第4章_天津大学侯春萍老师通信原理课件之卷积编码.ppt

天津大学电子信息工程学院 Chapter 4 Convolutional Encoding 4. 1 Introduction Linear Block Codes described by (n, k) two integers, n and k a generator polynomial The characteristic of linear block codes Each output codeword n-tuple is uniquely determined by the input codeword k-tuple. The rate of the code is k/n. Convolutional Code described by (n, k,K) three integers, n , k , K k：k-tuple input codeword n：n-tuple output codeword K：constraint length In practice, n and k are small and K is varied to control the capability and complexity of the code. The characteristic of Convolutional code Each output codeword n-tuple is not only a function of an input k-tuple, but also a function of the previous K-1 input k-tuples. The rate of the code is about k/n. 4.2 Convolutional Encoding 2.2.1 Convolutional Encoder kK –stage shift register n modulo-2 adders Convolution Encoder kK-stage shift registers n modulo-2 adders. Constraint length K The number of k-bit codewords over which a single information bit can influence the encoder output. Input (k bit)： k information bits (an input codeword) are shifted into the encoder at a time. Output (n bit)： The outputs of the n adders are sequentially sampled and transmitted. 4.2.2 Convolutional Encoder Representation There are several methods used for representing a convolutional encoder. Connection Representation connection pictorial connection vectors connection polynomial state diagram tree diagram trellis diagram 1 Connection Representation （ 1 ）Connection pictorial Taking (2, 1, 3) convolutional encoder as an example. n=?，k=?，K=?约束常数和多少个输入码字有关（已经输入的k-1个，当前输入的一个） The code rate = ? The choice of connections between the adders and the stages of the register gives rise to the characteristics of the code. The different connection method results in a different code. Are the connections arbitrarily changed ? Why? How to find a good code in general? What is a good code? Output sequence：11 10 00 10 11； The leftmost symbol represents the earl