Part I

Regular Concatenated Codes and Their Design

List of Symbols in Part I

General notation

• The superscript ^* is used to indicate complex conjugation. Therefore, a^* represents the complex conjugate of the variable a.
• The superscript ^T is used to denote the matrix transpose operation. Therefore, a^T represents the transpose of the matrix a.
• The superscript ^H is used to indicate the complex conjugate transpose operation. Therefore, a^H represents the complex conjugate transpose of the matrix a.
• The notation represents the estimate of x.

Special symbols

A	A random discrete source.
	A source alphabet.
A	The area under an EXIT curve.
	The area under the inverse curve of an EXIT function.
Ac	The a priori Logarithmic Likelihood Ratios (LLRs) of the encoded bits.
Au	The a priori LLRs of the information bits.
Ak	The forward recursion metric of a MAP decoder in the log domain.
ai	The legitimate symbols of a source alphabet.
Bk	The backward recursion metric of a MAP decoder in the log domain.
bmin	The overall minimum block distance of a VLC.
C	A VLC.
C	The encoded output sequence of a trellis encoder.
Ck	The encoded output symbol of a trellis encoder.
CUI	The channel capacity when using uniformly distributed input.
cmin	The minimum convergence distance of the VLC.
cj	A VLC codeword.
c(e)	The output symbol associated with an edge e in a trellis.
dbk	The minimum block distance for the length Lk of a VLC.
dc	The convergence distance between two different-length codewords.
dd	The divergence distance between two different-length codewords.
df	The free distance of a VLC.
dmin	The minimum divergence distance of a VLC.
dh	The Hamming distance between two identical-length VLC codewords.
Eu	The a posteriori LLRs of the information bits.
Ec	The a posteriori LLRs of the encoded bits.
Eb	Bit energy.
Eb/N0	Ratio of the bit energy to the noise power spectral density.
Es	Symbol energy.
Es/N0	Ratio of the symbol energy to the noise power spectral density.
e	The edge of a trellis.
FN	The extended code of order N of a VLC.
gk	The generator polynomials of a convolutional code.
H	The entropy of a source.
hk	The coefficients of a channel impulse response.
Ii	The information carried by a source symbol.
	The average codeword length of a VLC.
l(cj)	The length of a VLC codeword cj in terms of code symbols, or bits for binary codes.
N0	Single-sided power spectral density of white noise.
n	The length distribution vector of a VLC.
Pi	The state probabilities of a discrete Markov model.
pi	The source symbol probabilities.
pij	The state transition probabilities of a discrete Markov model.
R	Coding rate.
RI	The source information rate measured in bits/second.
Rs	The source emission rate measured in symbols/second.
S	The set of valid states of a trellis encoder.
sS(e)	The starting state of an edge e in a trellis.
sE(e)	The ending state of an edge e in a trellis.
U	The input symbol sequence of a trellis encoder.
Uk	The input symbol of a trellis encoder.
u(e)	The input symbol associated with an edge e in a trellis.
Xi	The states of a discrete Markov model.
α	The forward recursion metric of a MAP decoder.
β	The backward recursion metric of a MAP decoder.
γ	The branch transition metric of a MAP decoder.
ρ	The correlation coefficient of a first-order Markov model.
η	The efficiency of a VLC.
ν	The code memory.
Γk	The branch transition metric of a MAP decoder in the log domain.
Π	Interleaver.
Π-1	Deinterleaver.