Linear Block Codes - mohammad alshaikh site.ppt
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1、Linear Block Codes,Mahdi BarhoushMohammad Hanaysheh,Introduction to Block Codes,*Block codes introduce controlled amounts of redundancy into a transmitted data stream.*Block code systems divide uncoded data stream into fixed size blocks(k symbol),then add redundancy to each block(n-k symbols)to form
2、 the encoded data stream.*(k information symbol)+(n-k parity check symbol)(n symbol code word)*Parity or redundancy bits are used for error detection and correction.,*Here,we have(n,k)code with rate R=k/n.*If the symbol is either 0 or 1 Binary block code,symbols are named bits.*There are 2n possible
3、 code words in a binary block code of length n.*From these,we choose 2k code words to be mapped to M=2k different message.*Thus,a block of k information bits is mapped into a code word of length n selected from the set M=2 k code words.*Any code has a weight which is the number of nonzero elements t
4、hat it contains.,*Hamming distance is the number of differences between the corresponding elements in any two code words.(measure of difference between any two code words)Ex.dh(1100,1111)=2 dh(1100,1101)=1Then 1100 is closer to 1101*The smallest hamming distance between any two code words is called
5、the minimum hamming distance dh min.*The idea with error correction codes is to pick the 2k code words of the 2n total possible code words which are far enough apart(in terms of Hamming distance)to guaranteeyou are able to correct a certain number of errors.*dh min=2*Ct+Dt+1,Linearity:*The block cod
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