Interleaver design:randomly generated. 5.11.2 More About BICM:Info ation-theoretic aspects [Gallager68,Caire98] In Chapter 6 of [Gallager68],Gallager proved a coding theorem for parity-check codes, which may be addressed as follows. Theorem:Binary linear codes can be used to achieve capacity on an arbitrary discrete memoryless channel. Binary FEC Encoder Mapper Figure 5.11.5 Gallager also demonstrated a simple algorithm to generate codewords with the probability distrib utions required to achieve the resul of the coding theorem.However,the problem is that finding decoding algorithm is not simple. Fig.5.11.6 shows an example,where each channel codeword is a sequence of N ternary independent digits with the probabilities O(a)=3/8,(b)=3/8 and O(c)-2/8.We will call it Gallager mapping later. Mapper→ a label 000- 001 ≥ya 010 101 110 111 (b) Figure 5.11.6 An example for use of binary codeson a DMC.(a)System model.(b)Mapping rule Now.BICM-ID with the use of Turbo-like codes provides an effective solution.Joint demapping-decoding greatly reduces the decoding complexity. Turbolike Encoder Mapper Arbitrary Binary DMC Iterative Decoder 15 25 „ Interleaver design: randomly generated. 5.11.2 More About BICM: Information-theoretic aspects [Gallager68, Caire98] In Chapter 6 of [Gallager68], Gallager proved a coding theorem for parity-check codes, which may be addressed as follows. „ Theorem: Binary linear codes can be used to achieve capacity on an arbitrary discrete memoryless channel. Figure 5.11.5 Gallager also demonstrated a simple algorithm to generate codewords with the probability distributions required to achieve the results of the coding theorem. However, the problem is that finding decoding algorithm is not simple. Fig. 5.11.6 shows an example, where each channel codeword is a sequence of N ternary independent digits with the probabilities Q(a)=3/8, Q(b)=3/8 and Q(c)=2/8. We will call it Gallager mapping later. (a) 000 001 010 a 011 100 101 b 110 111 c label x (b) Figure 5.11.6 An example for use of binary codes on a DMC. (a) System model. (b) Mapping rule Now, BICM-ID with the use of Turbo-like codes provides an effective solution. Joint demapping-decoding greatly reduces the decoding complexity. ∏