. We then derive bounds on the associated matrix ratedistortion function via a suitable matrix version of the covering lemma.