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, aT represents the transpose of the matrix a.
- The superscript H is used to indicate the complex conjugate transpose operation. Therefore, aH 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. |