A Auxiliary Lemmas

We present some preliminary lemmas in this section. Most of them are basic inequalities in Information Theory, so they are only for auxiliary purposes in our proofs of the main theorems and the corollaries. We refer to Lemma 6.2 of the book Gray ( 2011). We refer to Theorem 14 of the article Liese and Vajda ( 2006). Assume that there are M disjoint / 2 -balls.