t02 Transmission has a per-bit floor
Supplied working report; original verdicts not validated.
Review status: Needs review. This is an archival source note, not a passed proof.
notes.md
# t02 Transmission has a per-bit floor Shannon capacity gives C = B log2(1 + P/(N0 B)), so Eb/N0 = P/(N0 C) = (2^eta - 1)/eta with eta = C/B the spectral efficiency. As eta approaches zero the ratio tends to ln 2 = 0.6931 (about -1.59 dB); it then rises monotonically with eta. At fixed transmit power, Eb/N0 falls monotonically with bandwidth toward the same floor, so there is a hard floor but no finite 'optimal' bandwidth: the limit is approached only at infinite bandwidth. The core of the posted claim - a floor set by the noise-to-bandwidth ratio - is therefore supported. The phrase 'bottom out at an optimal bandwidth' is the only part that is not literally correct, and the test records that precisely.