Unformatted text preview: sed to obtain greater coding gains than those
provided by concatenated coding systems.
An LDPC code is specified indirectly by a vbyw parity check matrix H consisting of v
linearly independent rows. Parity check matrices may include additional linearly dependent
rows without changing the code. A coded sequence of w bits must lie in the w–v dimensional
dual space of H; that is, it must satisfy all v parity check equations corresponding to the v
rows of H. Alternatively, the code can be described through a (w–v)byw generator matrix
G; such that a coded sequence lies in the w–v dimensional space of G. An encoder maps an
input frame of k information bits uniquely into a codeword of n bits. LDPC codes may be
shortened or expurgated so that k<w–v, and the remaining dimensions of the code remain
unused. LDPC codes may also be extended or punctured to make n greater or less than w.
The distinguishing feature of LDPC codes is to have a low density of ones in the matrix H.
Conversely, the generator matrix G is usually dense; that is, its density of ones is in the same
order of that of zeros, at least for the nonsystematic part of G.
Subsection 7.3 describes a code with a rate of 223/255 (approximately 7/8), and 7.4 describes
a set of nine codes with rates 1/2, 2/3, and 4/5. These codes are systematic and nontransparent.
7.2
7.2.1 GENERAL
SYNCHRONIZATION 7.2.1.1 The (8160,7136) code defined in 7.3 shall be used with the 32bit ASM shown in
figure 81.
7.2.1.2 All of the nine codes with rates 1/2, 2/3, and 4/5, defined in 7.4, shall be used with
the 64bit ASM shown in figure 82.
NOTE – Differential encoding does not provide benefits with LDPC codes, and the ASM
can also be used to resolve phase ambiguities. In fact, differential encoding
before the LDPC encoder cannot be used because the LDPC codes recommended
in this document are nontransparent, and differential encoding after the LDPC
encoder is not advised because it introduces considerable loss of performance. It
also would require differential detection, which is more complex with soft
symbols. This implies that phase ambiguities h...
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