Consider the extended (8, 4) Hamming code defined in Problem 1.23 and suppose that it is used to communicate over the BSC. Show that the bit-flipping algorithm with adaptive threshold corrects all...

Consider the extended (8, 4) Hamming code defined in Problem 1.23 and suppose that it is used to communicate over the BSC. Show that the bit-flipping algorithm with adaptive threshold corrects all single errors and that there exists a double error which the algorithm does not correct.

Problem 1.23

Draw the Tanner graph for the extended (8, 4) Hamming code defined by the parity-check matrix