Results 1 to 6 of 6

Math Help - error correcting code

  1. #1
    Junior Member
    Joined
    Sep 2009
    Posts
    36

    error correcting code

    In model of a communication channel, we take
    the probability p of error to be < 1/2. Why not consider the
    case 1 ≥ p > 1/2? What if p = 1/2?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor chisigma's Avatar
    Joined
    Mar 2009
    From
    near Piacenza (Italy)
    Posts
    2,162
    Thanks
    5
    In...

    Information theory - Wikipedia, the free encyclopedia

    ... the concept of binary entropy function is defined as...

    H_{b} (p) = -p\cdot \log_{2} p - (1-p) \cdot \log_{2} (1-p) (1)

    In (1) p is the probability that a binary transmitted symbol is received 'correct', so that 1-p is the 'error probability'. It is easy to see in (1) that 0 \le H_{b} (p) \le 1 and that H_{b} (p) is 'mirror imaging' respect to p=\frac{1}{2} , i.e. is...

    H_{b} (p) = H_{b} (1-p) (2)

    ... so that, from the point of view of the information theory, trasmission channels with p=1 and p=0 are perfectly equivalent ...

    Kind regards

    \chi \sigma
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Sep 2009
    Posts
    36

    wat

    i dont understand what happens when p = 1/2
    Last edited by amberxinya; February 13th 2010 at 03:31 AM.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    Sep 2009
    Posts
    36

    right

    so u say that H(1/2)=1 reaches its maximum at p=1/2
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor chisigma's Avatar
    Joined
    Mar 2009
    From
    near Piacenza (Italy)
    Posts
    2,162
    Thanks
    5
    The condition p=\frac{1}{2} means that You don't trasmit any information through the channel... effectively an equivalent 'binary stream' can be obtained at the receiver with an [unbiased] coin toss ...

    Kind regards

    \chi \sigma
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Newbie
    Joined
    Mar 2009
    Posts
    12
    Quote Originally Posted by amberxinya View Post
    In model of a communication channel, we take
    the probability p of error to be < 1/2. Why not consider the
    case 1 ≥ p > 1/2? What if p = 1/2?
    Think of it this way: If I predict whether a coin toss will come up heads or tails with error > 0.5, then you would simply begin using the opposite of my prediction as an (obviously) better prediction.


    -Will Dwinnell
    Data Mining in MATLAB
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. The [5,2] error correcting code
    Posted in the Number Theory Forum
    Replies: 3
    Last Post: July 25th 2010, 08:03 AM
  2. Error Correcting Codes - Plotkin Bound
    Posted in the Advanced Math Topics Forum
    Replies: 3
    Last Post: February 12th 2010, 04:13 AM
  3. Error Correcting Code
    Posted in the Advanced Math Topics Forum
    Replies: 0
    Last Post: January 25th 2010, 07:44 PM
  4. correcting an isbn number (maybe with hamming code?)
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: December 15th 2009, 02:37 AM
  5. Error-correcting code proof
    Posted in the Discrete Math Forum
    Replies: 0
    Last Post: September 18th 2008, 10:21 PM

Search Tags


/mathhelpforum @mathhelpforum