Channel
Instructions
    Quick theory overview:
  • The conditional distribution of a \( BEC(\epsilon) \) Channel is given by:

    \( p(\boldsymbol{y}|\boldsymbol{x_i}) = \begin{cases} \epsilon^{w_e(y)}(1-\epsilon)^{n-w_e(y)} & \text{if} \ {x} \ \text{and} \ {y} \ \text{are compatible} \\ 0 & \text{otherwise} \end{cases}\)

    The estimate of the transmitted codeword is given by:

    \(\hat{\boldsymbol{x}}=arg_{\boldsymbol{x}\in{\cal C}}\max\langle\boldsymbol{y},\boldsymbol{x}\rangle\)


    Procedure:
  • Step 1: Enter the likelihoods of \(\boldsymbol{y}\) given codewords and click on the "Submit" button to verify the likelihoods.
      Note: If a codeword is incompatible with the vector \(\boldsymbol{y}\), enter '0' as the result in the boxes corresponding to the codewords.
      Note: Kindly round the value to three decimal places, rounding up to the nearest decimal.
  • Step 2: Select the maximum likelihood estimate codeword from the dropdown. If there is more than one possible codeword, select the codeword that occurs first.
  • Step 3: After clicking on the "Next" button, the next question will appear. Select all the transmitted vectors that lead to a decoding error when using maximum likelihood decoding.

Consider codeword {c1  =(), c2=  ()} and ε(e)

Maximum Likelihood:
Observations