Các mã Turbo FEC mạnh mẽ nhất, được phát triển vào năm 1993 bởi Claude Berrou. Họ cho phép truyền thông tin liên lạc gần gũi hơn với giới hạn Shannon. Một mã turbo gồm hai lập trình viên và interleaver để các thông tin bên ngoài được sử dụng đệ quy để tối đa hóa xác suất mà dữ liệu được giải mã một cách chính xác. | 80 Satellite Networking Principles and Protocols Turbo codes Turbo codes are the most powerful FEC developed in 1993 by Claude Berrou. They enable communication transmissions closer to the Shannon limit. A turbo code consists of two coders and one interleaver so that the extrinsic information is used recursively to maximise the probability that the data is decoded correctly. Each of the two codes can be any of the existing coders. Without going into the detail of turbo codes we will only illustrate the concepts of the turbo coder and decoder using Figures and respectively. The encoder is simple and straightforward. The decoder is more complicated where the extrinsic information is used recursively. The most convenient representation for this concept is to introduce the soft estimation of x dp d2 d3 d4 in decoder 1 expressed as the log-likelihood ratio P di 1lx y 4 x p di 0lx y 2 x P di 1lx z 1 x P di 0 x z 1 x 4 l1 x a l1 di l1 x l1 x - l2 x 4 l2 x a di h x l2 x -l1 x where i2 x is set as 0 in the first iteration. An estimation of the message x dp d2 d d is calculated by hard limiting that log-likelihood ratio l2 x at the out put of decoder 2 as the following x signtTix l1 di log log i 1 2 3 4 i 1 2 3 4 where the sign function operates on each element of l2 x individually. d4 d3 d2 dj Figure Block diagram of turbo encoder Satellite Orbits and Networking Concepts 81 Figure Block diagram of turbo decoder Performance of FEC The receiver can decode the data in most cases even it has been corrupted during transmission making use of FEC techniques. The receiver may not be able to recover the data if there are too many bits corrupted since it can only tolerate a certain level of errors. We have seen that the Eb N0 is the parameter affecting the error performance of satellite transmission for given codes and bandwidth resources. The FEC enables satellite links to tolerate higher transmission errors than the uncoded data in terms of error .
