Smallest set (typical set)
Given the following table of sequences, I'm trying to find the smallest set with probability $p = 0.9$.
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
asked Nov 22 '18 at 11:52
Steven Raaijmakers
1175
add a comment |
Given the following table of sequences, I'm trying to find the smallest set with probability $p = 0.9$.
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
asked Nov 22 '18 at 11:52
Steven Raaijmakers
1175
what you call length is unclear to me. do you mean hamming weight? And why would you minimize it?
– kodlu
Nov 24 '18 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 '18 at 0:27
add a comment |
Given the following table of sequences, I'm trying to find the smallest set with probability $p = 0.9$.
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
asked Nov 22 '18 at 11:52
Steven Raaijmakers
1175
Given the following table of sequences, I'm trying to find the smallest set with probability $p = 0.9$.
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
information-theory
asked Nov 22 '18 at 11:52
Steven Raaijmakers
1175
asked Nov 22 '18 at 11:52
Steven Raaijmakers
1175
asked Nov 22 '18 at 11:52
Steven Raaijmakers
1175
asked Nov 22 '18 at 11:52
Steven Raaijmakers
1175
asked Nov 22 '18 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 '18 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 '18 at 0:27
add a comment |
what you call length is unclear to me. do you mean hamming weight? And why would you minimize it?
– kodlu
Nov 24 '18 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 '18 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 '18 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 '18 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 '18 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 '18 at 0:27
add a comment |
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.
answered Nov 24 '18 at 1:22
leonbloy
40.4k645107
add a comment |
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1 Answer
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1 Answer
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active
oldest
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oldest
votes
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.
answered Nov 24 '18 at 1:22
leonbloy
40.4k645107
add a comment |
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.
answered Nov 24 '18 at 1:22
leonbloy
40.4k645107
add a comment |
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.
answered Nov 24 '18 at 1:22
leonbloy
40.4k645107
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.
answered Nov 24 '18 at 1:22
leonbloy
40.4k645107
answered Nov 24 '18 at 1:22
leonbloy
40.4k645107
answered Nov 24 '18 at 1:22
leonbloy
40.4k645107
answered Nov 24 '18 at 1:22
leonbloy
40.4k645107
40.4k645107
add a comment |
add a comment |
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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 '18 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 '18 at 0:27