Channel
Instructions
    Quick theory overview:
  • The conditional distribution of AWGN Channel is given by:

    \( p(\boldsymbol{y}|\boldsymbol{x})=\frac{1}{(\pi N_0)^{n/2}}e^{-\frac{(||\boldsymbol{y}-\boldsymbol{x}||^2)}{N_0}}\)

    The estimate of the transmitted codeword is given by:

    \(\hat{\boldsymbol{x}}=arg_{\boldsymbol{x}\in{\cal C}}\max\frac{1}{(\pi N_0)^{n/2}}e^{-\frac{(||\boldsymbol{y}-\boldsymbol{x}||^2)}{N_0}}=arg_{\boldsymbol{x}\in{\cal C}}\max\langle\boldsymbol{y},\boldsymbol{x}\rangle\)


    Procedure:
  • Step 1: Enter the likelihoods of \(\boldsymbol{y}\) given codewords and click on the "Check" button to verify the likelihoods.
  • Step 2: Select the maximum likelihood estimate codeword from the dropdown.
  • Step 3: Click on "Yes" if the maximum likelihood estimate codeword is same as the transmitted codeword, else click on "No". "Next" button will appear after selecting the correct option.
  • Step 4: After clicking on the "Next" button, the next question will appear. Select all the received vectors that lead to a decoding error when using maximum likelihood decoding.

Consider a codeword,

For the monomial , enter the sub-codeword sums :

Observations