diff --git a/sw/decoders/proximal.py b/sw/decoders/proximal.py
index aa226d8..805ea9b 100644
--- a/sw/decoders/proximal.py
+++ b/sw/decoders/proximal.py
@@ -79,10 +79,9 @@ class ProximalDecoder:
     def _check_parity(self, y_hat: np.array) -> bool:
         """Perform a parity check for a given codeword.
 
-        :param y_hat: codeword to be checked (element of [-1, 1]^n)
+        :param y_hat: codeword to be checked (element of [0, 1]^n)
         :return: True if the parity check passes, i.e. the codeword is valid. False otherwise
         """
-        y_hat_binary = (y_hat == 1) * 1  # Map the codeword from [-1, 1]^n to [0, 1]^n
         syndrome = np.dot(self._H, y_hat) % 2
         return not np.any(syndrome)
 
@@ -96,15 +95,16 @@ class ProximalDecoder:
             and 'w' is noise)
         :return: Most probably sent dataword (element of [0, 1]^k)
         """
-        s = 0
-        x_hat = 0
+        s = np.zeros(y.size)
+        x_hat = np.zeros(y.size)
         for k in range(self._K):
             r = s - self._step_size * self._L_awgn(s, y)
 
             s = r - self._gamma * self._grad_h(r)
             s = self._projection(s)  # Equation (15)
 
-            x_hat = (np.sign(s) == 1) * 1
+            x_hat = np.sign(s)
+            x_hat = (x_hat == 1) * 1  # Map the codeword from [-1, 1]^n to [0, 1]^n
 
             if self._check_parity(x_hat):
                 break