My problem is that I want to bind Control + Backspace combination to backward-delete-word function. However, it doesn't seem possible because emacs doesn't detect the Control key in combination with backspace.
I detected that by looking at the "logger" (C-h l). So if I press Backspace, it shows DEL. If I press Control + Backspace, it still shows DEL.
Is there any way to achieve that?
I have read and tried other questions, but couldn't fix it.
As @phils pointed out, if you are using Emacs in a terminal (e.g. emacs -nw) instead of as a GUI (no -nw command-line option), and if you are not on MS Windows, then by default certain key sequences are not available to you.
However, it might still be possible for you to configure the terminal (e.g., xterm) so that it in fact supports some such key sequences for Emacs. See this comment by the Emacs maintainer in the discussion of Emacs bug #10387.
(That said, you might find it simpler to just use a different key sequence. Or switch to the GUI version of Emacs.)