Entropy of a language












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Im supposed to calculate the entropy of following language $L={x,y,z,w}$



Symbols have following probability of occurrence:
$p(x)=frac{1}{2},quad p(y)=frac{1}{4},quad p(z)=p(w)=frac{1}{8}$

,and they occur independently.



Formula given is $$lim_{nrightarrow infty}frac{H(L^n)}{n}$$
and regular entropy $H(x)=-sum p(x_i)log p(x_i)$



I just can't figure out $H(L^n)$. For single symbol its easy, but having strings length of $n$.. Thanks in advance.






combinatorics coding-theory







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    0












    $begingroup$


    Im supposed to calculate the entropy of following language $L={x,y,z,w}$



    Symbols have following probability of occurrence:
    $p(x)=frac{1}{2},quad p(y)=frac{1}{4},quad p(z)=p(w)=frac{1}{8}$

    ,and they occur independently.



    Formula given is $$lim_{nrightarrow infty}frac{H(L^n)}{n}$$
    and regular entropy $H(x)=-sum p(x_i)log p(x_i)$



    I just can't figure out $H(L^n)$. For single symbol its easy, but having strings length of $n$.. Thanks in advance.






    combinatorics coding-theory







    share|cite|improve this question









    $endgroup$















      0












      0








      0


      1



      $begingroup$


      Im supposed to calculate the entropy of following language $L={x,y,z,w}$



      Symbols have following probability of occurrence:
      $p(x)=frac{1}{2},quad p(y)=frac{1}{4},quad p(z)=p(w)=frac{1}{8}$

      ,and they occur independently.



      Formula given is $$lim_{nrightarrow infty}frac{H(L^n)}{n}$$
      and regular entropy $H(x)=-sum p(x_i)log p(x_i)$



      I just can't figure out $H(L^n)$. For single symbol its easy, but having strings length of $n$.. Thanks in advance.






      combinatorics coding-theory







      share|cite|improve this question









      $endgroup$




      Im supposed to calculate the entropy of following language $L={x,y,z,w}$



      Symbols have following probability of occurrence:
      $p(x)=frac{1}{2},quad p(y)=frac{1}{4},quad p(z)=p(w)=frac{1}{8}$

      ,and they occur independently.



      Formula given is $$lim_{nrightarrow infty}frac{H(L^n)}{n}$$
      and regular entropy $H(x)=-sum p(x_i)log p(x_i)$



      I just can't figure out $H(L^n)$. For single symbol its easy, but having strings length of $n$.. Thanks in advance.






      combinatorics coding-theory




      combinatorics coding-theory






      share|cite|improve this question













      share|cite|improve this question











      share|cite|improve this question




      share|cite|improve this question










      asked Jan 31 at 18:46









      Yulia23576Yulia23576

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          $begingroup$

          Hint:



          Use the statement "they occur independently" to arrive at
          $$H(L^n)=nH(L).$$






          share|cite|improve this answer











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            $begingroup$

            Hint:



            Use the statement "they occur independently" to arrive at
            $$H(L^n)=nH(L).$$






            share|cite|improve this answer











            $endgroup$


















              2












              $begingroup$

              Hint:



              Use the statement "they occur independently" to arrive at
              $$H(L^n)=nH(L).$$






              share|cite|improve this answer











              $endgroup$
















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                2








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                $begingroup$

                Hint:



                Use the statement "they occur independently" to arrive at
                $$H(L^n)=nH(L).$$






                share|cite|improve this answer











                $endgroup$



                Hint:



                Use the statement "they occur independently" to arrive at
                $$H(L^n)=nH(L).$$







                share|cite|improve this answer














                share|cite|improve this answer



                share|cite|improve this answer








                edited Jan 31 at 20:17

























                answered Jan 31 at 19:11









                Math LoverMath Lover

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