一般信道容量的计算方法

$$\begin{gathered} 由拉格朗日乘子法对L=I(X;Y)-\lambda \sum _i{p}_i对p_i求导可得公式 \\ \sum _{j=1}^{m}p(y_j/x_i)log(\frac{p(y_j/x_i)}{p(y_i)})=lo{g}_{2}e+\lambda \\ 引入C：\sum _{j=1}^{m}p(y_j/x_i)log(\frac{p(y_j/x_i)}{p(y_i)})=C \\ 分离定值：\sum _{j=1}^{m}p(y_j/x_i)log(p(y_j/x_i))=C+\sum _{j=1}^{m}p(y_j/x_i)log(p(y_i)) \\ \sum _{j=1}^{m}p(y_j/x_i)=1,\sum _{j=1}^{m}p(y_j/x_i)log(p(y_j/x_i))=\sum _{j=1}^{m}p(y_j/x_i)log(p(y_i)+C) \\ 求解p(y_i)+C，由转移概率再解出p_i \end{gathered}$$

$$\begin{gathered} 如果是对称信道则用公式I(X;Y)=logs-某一行的熵 \\ H(Y)=logs \end{gathered}$$