Hello this is a introduction to error correction and error detection mistakes explain what we mean by
both of those terms.
When we send information we need to encode it.
This is a topic called coding theory.
There are several different ways that we can encode it now.
First of all let's just mention that practically there's two types of ways to have information.
We could have analog let me analog and we can have digital.
That is to say that we could have things in a wave like you might see you know like light waves and
then we can also have things in zeros and ones the the low part being a zero in the hyper being the
one so there would be a 0 0 0 0 0 1 1 0 1 extra and we can encode this information in waves as well.
The details aren't super important right now but the point is that when we send information this is
how it looks it's really in terms of zeros and ones whether it's a wave like this or whether it's just
an electrical current It's either on or off for high or low or whatever you might call it the computer
has a ma modulator modem that does this that switches from one to the other and inside the computer
that's where it everything is digital then we would send it perhaps let's say on a on a wire that's
going to you know that would be analog in some way or another.
So how do we send information efficiently if I want to send this message right.
I want to send this message how do I know that this is the message sent that nothing else got switched.
Right.
So I need to have two things I need to detect if there is an air I needed to correct an error.
So one simple way to make sure that this is the right message is I send it three times.
OK.
Now there's a couple of questions that you might say which is.
So let's say you did send it three times.
1 0 1 0 1 0 0.
How do you know you know which is the message and that it begins and starts and stops and ends.
OK.
How do you know that this isn't the whole message you know I would break it into three.
This seems to be a fair amount of calculation in ideas that would be built into that.
Sounds doable but send it three times and then if this is a mistake and if they say a certain positions
or mistakes or we'll make this into a different number right here this is going to instead be a one
day will make this into a one.
So now it reads this sees this is a one sees a discrepancy in the same positions and it gives the best
two out of three now.
So that would be a zero so we'll switch it.
So that's a reasonable system that we could guess with the problem of course is that it's going to give
us a lot of overhead.
So one detecting it sounds in correcting it is done.
But it's quite a bit of information that all needs to get there you know properly which efficiently
you know and not necessarily Will that happen.
So we need to be able to do it one from computer to computer or network to network or something like
that.
So that's pretty fast so perhaps you know we have some leeway there but we also need to get it from
you know little guy on earth all the way out to space we'll call this some satellites.
You know that's out of here.
That's my.
That's OK it's a pretty doesn't look like a satellite at all.
But just as well.
So we have somewhere in space we have a satellite so we might need to get information back and forth.
I understand understanding go one way.
But either way this could be a very far distance over here so we have to have a system that one you
know can deal with all kinds of situations small situations and big situations the big situations are
going to need to incorporate error correction because we can't go back and forth because a simple way
would let's say let's say this is me and this is you and I send the message 1 0 0 1 and I get that to
you and you say did you send one 001 and I say yes I did 1 0 0 1 so we could go back and forth.
If it's just me and you and we can keep doing that.
And presumably if we do something like that then you know we'll be right for the most part.
You know that sounds like a pretty reasonable system.
I send you this check.
Oh did you.
And then I said yes I did.
Now if I know now it could be that there will be errors in there but it sounds pretty reasonable that
something like that will happen.
However like we said you may need real error correction if it's going to be very very far and you can't
really send it somewhere.
So you may not want to have a system that has to ask three times to do it and also to do it in and also
maybe you don't even want any error correction.
Let me explain why.
Let's say I send information and I send back the information or lack of information lack of information
or lack of information.
What if the errors are like this and like this and maybe one small one over there it could be that that's
not that big a deal for instance let's say you have a send a movie or a picture.
Right.
And then somewhere in between in one of the frames this is wrong.
OK but so what.
It's not going to be the big deal if it went into pixels or three pictures or 10 pixels off.
And perhaps the correction might just be that as it goes it is you know a from pick from frame to frame
maybe it looks at the frames in general but doesn't need to be even that good a correction it could
even get rid of the corrections so.
So there's a couple of colors that are just slightly off.
It's probably not the big deal.
So we may not even need correction as we said depending on what it is either because I can go back and
forth and do that or because it's not that big a deal to have an error somewhere but like we said before
going out the space and relaying information you know that is important.
For instance if I'm relaying bank information from me to bang can I say give somebody you know a million
dollars.
What I want to know is the right person and two I want to know that not only is it the right person
but it's it's the right amount of money.
So being off by a couple of zeros is pretty important.
One zero is is is just is quite important as well having the decimal somewhere etc. so that you know
we will want to have something that we got to be one secure k it can be that others could you know should
be able to read this so that's something that we need to talk about.
We need to have detecting if there an error.
As we said before detected and then we have over here as well correction which depending on the circumstance
may be very important it may be less important but we've got to figure it out or with ones and zeros
and stuff like that because ones and zeros are the system that we're using send information.
So if you were to say well you wrote the word but it came out the word the-I you know so we know it's
probably that.
Well if it's a word that might be OK and maybe there's other ways to do it if something like that but
maybe the computer is not as smart as you think it is because maybe you did mean that you know.
So again we're talking about zeros and ones which will change the balance just a little bit even though
of course you could interpret it into something else.
It doesn't have to be meaningful for instance a million dollars is just as meaningful as a thousand
dollars.
So when you have that system.
Correct.
So we've got to figure something out.
And that's exactly what we're going to be talking about error correction and error detection.