I have been working on viterbi decoder in matlab2009 on simple 1/2 rate convolutional encoder.
Here is my code
trel = poly2trellis(3,[7 5]);
msg = [ 0 1 0 1 1 1 0 0 1 0 1 0 0 0 1 ];
code = convenc(msg,trel);
% Traceback Length
tblen = 5;
ucode = real(awgn(1-2*code,tblen,'measured'));
dcd = vitdec(ucode,trel,tblen,'cont','unquant');
According to this input code
i am getting the code = 00 11 10 00 01 10 01 11 11 10 00 10 11 00 11
which is correct
but talking about the dcd which is output after viterbi decoder is coming incorrect
i.e 000000101110010. which is far different from my msg input.
guide me where i am going incorrect
The decoded output depends on the type of opmode Input you selected.
In case of cont, there is a delay in the output equal to tblen number of symbols whereas there are 'term' and trunc modes as well.
You can compare the initial msg(1,end-tblen) symbols with dcd(1,tblen+1:end). They are same!
You may check vitdec at Matlab help.
Related
Want to convert the alphabet to numerical values and transform it back to alphabets using some mathematical techniques like fast Fourier transform in MATLAB.
Example:
The following is the text saved in "text2figure.txt" file
Hi how r u am fine take care of your health
thank u very much
am 2.0
Reading it in MATLAB:
data=fopen('text2figure.txt','r')
d=fscanf(data,'%s')
temp = fileread( 'text2figure.txt' )
temp = regexprep( temp, ' {6}', ' NaN' )
c=cellstr(temp(:))'
Now I wish to convert cell array with spaces to numerical values/integers:
coding = 'abcdefghijklmnñopqrstuvwxyz .,;'
str = temp %// example text
[~, result] = ismember(str, coding)
y=result
result =
Columns 1 through 18
0 9 28 8 16 24 28 19 28 22 28 1 13 28 6 9 14 5
Columns 19 through 36
28 21 1 11 5 28 3 1 19 5 28 16 6 28 26 16 22 19
Columns 37 through 54
28 8 5 1 12 21 8 28 0 0 21 8 1 14 11 28 22 28
Columns 55 through 71
23 5 19 26 28 13 22 3 8 0 0 1 13 28 0 29 0
Now I wish to convert the numerical values back to alphabets:
Hi how r u am fine take care of your health
thank u very much
am 2.0
How to write a MATLAB code to return the numerical values in the variable result to alphabets?
Most of the code in the question doesn't have any useful effects. These three lines are the ones that lead to result:
str = fileread('test2figure.txt');
coding = 'abcdefghijklmnñopqrstuvwxyz .,;';
[~, result] = ismember(str, coding);
ismember returns, in the second output argument, the indices into coding for each element of str. Thus, result are indices that we can use to index into coding:
out = coding(result);
However, this does not work because some elements of str do not occur in coding, and for those elements ismember returns 0, which is not a valid index. We can replace the zeros with a new character:
coding = ['*',coding];
out = coding(result+1);
Basically, we're shifting each code by one, adding a new code for 1.
One of the characters we're missing here is the newline character. Thus the three lines have become one line. You can add a code for the newline character by adding it to the coding table:
str = fileread('test2figure.txt');
coding = ['abcdefghijklmnñopqrstuvwxyz .,;',char(10)]; % char(10) is the newline character
[~, result] = ismember(str, coding);
coding = ['*',coding];
out = coding(result+1);
All of this is easier to achieve just using the ASCII code table:
str = fileread('test2figure.txt');
result = double(str);
out = char(result);
I'd like to obtain all unique products for a given vector.
For example, given a:
a = [4,10,12,3,6]
I want to obtain a matrix that contains the results of:
4*10
4*12
4*3
4*6
10*12
10*3
10*6
12*3
12*6
3*6
Is there a short and/or quick way of doing this in MATLAB?
EDIT: a may contain duplicate numbers, giving duplicate products - and these must be kept.
Given:
a =
4 10 12 3 6
Construct the matrix of all pairwise products:
>> all_products = a .* a.'
all_products =
16 40 48 12 24
40 100 120 30 60
48 120 144 36 72
12 30 36 9 18
24 60 72 18 36
Now, construct a mask to keep only those values below the main diagonal:
>> mask = tril(true(size(all_products)), -1)
mask =
0 0 0 0 0
1 0 0 0 0
1 1 0 0 0
1 1 1 0 0
1 1 1 1 0
and apply the mask to the product matrix:
>> unique_products = all_products(mask)
unique_products =
40
48
12
24
120
30
60
36
72
18
If you have the Statistics Toolbox, you can abuse pdist, which considers only one of the two possible orders for each pair:
result = pdist(a(:), #times);
One option involves nchoosek, which returns all combinations of k elements out of a vector, each row is one combination. prod computes the product of rows or columns:
a = [4,10,12,3,6];
b = nchoosek(a,2);
b = prod(b,2); % 2 indicates rows
Try starting with this. Have the unique function filter out the result of multiplying a by itself.
b = unique(a*a')
I have a file that looks like this (with real data and much bigger):
A B C D E F G H I
1 105.28 1 22 84 2 10.55 21 2
2 357.01 0 32 34 1 11.43 28 1
3 150.23 3 78 22 0 12.02 11 0
4 357.01 0 32 34 1 11.43 28 1
5 357.01 0 32 34 1 11.43 28 1
6 357.01 0 32 34 1 11.43 28 1
...
17000 357.01 0 32 34 1 11.43 28 1
I want to import all the numerical value into a matrix, skipping the headlines. For that purpose I use this code:
Filename = 'test.txt';
A = dlmread(Filename,' ',1,0); %Imports the whole data into a matrix
The problem with this is just that A is a 17 000 * 1 vector instead of a matrix with several columns. If I manual edit the data file, remove the headlines and just run this it works:
A = dlmread(Filename); %Imports the whole data into a matrix
But I would prefer not to do this since the headlines are used later on in the code. Any advice how to get this work?
edit: solved by using
' '
instead of just
' '
Use the import tool.
Make sure you choose the data.
Generate script.
I have a matrix of measured angles between M planes
0 52 77 79
52 0 10 14
77 10 0 3
79 14 3 0
I have a list of known angles between planes, which is an N-by-N matrix which I name rho. Here's is a subset of it (it's too large to display):
0 51 68 75 78 81 82
51 0 17 24 28 30 32
68 17 0 7 11 13 15
75 24 7 0 4 6 8
78 28 11 4 0 2 4
81 30 13 6 2 0 2
82 32 15 8 4 2 0
My mission is to find the set of M planes whose angles in rho are nearest to the measured angles.
For example, the measured angles for the planes shown above are relatively close to the known angles between planes 1, 2, 4 and 6.
Put differently, I need to find a set of points in a distance matrix (which uses cosine-related distances) which matches a set of distances I measured. This can also be thought of as matching a pattern to a mold.
In my problem, I have M=5 and N=415.
I really tried to get my head around it but have run out of time. So currently I'm using the simplest method: iterating over every possible combination of 3 planes but this is slow and currently written only for M=3. I then return a list of matching planes sorted by a matching score:
function [scores] = which_zones(rho, angles)
N = size(rho,1);
scores = zeros(N^3, 4);
index = 1;
for i=1:N-2
for j=(i+1):N-1
for k=(j+1):N
found_angles = [rho(i,j) rho(i,k) rho(j,k)];
score = sqrt(sum((found_angles-angles).^2));
scores(index,:)=[score i j k];
index = index + 1;
end
end;
end
scores=scores(1:(index-1),:); % was too lazy to pre-calculate #
scores=sortrows(scores, 1);
end
I have a feeling pdist2 might help but not sure how. I would appreciate any help in figuring this out.
There is http://www.mathworks.nl/help/matlab/ref/dsearchn.html for closest point search, but that requires same dimensionality. I think you have to bruteforce find it anyway because it's just a special problem.
Here's a way to bruteforce iterate over all unique combinations of the second matrix and calculate the score, after that you can find the one with the minimum score.
A=[ 0 52 77 79;
52 0 10 14;
77 10 0 3;
79 14 3 0];
B=[ 0 51 68 75 78 81 82;
51 0 17 24 28 30 32;
68 17 0 7 11 13 15;
75 24 7 0 4 6 8;
78 28 11 4 0 2 4;
81 30 13 6 2 0 2;
82 32 15 8 4 2 0];
M = size(A,1);
N = size(B,1);
% find all unique permutations of `1:M`
idx = nchoosek(1:N,M);
K = size(idx,1); % number of combinations = valid candidates for matching A
score = NaN(K,1);
idx_triu = triu(true(M,M),1);
Atriu = A(idx_triu);
for ii=1:K
partB = B(idx(ii,:),idx(ii,:));
partB_triu = partB(idx_triu);
score = norm(Atriu-partB_triu,2);
end
[~, best_match_idx] = min(score);
best_match = idx(best_match_idx,:);
The solution of your example actually is [1 2 3 4], so the upperleft part of B and not [1 2 4 6].
This would theoretically solve your problem, and I don't know how to make this algorithm any faster. But it will still be slow for large numbers. For example for your case of M=5 and N=415, there are 100 128 170 583 combinations of B which are a possible solution; just generating the selector indices is impossible in 32-bit because you can't address them all.
I think the real optimization here lies in cutting away some of the planes in the NxN matrix in a preceding filtering part.
Here's an interesting question :)
I have two "vectors of matrices" which I want to tile like the hankel function does for regular vertices.
For example:
Column Vector:
10
00
20
00
30
00
Row vector:
30 40 50 60
00 00 00 00
The resulting matrix needs to be:
10 20 30 40
00 00 00 00
20 30 40 50
00 00 00 00
30 40 50 60
00 00 00 00
Note that the 0 values can be changed, the resulting structure is the important part.
A related question:
I looked in the command "edit repmat" and saw some interesting syntax I couldn't find help for:
A=[1,3;2,4];
X=[1,1;2,2];
B=A(X,X);
and B ends up being
1 3 1 3
2 4 2 4
1 3 1 3
2 4 2 4
which is basically repmat(A,2,2);
So my question is, what is this syntax: A(X,X)?
Thanks a lot!
Ofer
If you want to tile a set of matrices the way HANKEL tiles values, here's one way you can do it. First, you can put all of your unique matrices in one cell array:
mat = [1 0; 0 0];
cArray = {mat 2.*mat 3.*mat 4.*mat 5.*mat 6.*mat}; %# Your 6 unique matrices
Now, if you want the first 3 matrices running down the first column and the last 4 matrices running across the last row, you can create an index matrix using HANKEL:
>> index = hankel(1:3,3:6);
index =
1 2 3 4
2 3 4 5
3 4 5 6
Then index your cell array with index and use CELL2MAT to convert the resulting cell array to one matrix:
>> cell2mat(cArray(index))
ans =
1 0 2 0 3 0 4 0
0 0 0 0 0 0 0 0
2 0 3 0 4 0 5 0
0 0 0 0 0 0 0 0
3 0 4 0 5 0 6 0
0 0 0 0 0 0 0 0
For the second part of your question, when you perform an indexing operation like A(X,Y), you are using the elements of X as row indices and the elements of Y as column indices into A. Every combination of values in X and Y is used. So, if X = [x1 x2 x3 x4] and Y = [y1 y2 y3 y4], then the result of B = A(X,Y) is equivalent to:
B = [A(x1,y1) A(x1,y2) A(x1,y3) A(x1,y4); ...
A(x2,y1) A(x2,y2) A(x2,y3) A(x2,y4); ...
A(x3,y1) A(x3,y2) A(x3,y3) A(x3,y4); ...
A(x4,y1) A(x4,y2) A(x4,y3) A(x4,y4)];