Uniquely Decodeable Code Weak vs Strong Def

Hi,
I just started learning code theory and in class he talked about UD codes.

In class we defined a UD code as one such that every distinct
concatenation of n codewords is distinct for every n; in other words, if
\[x_1 ... x_n \] \[\neq\] \[ y_1 ... y_n,\]
then
\[C(x_1) ... C(x_n) \neq\] \[ C(y_1) ... C(y_2)\]
for every n.

Then in class the professor mentioned a stronger proof of this which makes more
sense to determine a UD code.
if \[x_1 ... x_m \neq\] \[y_1 ... y_n,\]
then
\[C(x_1) ... C(x_m)\neq\] \[C(y_1) ... C(y_2)\]
for every m,n.

The stronger def is easier to define a UD code for example,
A 0
B 11
C 011

AB(011) = C(011) hence it is not UD but with the weak def of UD I am not so sure.

It was later mentioned that the weaker definition implies the stronger definition and I don't see how this works?

SeriousTyro said:

hence it is not UD but with the weak def of UD I am not so sure.

Click to expand...

You are correct this is not true. i.e. it does not a UD code for this particular type of code. For equilength codes this criteria works better. (i.e. reasonable good assumption for ECC but doesn't work well with data compression)

It was later mentioned that the weaker definition implies the stronger definition and I don't see how this works?

Click to expand...

There could have been a misinterpretation/misrepresentation here, which is probably the case. A strong definition => a weak definition is true but not vice-versa.