Question

Q2 : Assume we are having a linear block coding, use Hamming code to do the following

A. Encode the dataword 10011010 ?

B. Examine the codeword 10100110001000 to see if it is correct or not? If you think is incorrect, then show the position of the bit causing the error and correct as appropriate?

Answer 1

Part A:

For encoding to Hamming code we should create the data word leaving space for parity bit(all positions that are power of 2 i.e. 1,2,4,8.... and all other bits are for data to be encoded) as: _ _ 1 _ 0 0 1 _ 1 0 1 0.

Parity bit at position 1: even parity(P1: _10111) hence parity bit at 1 position is 0 i.e _ _ 1 _ 0 0 1 _ 1 0 1 0

Parity bit at position 2: odd parity(P2: _10101) hence parity bit at 2 position is 1 i.e 0 _ 1 _ 0 0 1 _ 1 0 1 0

Parity bit at position 4: odd parity(P4: _0010) hence parity bit at 4 position is 1 i.e 0 1 1 _ 0 0 1 _ 1 0 1 0

Parity bit at position 8: even parity(P8: _1010) hence parity bit at 8 position is 0 i.e 0 1 1 1 0 0 1 _ 1 0 1 0

Ans: 011100101010

Part B:

No it is not correct. For checking correctness we have to check for position 1,2,4,8,16..

for parity 1: P1:_101010 ie odd hence 1 which is correct

for parity 2: P2:_1110100 ie even hence 0 which is correct

for parity 4: P4:_011000 ie odd hence it should be 1 but it is incorrect in given code

for parity 8: P8:_001000 ie odd hence it should be 1 but it is incorrect in given code

there is issue with 4th and 8th position hence we could say 12(4+8) is location of bad bit. If we make 12th bit 1 ie new correct codeword is 10100110001100