tailieunhanh - Theory and applications of ofdm and cdma wideband wireless communications phần 4

Hình 3,6 lưới mắt cáo sơ đồ cho (1 + D 2, 1 + D + D 2) xoắn mã. được mô tả bởi liên tục phụ thêm quá trình chuyển đổi như thể hiện trong hình . Điều này được gọi là một sơ đồ lưới mắt cáo. Với một nhà nước được xác định ban đầu của sổ đăng ký thay đổi (thường là nhà nước allzero), mỗi từ mã được đặc trưng bởi thứ tự của quá trình chuyển đổi nhất định. | CHANNEL CODING 117 Figure Trellis diagram for the 1 D2 1 D D2 convolutional code. be depicted by successively appending such transitions as shown in Figure . This is called a trellis diagram. Given a defined initial state of the shift register usually the allzero state each code word is characterized by sequence of certain transitions. We call this a path in the trellis. In Figure the path corresponding to the data word 1000 0111 0100 and the code word 11 01 11 00 00 11 10 01 10 00 01 11 is depicted by bold lines for the transitions in the trellis. In this example the last m 2 bits are zero and as a consequence the final state in the trellis is the all-zero state. It is common practice to start and to stop with the all-zero state because it helps the decoder. This can easily be achieved by appending m zeros - the so-called tail bits - to the useful bit stream. State diagrams One can also characterize the encoder by states and inputs and their corresponding transitions as depicted in part a of Figure for the code under consideration. This is known as a Mealy automat. To evaluate the free distance of a code it is convenient to cut open the automat diagram as depicted in part b of Figure . Each path code word that starts in the all-zero state and comes back to that state can be visualized by a sequence of states that starts at the all-zero state on the left and ends at the all-zero state on the right. We look at the coded bits in the labeling bi c1ic2i and count the bits that have the value one. This is just the Hamming distance between the code word corresponding to that sequence and the all-zero code word. From the diagram one can easily obtain the smallest distance dfree to the all-zero code word. For the code of our example the minimum distance corresponds to the sequence of transitions 00 10 01 00 and turns out to be dfree 5. The alternative sequence 00 10 11 01 00 has the distance d 6. All other sequences include loops that produce higher .