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Question
The parity check matrix of a(7,4) linear block codes is given by,If the code word received at the output of the channel is [1110100]. If there is a possibility for at most one−bit error due to channel noise, then the correct code wordtransmitted at the input of the channel will be.H=⎡⎢⎣111010010110101111001⎤⎥⎦
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Solution
The correct option is D [1 1 1 0 1 0 0]
Syndrome vector, =rHT=[11101000]⎡⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢⎣111101110011100010001⎤⎥
⎥
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⎥
⎥
⎥
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⎥
⎥⎦=[0 0 0]The syndrome vector has all zeros. It means that, there is error no error in the received code word.So the transmitted code word is same as the received code word.Note: In the problems related to linear block codes, use EX−OR opration whenever there is anaddition operation of bits.
Syndrome vector, =rHT=[11101000]⎡⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢⎣111101110011100010001⎤⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥⎦=[0 0 0]The syndrome vector has all zeros. It means that, there is error no error in the received code word.So the transmitted code word is same as the received code word.Note: In the problems related to linear block codes, use EX−OR opration whenever there is anaddition operation of bits.
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