Digital Communications 1

Notations

:

alphabet associated with variable X

A:

transformation matrix

A(D):

weight enumerator function WEF

A_d:

number of codewords with weight d

A(W, Z):

weight enumerator function IRWEF

A_w,z:

number of codewords with weight w + z

B:

bandwidth

B:

inverse transformation matrix

c:

codeword

c(p):

polynomial associated with a codeword

C:

capacity in Sh/dimension

C′:

capacity in Sh/s

D:

variable associated with the weight or delay or distortion

D(R):

distortion rate function

D_B:

binary rate

D_N:

average distortion per dimension

D_S:

symbol rate

d:

distance of Hamming weight

d_min:

minimum distance

e:

correction capability

e:

error vector

E[x]:

expectation of the random variable x

E_b:

energy per bit

E_s:

energy per symbol

e_d:

detection capability

:

Galois Field with q elements

g(p):

polynomial generator

G:

prototype filter

G:

generator matrix

γ_xx(f):

power spectrum density of the random process x

H:

parity check matrix

H(X):

entropy of X

H_D(X):

differential entropy of X

I(X; Y):

average mutual information between variables X and Y

k:

number of bits per information word (convolutional code)

K:

number of symbols per information word (block code)

n_i:

noise sample at time i or length of the i-the message

N:

noise power or number of symbols per codeword

n:

number of bits per codeword (convolutional ...