Abstract
Following the asymptotic analysis of BP decoding, we now study the achievable rates of BATS codes and the design of degree distributions based on the sufficient condition in Theorem 5.2. We assume that the batch degrees and the transfer matrix ranks are “asymptotically independent”. Specifically, there exist a degree distribution Ψ =(Ψ1, …ΨD) and a rank distribution (h0, h1, …, hM) such that ∏d, r = Ψdhr, which implies that the empirical batch degree distribution converges in probability to Ψ and the empirical transfer matrix rank distribution converges in probability to (h0, h1, …, hM). The BATS code model described in Chapter 2 satisfies the above assumption.
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