

notes and comment for decxham.asm and formham.asm

hamming code encoding example...

	. generation of check bit value

                     transmitted bits
check bit  m    x1    x2    a    x4    b    c    d
---------  -    --    --    -    --    -    -    -

    x1                      *          *         *
    x2                      *               *    *
    x4                                 *    *    *
    m      *    *     *     *    *     *    *    *


    find the check bit values for the following 
    information bits. use odd parity.


                                         a    b    c    d
                                         -    -    -    -
                                         1    0    1    1


     x1 = a, b, d      therefore x1 = 1
     x2 = a, c, d      therefore x2 = 0
     x4 = b, c, d      therefore x4 = 1
     m = x1, x2, x4, a, b, c, d     therefore m = 0

     the coded bits are:

     m    x1    x2    a    x4    b    c    d
     -    --    --    -    --    -    -    -
     0    1     0     1    1     0    1    1

hamming decoding example...

           .checking for errors at the receiver


                             transmitted bits
parity checks    m    x1    x2    a    x4    b    c    d
-------------    -    --    --    -    --    -    -    -
    ck1               *           *          *         *
    ck2                     *     *               *    *
    ck4                                *     *    *    *
    mck          *    *     *     *    *     *    *    *



     parity check results
mck    ck1    ck2    ck4                bit in error
---    ---    ---    ---                -----------
f      f      f      f                       d
f      f      f      p                       a
f      f      p      f                       b
f      f      p      p                       x1
f      p      f      f                       c
f      p      f      p                       x2
f      p      p      f                       x4
f      p      p      p                       m
p      f      f      f                 double error
p      f      f      p                   "      "
p      f      p      f                   "      "
p      f      p      p                   "      "
p      p      f      f                   "      "
p      p      f      p                   "      "
p      p      p      f                   "      "
p      p      p      p                    no error


p-parity check passes        f-parity check fails






caution

 this project just sort of happened without any real objective
or goal. the routines seem to work well when beat around with
ddt, but i really don't know what would happen if they were
linked to your favorite modem program. that is for you to find
out!. my experiment is over for the meantime. maybe i will put
together a doc file on error correction techniques, better still
, maybe this project will stimulate someone active in data comm.
to bring us all up to date.




                                      rod hart
                                      wa3mez

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