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A rate tuple is said to be achievable if there exists a code with and (4).
A rate tuple is said to be achievable if there exists a code such that and (29).
A common message secrecy rate,, is said to be achievable if there exists a code such that, and (17).
A sum secrecy rate,, is said to be achievable if there exists a code such that, and (21).
For any and sufficiently large, there exists a code with the rates,,, and given by (46) such that (1), (2), (3) for all, (4) for all.
A rate tuple (R1,R2,R s ) of nonnegative real values is achievable if for any η>0, 0<ε<1 there exists a code such that 1 n log M a ≥ R a - η, a = 1, 2, s, (3).
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First, we assume that there exists a coding strategy that achieves the capacity region of the Gaussian multiple-access channel.
All this leads to the hypothesis that there existed a code, GNS, reflecting the biosynthetic relationships between these six amino acids which, as it defines the very earliest phases of genetic code origin, removes the main difficulty of the coevolution theory.
Then there exists a prefix code (C) for (mathcal Z ) such that for all (z in mathcal Z ), (L_{C} z) = lceil -mathrm{log}_{2} P z rceil ).
Fix ε=δ/2, by the definition of achievable rates, there exists a chunked code with n chunks for all sufficiently large n such that at least m n input packets are recovered with probability at least 1−ε.
In fact, a sub-code for the corresponding two modes of tRNA recognition exists – a sub-code that operates with complementary anticodons flanked by evolutionarily conserved 5'U and R3' nucleotides, and therefore has little if anything to do with p-aaRSs that often recognize solely the acceptor stem, and do not interact with the anticodon at all [ 11, 12].
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com