Smallest set (typical set)











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Given the following table of sequences, I'm trying to find the smallest set with probability $p = 0.9$.



enter image description here



The smallest set consists of some sequences from the table, which probability (column 3) should add up to $p$, while the length (found in the second column) is being minimized.



I'm struggling to find a good approach to find the smallest set, without just trying a lot of options and checking their length. Therefore I was wondering if there exists a fast approach to find the smallest set, given such a table.










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  • what you call length is unclear to me. do you mean hamming weight? And why would you minimize it?
    – kodlu
    Nov 24 at 0:25










  • And what is the probability parameter in the binomial distribution? You use $p=0.9$ but this is not the $p$ in the equations generating column 3, that looks more like $papprox 15/25,$ judging by the peak in the binomial distribution.
    – kodlu
    Nov 24 at 0:27















up vote
0
down vote

favorite












Given the following table of sequences, I'm trying to find the smallest set with probability $p = 0.9$.



enter image description here



The smallest set consists of some sequences from the table, which probability (column 3) should add up to $p$, while the length (found in the second column) is being minimized.



I'm struggling to find a good approach to find the smallest set, without just trying a lot of options and checking their length. Therefore I was wondering if there exists a fast approach to find the smallest set, given such a table.










share|cite|improve this question






















  • what you call length is unclear to me. do you mean hamming weight? And why would you minimize it?
    – kodlu
    Nov 24 at 0:25










  • And what is the probability parameter in the binomial distribution? You use $p=0.9$ but this is not the $p$ in the equations generating column 3, that looks more like $papprox 15/25,$ judging by the peak in the binomial distribution.
    – kodlu
    Nov 24 at 0:27













up vote
0
down vote

favorite









up vote
0
down vote

favorite











Given the following table of sequences, I'm trying to find the smallest set with probability $p = 0.9$.



enter image description here



The smallest set consists of some sequences from the table, which probability (column 3) should add up to $p$, while the length (found in the second column) is being minimized.



I'm struggling to find a good approach to find the smallest set, without just trying a lot of options and checking their length. Therefore I was wondering if there exists a fast approach to find the smallest set, given such a table.










share|cite|improve this question













Given the following table of sequences, I'm trying to find the smallest set with probability $p = 0.9$.



enter image description here



The smallest set consists of some sequences from the table, which probability (column 3) should add up to $p$, while the length (found in the second column) is being minimized.



I'm struggling to find a good approach to find the smallest set, without just trying a lot of options and checking their length. Therefore I was wondering if there exists a fast approach to find the smallest set, given such a table.







information-theory






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asked Nov 22 at 11:52









Steven Raaijmakers

1175




1175












  • what you call length is unclear to me. do you mean hamming weight? And why would you minimize it?
    – kodlu
    Nov 24 at 0:25










  • And what is the probability parameter in the binomial distribution? You use $p=0.9$ but this is not the $p$ in the equations generating column 3, that looks more like $papprox 15/25,$ judging by the peak in the binomial distribution.
    – kodlu
    Nov 24 at 0:27


















  • what you call length is unclear to me. do you mean hamming weight? And why would you minimize it?
    – kodlu
    Nov 24 at 0:25










  • And what is the probability parameter in the binomial distribution? You use $p=0.9$ but this is not the $p$ in the equations generating column 3, that looks more like $papprox 15/25,$ judging by the peak in the binomial distribution.
    – kodlu
    Nov 24 at 0:27
















what you call length is unclear to me. do you mean hamming weight? And why would you minimize it?
– kodlu
Nov 24 at 0:25




what you call length is unclear to me. do you mean hamming weight? And why would you minimize it?
– kodlu
Nov 24 at 0:25












And what is the probability parameter in the binomial distribution? You use $p=0.9$ but this is not the $p$ in the equations generating column 3, that looks more like $papprox 15/25,$ judging by the peak in the binomial distribution.
– kodlu
Nov 24 at 0:27




And what is the probability parameter in the binomial distribution? You use $p=0.9$ but this is not the $p$ in the equations generating column 3, that looks more like $papprox 15/25,$ judging by the peak in the binomial distribution.
– kodlu
Nov 24 at 0:27










1 Answer
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The smallest set should be (obviously?) formed by picking the most probable sequences.



For that, you should add to your sheet that column (probability of each sequence). In this case, because $p>0.5$, it should be clear that the most probable sequences are in the last rows (greater $k$, greater probability).



Hence you should acummulate the (total) probability of those sequences, until you get your total desired probability.






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    1 Answer
    1






    active

    oldest

    votes








    1 Answer
    1






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes








    up vote
    1
    down vote



    accepted










    The smallest set should be (obviously?) formed by picking the most probable sequences.



    For that, you should add to your sheet that column (probability of each sequence). In this case, because $p>0.5$, it should be clear that the most probable sequences are in the last rows (greater $k$, greater probability).



    Hence you should acummulate the (total) probability of those sequences, until you get your total desired probability.






    share|cite|improve this answer

























      up vote
      1
      down vote



      accepted










      The smallest set should be (obviously?) formed by picking the most probable sequences.



      For that, you should add to your sheet that column (probability of each sequence). In this case, because $p>0.5$, it should be clear that the most probable sequences are in the last rows (greater $k$, greater probability).



      Hence you should acummulate the (total) probability of those sequences, until you get your total desired probability.






      share|cite|improve this answer























        up vote
        1
        down vote



        accepted







        up vote
        1
        down vote



        accepted






        The smallest set should be (obviously?) formed by picking the most probable sequences.



        For that, you should add to your sheet that column (probability of each sequence). In this case, because $p>0.5$, it should be clear that the most probable sequences are in the last rows (greater $k$, greater probability).



        Hence you should acummulate the (total) probability of those sequences, until you get your total desired probability.






        share|cite|improve this answer












        The smallest set should be (obviously?) formed by picking the most probable sequences.



        For that, you should add to your sheet that column (probability of each sequence). In this case, because $p>0.5$, it should be clear that the most probable sequences are in the last rows (greater $k$, greater probability).



        Hence you should acummulate the (total) probability of those sequences, until you get your total desired probability.







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered Nov 24 at 1:22









        leonbloy

        40.1k645107




        40.1k645107






























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