Finite-Length Analysis of Irregular Expurgated LDPC Codes under ...
Finite-Length Analysis of Irregular Expurgated LDPC Codes under ...
Finite-Length Analysis of Irregular Expurgated LDPC Codes under ...
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Number <strong>of</strong> cycles<br />
The basic fact<br />
If G has k cycles<br />
P n (G) = Θ(n −k ).<br />
The large blocklength limit <strong>of</strong> the bit error probability<br />
P b (∞, ǫ, t) = lim<br />
n→∞<br />
= lim<br />
n→∞<br />
∑<br />
P n (G)P b (G, ǫ)<br />
G ∈ the set <strong>of</strong> all neighborhoods <strong>of</strong> depth t<br />
∑<br />
P n (G)P b (G, ǫ) .<br />
G ∈ the set <strong>of</strong> all cycle-free neighborhoods <strong>of</strong> depth t<br />
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