Invertible Low-Divergence Coding

Divergence Scaling for Distribution Matching

“…We apply Corollary 1 to an example that corresponds to optimal DM [1]. Consider a target pmf Q T , e.g., a shaping pmf for energy-efficient communication.…”

“…The problem of DM, as described in [1], [3], is to choose a codebook S of strings a n so that the divergence…”

“…and the rate in bits per symbol is R info = 1 n log 2 |S|. The paper [1,Prop. 3] shows that optimal S have all strings a n satisfying X (π(a n ) Q T ) ≤ I for some I, see (22).…”

“…3] shows that optimal S have all strings a n satisfying X (π(a n ) Q T ) ≤ I for some I, see (22). The paper [3] shows that for L = 2 the divergence D (P A n Q n T ) of the best S scales as 1 2 log 2 n with n, i.e., binary DMs cannot provide low divergence. We prove the same result for general discrete alphabets A by using Lemmas 1-5 and Theorem 2.…”

“…Distribution matchers (DMs) are random number generators with a one-to-one mapping [1]. An important application of DMs is probabilistic amplitude shaping for energy-efficient communication [2].…”