Notations
:- alphabet associated with variable X
- A:
- transformation matrix
- A(D):
- weight enumerator function WEF
- Ad:
- number of codewords with weight d
- A(W, Z):
- weight enumerator function IRWEF
- Aw,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
- DB:
- binary rate
- DN:
- average distortion per dimension
- DS:
- symbol rate
- d:
- distance of Hamming weight
- dmin:
- minimum distance
- e:
- correction capability
- e:
- error vector
- E[x]:
- expectation of the random variable x
- Eb:
- energy per bit
- Es:
- energy per symbol
- ed:
- detection capability
:- Galois Field with q elements
- g(p):
- polynomial generator
- G:
- prototype filter
- G:
- generator matrix
- γxx(f):
- power spectrum density of the random process x
- H:
- parity check matrix
- H(X):
- entropy of X
- HD(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)
- ni:
- 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 code)
- N0:
- unilateral noise power spectral density
- P:
- signal power
- Pe:
- symbol error probability
- p:
- transition probability for binary symmetric channel
- p(x):
- probability density
- Q:
- size of alphabet
- R:
- rate
- Rss(t):
- autocorrelation function of the random process s
- R(D):
- rate-distortion function
- s:
- error syndrome
- T:
- symbol duration
- Tb:
- bit duration
- s(p):
- polynomial associated with the syndrome
- u:
- information word
- u(p):
- polynomial associated with the information word
- w:
- weight of the information word
- W:
- variable associated with the weight of the information sequence
- X:
- variable associated with the channel input signal
- x:
- transmitted word
- y:
- received word after matched filtering and sampling
- Y:
- variable associated with the channel output signal
- z:
- weight of the redundancy sequence
- Z:
- variable associated with the weight of the redundancy sequence
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