Chap 10. Error Detection and Error correction

Chap 10. Error Detection and Error correction

* single bit error , burst error

* detection vs correction

* block coding, convolution coding

Block coding

* dataword -> codeword

* hamming distance(s + 1 = dm)

* linear block coding (parity check bit)

Parity check bit

* Linear block coding - codeword - xor -> codeword

* 1 even number 

* 1 number  -> syndrome 1- odd, syndrome 0 - even

Cyclic Code

* special linear block coding - cyclic(shift left)

* dataword / divisor -> dataword + remainder = codeword

* generator= divisor , syndrome = codeword/generator, 

* syndrome == 0 (error or no error) / syndrome ! = 0 (must error)

* polynomial expression 

* Single bit error -> x^0 == 1

* two single bit error -> x^i~x^j

* odd error -> generator must include (x+1)

* burst error -> L <= r 

* Checksum = data sum (carry add) -> 1's complement -> data sum + 1's complement -> final check sum

* Forward error correction -> for real time

* Chunk interleaving (row / col -> for lost)