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).
A rate tuple (R1,R2,S,T) of nonnegative real values is achievable over the channel C RS if there exists a code (n,M1,M2,L s,N s,ε) such that for any arbitrary 0<ε<1 and η>0 1 n log M a ≥ R a - η, a ∈ { 1, 2 }, (6) 1 n log L s ≥ S - η, (7) 1 n log N s ≥ T - η, (8).
As we aim at minimizing both the bitrate and the resulting error, P has to be an entropy-constrained vector quantized first according to the rate-distortion theory[17] to obtain p ~. Thus, for a target maximal average distortion D = E [ δ ( P, P ~ ) ], the Shannon theorem tells us that there exists a code of minimal rate R = H ( P ~ ).
First, we assume that there exists a coding strategy that achieves the capacity region of the Gaussian multiple-access channel.
We say that a rate R is achievable by chunked codes using BP decoding if for any constant ε>0, there exists a chunked code with k≥(R−ε m n input packets and n chunks for all sufficiently large n such that with probability at least 1−ε, when the BP decoding stops, at least (R−ε m n input packets are recovered.
