What's the smallest signal to noise ratio for which a signal has been extracted?

Suppose we have some physical variable $$y$$ that is changing in some way and we want to detect this change in the presence of noise (e.g. white noise) in that same physical quantity. For example $$y$$ is an electric field amplitude and there is black body radiation or something like that. If we know of some pattern to be expected in the change of $$y$$ then this helps to detect it against the noise. For example $$y$$ could be an oscillation at a very well-defined frequency and we know the phase, so we can use a lock-in amplifier (also known as phase-sensitive detection). Or, $$y$$ could be a binary message encoded using an error-correcting code (e.g. transmission from space probes). By such ingenuity one can extract very low-level signals against very noisy backgrounds. What is the best anyone has ever done? What limits have been encountered?

I was aware when asking that this is a somewhat ill-defined question because for many types of noise you can do better by averaging if the signal lasts long enough. But typically the signal is not permanent. I am asking about what really happens, especially in the presence of thermal noise, when people want to communicate or measure. For example, what is the noise at LIGO (in the relevant frequency band) before signal processing? Here for example I mean the noise in the photocurrent at the light detectors (converted into equivalent strain noise).

• Doesn't this depend on how you define signal and noise? In a one second exposure with a telescope, you might have a signal to noise ratio of $0.1$ for some star. In a $10^4$ second exposure this rises to a signal to noise ratio of $10$. So does this count as an observation with an SNR of $10$ or $0.1$? Commented Dec 8, 2022 at 22:59
• I have detected/decoded binary phase shift coded signals at less than $CNR=-30dB$ where $CNR = 10log\frac{A^2}{k_BTW}$ and the signal is $\pm Acos(\omega t)$ and $W=1/T_b$, $T_b$ is the length of each $+$ or $-$ pseudo-random phase jump. In addition to thermal noise of relative intensity -30dB the signal was also covered by much worse narrow band "jamming", too. I know it can be done at $CNR=-40dB$, but much lower than that is probably classified. Commented Dec 9, 2022 at 3:19