Hamming碼的編碼和譯碼的Java程序

1、 Hamming碼的編碼和譯碼的Java程序1 程序設(shè)計(jì)理論依據(jù)程序設(shè)計(jì)的理論基礎(chǔ)是漢明碼的定義漢明碼的定義是一個(gè)線性分組碼,它的最小Hamming距離為3,能糾正全部一位錯(cuò)誤,它的校驗(yàn)矩陣H由全部-1個(gè)長度為r的非0,相異的二元列矢量組成.二元Hamming碼是完備碼.Hamming碼是一類非常重要的線性分組碼,它能糾正全部一位錯(cuò)誤,而且譯碼編碼都非常簡單接收矢量的伴隨式等于校驗(yàn)矩陣H中與出錯(cuò)位對(duì)應(yīng)的列矢量之和.因此,與可糾正的錯(cuò)誤形式對(duì)應(yīng)的H矩陣列矢量之和不應(yīng)為0 而且彼此可以區(qū)分,對(duì)于能糾正一位錯(cuò)誤的線性碼來說就是要求它的校驗(yàn)矩陣中每一列矢量是非0矢量同時(shí)要求每一列矢量彼此相異.因?yàn)槿绻?/p>

2、H中有一列0矢量,則與該列對(duì)應(yīng)的比特錯(cuò)誤就不可能被檢測出來.另外如果H中有2列矢量完全相同,則不可能區(qū)分與這2列矢量相對(duì)應(yīng)的2個(gè)比特錯(cuò)誤形式如果校驗(yàn)矩陣H有r=n-k 行, 則總共有-1個(gè)不相同的非0 r維列矢量.例如r=3，則存在-1個(gè)不同的列矢量 2 程序設(shè)計(jì)思想給出校驗(yàn)矩陣H 生成矩陣輸入碼為(7,4)Hamming碼,所有可能接收的編碼總數(shù)為 個(gè),由G生成的編碼數(shù)為16個(gè),H與這16個(gè)碼相乘得到的伴隨式為S=000 即S=HY如S=001 根據(jù)校驗(yàn)矩陣H, Y的第8位出錯(cuò),將Y的第8位異或1即該位求反將結(jié)果作為X'輸出3 算法根據(jù)教材3.1 給出校驗(yàn)矩陣H 和待處理的編碼矩Y3

3、.2 計(jì)算每個(gè)編碼對(duì)應(yīng)的伴隨式 3.3 如果S等于0 , 輸出=y3.4如果S等于H的某一列,例如S= ,對(duì)Y 的第i個(gè)分量求反將該位異或1,將結(jié)果作為輸出4 總結(jié) 根據(jù)教材中提供的算法,用筆算和觀察法進(jìn)行Hamming碼的編碼和譯碼是簡單易行的方法但用程序處理則要對(duì)數(shù)據(jù)結(jié)構(gòu)精心安排,能夠在Java語言中沒有提供二進(jìn)制數(shù)據(jù)類型的情況下以二進(jìn)制的方式處理并以二進(jìn)制的形式輸出數(shù)據(jù). 另外根據(jù)計(jì)算得到的伴隨式確定S在H中的列位置也需要技巧,盡管用觀察法很簡單.5 該程序從設(shè)計(jì)到最后檢驗(yàn)正確無誤本文提供的Hamming碼的編碼和譯碼的Java程序經(jīng)過與筆算和觀察法對(duì)比,在可靠性上兩者是完全一致的.如果

4、有充分的時(shí)間進(jìn)行完善,修改還可用于線性碼的編碼和譯碼.import java.awt.*; import java.io.*;import java.lang.*;public class Array50public static void main(String args)int Sbefore=new int30317;int S =new int3031;int ST =new int3013;int HT =new int 713;int nC =new int30;int counter,check,sign=0,finish;int i,j,k,r;int H=0,1,1,1,1,

5、0,0, 1,0,1,1,0,1,0, 1,1,0,1,0,0,1;int C=0,0,0,1,1,1,1,1,0,0,1,1,1,1,1,1,0,1,0,1,1, 1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,1, 1,0,0,0,1,0,1,1,0,0,1,1,1,1,1,1,0,1,0,1,0; int z =1,3,5; intnColumn=999; System.out.println("打印輸入二進(jìn)制代碼矩陣H"); for(r=0;r<C.length;r+) System.out.print(" C&quo

6、t;+r+"="); for(j=0;j<H0.length;j+) for(k=0;k<H00.length;k+) System.out.print(""+Crjk); System.out.println(); for(i=0;i<H.length;i+) counter=0; for(j=0;j<H0.length;j+) for(k=0;k<H00.length;k+) HTkji=Hijk; counter+;/ if(counter%3=0) System.out.print(" "); /

7、 System.out.println(""); System.out.println(); System.out.println("打印校驗(yàn)矩陣H"); for(i=0;i<HT.length;i+) counter=0; System.out.print("H"+i+"="); for(j=0;j<HT0.length;j+) for(k=0;k<HT00.length;k+) HTijk=Hkji; System.out.print(""+HTijk); counter+

8、; if(counter%3=0) System.out.print(" "); System.out.println(""); for(r=0;r<C.length;r+) for(i=0;i<H.length;i+) counter=0;/ System.out.print("Sbefore"+r+""+i+"="); for(j=0;j<H0.length;j+) for(k=0;k<H00.length;k+) Sbeforerijk=Hijk&Crjk;

9、/ System.out.print(""+Sbeforerijk); counter+;/ if(counter%7=0) System.out.print(" "); / System.out.println(""); for(r=0;r<C.length;r+) for(i=0;i<Sbefore0.length;i+) counter=check=0; for(j=0;j<Sbefore00.length;j+) for(k=0;k<H00.length;k+) if(Sbeforerijk=1) ch

10、eck=1; Srij=check; System.out.println(); System.out.println("打印伴隨式H"); for(i=0;i<C.length;i+) counter=0; System.out.print("S"+i+"="); for(j=0;j<ST0.length;j+) for(k=0;k<ST00.length;k+) STijk=Sikj; System.out.print(""+STijk); counter+; if(counter%3=0)

11、System.out.print(" "); System.out.println(""); for(r=0;r<C.length;r+)/ System.out.print(" S"+r+"="); for(i=0;i<S0.length;i+) counter=0; for(j=0;j<S00.length;j+)/ System.out.print(" S"+r+""+i+""+j+"="+Srij); / Sy

12、stem.out.print(""+Srij); counter+;/ if(counter%3=0) System.out.println(); System.out.println(); try System.in.read(); catch(Exception e) for(r=0;r<C.length;r+) finish=0; for(k=0;k<H00.length;k+) sign=0; / for(i=0;i<H.length;i+) for(j=0;j<H0.length;j+)/ System.out.println("

13、 S"+r+""+i+""+j+"="+Srij); try System.in.read(); catch(Exception e) System.out.println("begin"); for(r=0;r<C.length;r+) finish=0; nColumn=999; for(i=0;i<HT.length;i+)/ sign=0; / for(j=0;j<HT0.length;j+) for(k=0;k<HT00.length;k+) System.out.pri

14、ntln(" HT"+r+""+i+""+j+""+k+"="+STijk); if(HTijk!=STrjk) sign=1; break; else sign=0; if(sign=1) finish=0; break; else finish=1; if(finish=1)&&(i<HT.length) nColumn=i; break; if(nColumn>HT.length) System.out.println(" No error recei

15、ve=input"); else System.out.println("1 erroer occured in the position "+nColumn); System.out.println("system has change it"); Cr0nColumn=1; try System.in.read(); catch(Exception e)程序輸出如下所示輸入二進(jìn)制代碼矩陣 C0=0001111 C1=1001111 C2=1101011 C3=1101110 C4=1000100 C5=1101001 C6=1000101

16、C7=1001111 C8=1101010對(duì)應(yīng)伴隨式SS0=000S1=011S2=010S3=111S4=111S5=000S6=110S7=011S8=011出錯(cuò)位置 C0=0001111 No error receive=input C1=1001111 1 erroer occured in the position 0 system has change it C2=1101011 1 erroer occured in the position 5 system has change it C3=1101110 1 erroer occured in the position 3 system has change it C4=1000100 1 erroer occured in the position 3 system has change it C5=1101001 No error receive=input C6=1000101 1 erroer occured in the position 2 s