1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Determining PSD of 1uaternary (4-ary) line code

  1. Apr 10, 2013 #1
    1. The problem statement, all variables and given/known data
    Ok So this is an example from my text. Im having trouble following a portion of it and was curious if anyone could shed some light on it. Ive typed most of it and posted a screen shot of the second portion since there is a table involved.

    Determine the PSD of the quaternary (4-ary) baseband signaling. The 4-ary line code has four distinct symbols corresponding to the four different combinations of two message bits. One such mapping is:

    $$a_k= \begin{cases}-3 \ \ message \ bits \ 00\\
    -1 \ \ message \ bits \ 01\\
    +1 \ \ message \ bits \ 10\\
    +3 \ \ message \ bits \ 11 \end{cases}$$

    Therefore, all four values of ##a_k## are equally likely, each with a chance of 1 in 4. Recall that
    $$R_0=lim_{n→∞} \frac{1}{N} \sum_{k} a_k^2$$

    Within the summation, 1/4 of the ##a_k \ will \ be \ ±1, \ and \ ±3## thus,

    $$R_0=lim_{N→∞} \frac{1}{N} [\frac{N}{4}(-3)^2+\frac{N}{4}(-1)^2++\frac{N}{4}(1)^2++\frac{N}{4}(3)^2]=5$$

    Up to this poing I understand.

    Here is the second portion:
    2. Relevant equations

    3. The attempt at a solution
    I understand how to calculate ##R_0## from this example. I get lost when the text calculated R_n. I see how they created the table of all possible values for ##a_k*a_k+n## but when the ##R_n## equation is put together i get confused.

    In the paragraph below it they attempt to explain. Why are ±1 and ±9 equally likely (1 in 8) and ±1 are equally likely (1 in 4). I would have expected them to be the other way around.

    Can anyone shed some light or offer a better explanation?

    It would be much appreciated!

    Attached Files:

  2. jcsd
  3. Apr 11, 2013 #2

    I like Serena

    User Avatar
    Homework Helper

    The table contains 16 entries. Each is equally likely.
    The value 1 appears twice in the table, so the corresponding probability is ##\frac{2}{16}=\frac{1}{8}##.
    However, the value 3 appears four times in the table, so its probability is ##\frac{4}{16}=\frac{1}{4}##.
  4. Apr 11, 2013 #3
    Simple! Man I really should have seen that.

    Anyway thanks again for your help ILS!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted