Vì vậy, việc tính toán của x chuỗi nhị phân là không cần thiết. Bổ sung chỉ nhận được permuted ¯ giá trị zi, với những thay đổi dấu hiệu được đưa ra bởi * v tạo ra, được yêu cầu sau khi truyền nhị phân trên một kênh AWGN (kết quả đầu ra của một bộ lọc phù hợp) | 182 ITERATIVELY DECODABLE CODES In addition a number of interesting semianalytical tools have appeared in density evolution Richardson and Urbanke 2001 Gaussian approximation Gamal and Hammons 2001 and mutual information ten Brink 1999 2001 or SNR transfer Divsalar et al. 2001 characteristics to study the convergence properties of iterative decoding algorithms. The art of interleaving A critical component in achieving good performance with iterative decoding of a turbo code is the interleaver. In turbo codes the interleaver serves three main purposes 1 build very long codes with weight distributions that approach those of random codes 2 help in the iterative decoding process by decorrelating the input LLRs to the SISO decoders as much as possible and 3 proper termination of the trellis in a known state after the transmission of short to medium length frames to avoid edge effects that increase the multiplicity of low-weight paths in the trellises of the component codes. To emphasize the specific type of interleaver becomes an important factor to consider as the frame lengths or interleaver lengths become relatively small say up to one thousand symbols. There is a wealth of publications devoted to interleaver design for turbo codes. In this section a brief description of the basic interleaver types and pointers to the literature are given. In 1970 several types of optimum interleavers were introduced Ramsey 1970 . In particular an n1 n2 interleaver was defined as a device that reorders a sequence so that no contiguous sequence of n2 symbols in the reordered sequence contains any symbols that are separated by fewer than n1 symbols in the original ordering. Let. at1 aÍ2 aÍ3 . denote the output sequence from an n1 n2 interleaver where f1 i2 . are the positions of these symbols in the input sequence. Then the definition in the previous paragraph translates into the following condition ự-i j I n1 whenever i j I n2. It can be shown that the deinterleaver of an n1 n2 .
