diff --git a/sw/decoders/proximal.py b/sw/decoders/proximal.py
index 6cc64be..c368847 100644
--- a/sw/decoders/proximal.py
+++ b/sw/decoders/proximal.py
@@ -48,22 +48,22 @@ class ProximalDecoder:
 
         return result
 
-    def _projection(self, x):
+    def _projection(self, v):
         """Project a vector onto [-eta, eta]^n in order to avoid numerical instability.
         Detailed in 3.2, p. 3 (Equation (15)).
 
-        :param x: Vector to project
+        :param v: Vector to project
         :return: x clipped to [-eta, eta]^n
         """
-        return np.clip(x, -self._eta, self._eta)
+        return np.clip(v, -self._eta, self._eta)
 
-    def _check_parity(self, y_hat: np.array) -> bool:
+    def _check_parity(self, x_hat: np.array) -> bool:
         """Perform a parity check for a given codeword.
 
-        :param y_hat: codeword to be checked (element of [0, 1]^n)
+        :param x_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
         """
-        syndrome = np.dot(self._H, y_hat) % 2
+        syndrome = np.dot(self._H, x_hat) % 2
         return not np.any(syndrome)
 
     def decode(self, y: np.array) -> np.array:
diff --git a/sw/utility/codes.py b/sw/utility/codes.py
index 4800e0f..1e2a20d 100644
--- a/sw/utility/codes.py
+++ b/sw/utility/codes.py
@@ -13,7 +13,7 @@ import numpy as np
 
 def _parse_alist_header(header):
     size = header.split()
-    return int(size[0,]), int(size[1])
+    return int(size[0]), int(size[1])
 
 
 def read_alist_file(filename):
diff --git a/sw/utility/simulations.py b/sw/utility/simulations.py
index b4471d5..465dfa3 100644
--- a/sw/utility/simulations.py
+++ b/sw/utility/simulations.py
@@ -54,9 +54,9 @@ def test_decoder(x: np.array,
 
             y = noise.add_awgn(x_bpsk, SNR, signal_amp=np.sqrt(2))
 
-            y_hat = decoder.decode(y)
+            x_hat = decoder.decode(y)
 
-            total_bit_errors += count_bit_errors(x, y_hat)
+            total_bit_errors += count_bit_errors(x, x_hat)
             total_bits += x.size
 
             if total_bit_errors >= target_bit_errors: