ADC and PCM Modeling of digital source UESTC-Introduction Prof李晓峰 2
2.Modeling of digital source Various digital messages: W H A T H A T 100-1111-100-1111-100-1111 UESTC-Digital transmission through the AWGN channel Prof李晓峰 3
2.Modeling of digital source WH AT HAT 100-1111-100-1111-100-1111 Various digital messages: What's in common?Sequence of numbers,finite values,random n=xo,x2,X32X A random process UESTC-Digital transmission through the AWGN channel Prof李晓峰 4
2.Modeling of digital source A simple model for the digital information source is the DMS(discrete memoryless source). {xn}=xo,X1,X2,x3,…Xn,… A random process UESTC-Digital transmission through the AWGN channel Prof李晓峰 5
2.Modeling of digital source A simple model for the digital information source is the DMS(discrete memoryless source). {xn}=xo,x,X2,X3,…Xn, A random process A DMS is a discrete-time,discrete-and finite amplitude random process (RP),in which all variables are generated independently and with the identical distribution.This implies that the outputs of a DMS are i.i.d.RVs(random variables)from a finite set. To say the source is memoryless means that the RVs from the source are independent of each other. UESTC-Digital transmission through the AWGN channel Prof李晓峰 6
2.Modeling of digital source A simple model for the digital information source is the DMS(discrete memoryless source). {xn}=xo,1,X2,x3,…Xn,… A random process Let 4={a,a2,...,av}denote the set; p,P2,....P denote probabilities of the occurrence of the afs respectively. Suppose X is a rv.from the DMS.We have, P[X=a]=p(i=1,2,,M) A is called the alphabet of the DMS and a,a symbol.The src is said to be a M-ary source,while M is the size of the alphabet. UESTC-Digital transmission through the AWGN channel Prof李晓峰 7
2.Modeling of digital source Binary DMS is an example with M=2,for binary message, {x}=1,0,01,1,0…1,0,1 We have,4=(0,1),where P(X=1)=p 0≤p≤1 P(X=0)=1-p=q If p=0.5,the src is called a binary symmetric src,or BSS for short. UESTC-Digital transmission through the AWGN channel Prof李晓峰 8