coding

[Symbol]
x[n] = the nth transmitted symbol.
y[n] = the nth received symbol.
n[n] = the nth received noise.

y[n] = x[n] + n[n].

T: a time interval.
N: number of symbols in an interval (or orthogonal function for better definition).
W: bandwidth.
W = N/2T, by Nuquist sampling theorem.
N0 : noise spectral density.
n[n] = Normal(0, N0/2). From conservation of energy, total energy = N0*W = E[n[n]^2] * N/T. So the variance is linear proportion to noise spectral density. n[n] is the amplitude in time domain, whereas N0 is the amplitude^2 in the spectrum domain.
R : bit rate.
Eb = x[n]^2/R. Power per source bit. Eb is the symbol power spectral density. Eb*W = E[x[n]]*N/T.
SNR: Eb/N0 is dimensionless, reported in decibels.