Generate matrix of bits

Question

I would like to take an integer n defining the number of bits in my communication code and a vector defining the alphabet I am assigning to bits 0:n-1,

Answer 1

To easily convert zeros to -1 (and leave the ones intact) you can simply do

minusOnes = 2 * zeroOnes - 1;

Answer 2

You can also do it like this:

M = 2 * (dec2bin(0:7, 3)=='1')-1;

That returns:

M =
    -1    -1    -1
    -1    -1     1
    -1     1    -1
    -1     1     1
     1    -1    -1
     1    -1     1
     1     1    -1
     1     1     1

However, it's slower. I get 0.0012s (dec2bin) against 0.0002s (meshgrid+bitget) for 1024 values and 10 bits.

Answer 3

dec2bin is actually not the best way to approach the problem, because its result is an array of strings (i.e a matrix of characters), where each digit is a character. If you want '-1' to represent a logical "0", that would be two characters, and it introduces problems.

Consider an alternative method with bitget. Making use of Shai's suggestion, do the following:

[bits, values] = meshgrid(1:3, 0:7);
M = 2 * bitget(values, bits) - 1;

The will produce what you want:

M =
    -1    -1    -1
     1    -1    -1
    -1     1    -1
     1     1    -1
    -1    -1     1
     1    -1     1
    -1     1     1
     1     1     1