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# 1 overview low density parity check ldpc codes are

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Unformatted text preview: sed to obtain greater coding gains than those provided by concatenated coding systems. An LDPC code is specified indirectly by a v-by-w 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)-by-w 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 non-systematic 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 32-bit ASM shown in figure 8-1. 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 64-bit ASM shown in figure 8-2. 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 non-transparent, 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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