Sharper Upper Bounds for Unbalanced Uniquely Decodable Code Pairs [article]

Per Austrin, Petteri Kaski, Mikko Koivisto, Jesper Nederlof
2016 arXiv   pre-print
Two sets A, B ⊆{0, 1}^n form a Uniquely Decodable Code Pair (UDCP) if every pair a ∈ A, b ∈ B yields a distinct sum a+b, where the addition is over Z^n. We show that every UDCP A, B, with |A| = 2^(1-ϵ)n and |B| = 2^β n, satisfies β≤ 0.4228 +√(ϵ). For sufficiently small ϵ, this bound significantly improves previous bounds by Urbanke and Li [Information Theory Workshop '98] and Ordentlich and Shayevitz [2014, arXiv:1412.8415], which upper bound β by 0.4921 and 0.4798, respectively, as ϵ approaches 0.
arXiv:1605.00462v1 fatcat:bp6uutjjznan3l42c36vi7xcfq