课本为西安电子科技大学《信息论与编码理论》第二版。
信息论与编码理论
算数编码两个关键递推公式
算术编码递推公式
实现如下：
/**The class is used to Arithmeti Coding.
*tool：notepad++，jdk 1.8
*Date: 2018/5/31
*@author JFLIU
*@version 1.0
*说明：由于时间原因，没有严格异常检查，输入合法性检查，程序只能双字节输入变量（例如，a1，a2，b1等）。如果是二元编码，请用a1，a2（不要出现a0）等代替0，1。一个遗憾是，不能想到一个合理的方式解决尾数截断的进一。因为float，double在计算机的表示（IEEE 754标准）本人并不懂。对于P(ui),F(ui)，没有采用有理数（Java中没有），编写需要时间，故直接用小数了。注意：本例中向量用下划线表示了。
*/
import java.util.Scanner;
import java.util.List;
import java.util.ArrayList;
import java.util.Collections;
//随机变量类
class RandomVariable {
private double possibility = 0;
private String randomVariableName = null;
RandomVariable() {
}
RandomVariable(double possibility, String randomVariableName) {
this.possibility = possibility;
this.randomVariableName = randomVariableName;
}
public void setPossibility(double possibility) {
this.possibility = possibility;
}
public void setRandomVaribleName(String randomVariableName) {
this.randomVariableName = randomVariableName;
}
public void setRandomVarible(String randomVariableName, double possibility) {
this.randomVariableName = randomVariableName;
this.possibility = possibility;
}
public double getPossibility() {
return this.possibility;
}
public String getRandomVaribleName() {
return this.randomVariableName;
}
}
public class ArithmetiCoding {
private static int num = 0;
private static double p_ui = 1.f;
private static double p_uiAdd1 = 0.f;
private static double puiAdd1 = 0.f;
private static double f_ui = 0.f;
private static double f_uiAdd1 = 0.f;
private static double fuiAdd1 = 0.f;
private static int n_ui = 0;
private static RandomVariable[] randomVariable = null;
private static int theNumOfCharacterSet = 0;
private static List list = new ArrayList();
public static void main(String args[]) {
Scanner in = new Scanner(System.in);
System.out.print("请输入字符集个数: ");
try {
num = in.nextInt();
if(num <= 0) {
System.out.println("输入值应该大约0！");
System.exit(0);
}
} catch(Exception e) {
System.out.println("输入含有非法字符！");
System.exit(0);
}
inputFunction(num);
input();
}
public static void inputFunction(int num) {
randomVariable = new RandomVariable[num];
Scanner in = new Scanner(System.in);
for(int i=0; i < randomVariable.length; i++)
randomVariable[i]=new RandomVariable();
for(int i = 0; i < num; i++) {
System.out.print("请输入字符" + (i+1) +"及其概率: ");
randomVariable[i].setRandomVarible(in.next(),in.nextDouble());
list.add(randomVariable[i]);
}
}
public static void input() {
int index = 0;
String temp = "0.";
Scanner in = new Scanner(System.in);
System.out.print("信源序列，以逗号分割: ");
String str = in.nextLine();
String[] splitstr=str.split(",");
System.out.println();
System.out.println("序号\tui\tP(ui)\t\tF(ui)\t\tn(ui)\tS");
System.out.println((index++) + " \t空\t1 \t\t 0 \t\t 0 \t");
for(int i = 0;i < splitstr.length; i++){
fuiAdd1 = distributionFunction(splitstr[i]);
f_uiAdd1Function();
puiAdd1 = list.get(index(splitstr[i])-1).getPossibility();
p_uiAdd1Function();
n_ui = (int)(Math.ceil(-1*Math.log(p_uiAdd1)/Math.log(2)));
double binary = f_uiAdd1;
for(int j = 0; j < n_ui; j++) {
binary *= 2;
temp += (int)binary;
binary = binary - (int)binary;
}
System.out.println((index++)+"\t"+splitstr[i]+"\t"+String.format("%-12s",p_uiAdd1)+"\t"+String.format("%-10s",f_uiAdd1)+"\t"+n_ui+"\t"+temp);
f_ui = f_uiAdd1;
p_ui = p_uiAdd1;
temp = "0.";
}
}
public static int index(String randomVariableName) {
String temp = "";
for(int i = 1; i < randomVariableName.length(); i++) {
temp += randomVariableName.charAt(i);
}
return Integer.parseInt(temp);
}
//分布函数
public static double distributionFunction(String randomVariableName) {
double possibilityDistribution = 0.f;
for(int i = 0; i < index(randomVariableName) - 1; i++) {
possibilityDistribution += list.get(i).getPossibility();
}
return possibilityDistribution;
}
//递推公式
public static void p_uiAdd1Function() {
p_uiAdd1 = p_ui * puiAdd1;
}
public static void f_uiAdd1Function() {
f_uiAdd1 = f_ui + p_ui * fuiAdd1;
}
}
课本P65例3.4.3程序运行结果
P65例3.4.3程序运行结果
可见编码为10001101110100。
习题3.12
习题3.12
由于截断，实际编码为0101100111101。即最后一位应该补上一位。
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