the constraint that a certain constellation is employed;this is the benchmark for the e of coded communicatio Consi er a dis channel with input random process channel is fully characterized by the conditional probabilities Pyw)for all xAx and yeAr.i.e. P()=Pu(y).for k=1.2. (2.20) It should be noted that (2.20)implies that the channel is time-imariant in the sense that the probability distribution Pdoes not depend onk For such channels,the chanmel capaciry is defined as the maximum average mutual information /(X.Y)that can be obtained by choice of P(x),i.e., Cm(Y)=mgx [-HY (2.21) oe:When P(s fixed (),the""would then be). and the max in(1)will be removed.In Shannon type of capacity is more properly called an information rate. 位酒”一合潭给码图”一合道演码酒数字再闲 的，应色群酒台通译入字得图0 调制信道 编码信道（等效离散信道 2.6.1 Discrete-Valued Inputs and Outputs Consider a binary symmetric channel (BSC)with Ax =Ar =(0,1),and Phr(011)=Pux(110)=p.See Fig.2.13. 00 00 1-p 2-20 2-20 the constraint that a certain constellation is employed; this is the benchmark for the discussion of performance of coded communication systems. Consider a discrete-time memoryless channel with input random process {Xk} and output {Yk}, for which the current output Yk is independent of all inputs except Xk. Such a channel is fully characterized by the conditional probabilities PY|X (y|x) for all xX and yY; i.e. 1 1 1 1 | ( | ,., , , ,., ) ( | ) P y x x x y y P y x k k k k Y X k k − − = , for k=1,2,. (2.20) It should be noted that (2.20) implies that the channel is time-invariant in the sense that the probability distribution | Y Xk k P does not depend on k. For such channels, the channel capacity is defined as the maximum average mutual information I(X; Y ) that can be obtained by choice of P(x), i.e., max ( ; ) max [ ( ) ( | )] P P X X C I X Y H Y H Y X  = − (2.21) Note: When P(X) is fixed (e.g., a uniform distribution), the “capacity” would then be I(X; Y ), and the max in (2.21) will be removed. In Shannon theory, this type of capacity is more properly called an information rate. 2.6.1 Discrete-Valued Inputs and Outputs Consider a binary symmetric channel (BSC) with X = Y = {0, 1}, and | | (0 |1) (1| 0) P P p Y X Y X = = . See Fig. 2.13. 1 - p p 1 - p p 0 X 1 0 Y 1 信源 信源编码器 信道编码器 数字调制器 信 道 干 扰 信宿 信源译码器 信道译码器 数字解调器 调制信道 编码信道(等效离散信道) m u x x(t) n(t) y(t) m  u  y