feat(framing): class for header with hamming(7,4)

hamming_7_4_codec.py

@@ -0,0 +1,97 @@
+import numpy as np
+import numpy.typing as npt
+
+GEN_MATRIX = np.asarray([(1, 1, 1, 0, 0, 0, 0),
+                         (1, 0, 0, 1, 1, 0, 0),
+                         (0, 1, 0, 1, 0, 1, 0),
+                         (1, 1, 0, 1, 0, 0, 1),
+                         ])
+PARITY_MATRIX = np.asarray([(0, 0, 0, 1, 1, 1, 1),
+                            (0, 1, 1, 0, 0, 1, 1),
+                            (1, 0, 1, 0, 1, 0, 1),
+                            ])
+DECODER_MATRIX = np.asarray([(0, 0, 1, 0, 0, 0, 0,),
+                             (0, 0, 0, 0, 1, 0, 0,),
+                             (0, 0, 0, 0, 0, 1, 0,),
+                             (0, 0, 0, 0, 0, 0, 1,),
+                             ])
+
+
+def number_to_list(number: int, N: int) -> npt.NDArray:
+    """Return the last N bits of a number as an MSB-first array"""
+    return np.array([(number >> (N-1-i)) % 2 for i in range(0, N)])
+
+
+def list_to_number(array: npt.NDArray, N: int) -> int:
+    """Reconstruct a number from the first N elements of an MSB-first array"""
+    output = 0
+    for i in range(0, N):
+        output += array[i] << (N-1-i)
+    return output
+
+
+def encode_nibble(data: int) -> int:
+    """Encode the lower 4 bits of data as hamming(7,4)"""
+    data_asarr = number_to_list(data, 4)
+    output_asarr = (data_asarr @ GEN_MATRIX) % 2
+    return list_to_number(output_asarr, 7)
+
+
+def hamming_7_4_encode(data: list[int]) -> list[int]:
+    """Encode a list of ints using Hamming(7,4)
+       The returned list is twice as long as the list in the argument"""
+    data_encoded = []
+    for element in data:
+        data_encoded += [encode_nibble(element >> 4),
+                         encode_nibble(element % 16)]
+    return data_encoded
+
+
+def decode_nibble(data: int) -> int:
+    """decode a single nibble using the parity check matrix of Hamming(7,4).
+       This should correct 2 errors maximum."""
+    data_asarr = number_to_list(data, 7)
+    syndrome = (PARITY_MATRIX @ data_asarr) % 2
+    error = list_to_number(syndrome, 3)
+    if error == 0:
+        return list_to_number(data_asarr, 4)
+    data_asarr[error - 1] ^= 1
+    data_decoded = (DECODER_MATRIX @ data_asarr) % 2
+    return list_to_number(data_decoded, 4)
+
+
+def hamming_7_4_decode(data: list[int]) -> list[int]:
+    """Decode a list of ints using Hamming(7,4)
+       The returned list is half as long as the list in the argument"""
+    return [(decode_nibble(data[i]) << 4) + (decode_nibble(data[i + 1])) for i in range(0, len(data), 2)]
+
+
+if __name__ == "__main__":
+    msg = 'TEST DE HA5PLS'
+    data_in = [byte for byte in bytearray(msg.encode())]
+    data_encoded = hamming_7_4_encode(data_in)
+    print(f"Data sent: {msg}")
+
+    data_corrupted_1bit = [data ^ (1 << (idx % 7))
+                           for idx, data in enumerate(data_encoded)]
+    # print(f"Corrupt data with 1-bit errors: {data_corrupted_1bit}")
+    data_corrected_1bit = hamming_7_4_decode(data_corrupted_1bit)
+    data_corrected_1bit_str = [int.to_bytes(int(i), 1, "big").decode(
+        encoding="utf-8", errors="ignore") for i in data_corrected_1bit]
+    print(f"Recovered data from 1-bit errors: {data_corrected_1bit_str}")
+
+    data_corrupted_2bit = [data ^ (5 << (idx % 7))
+                           for idx, data in enumerate(data_encoded)]
+    # print(f"Corrupt data with 2-bit errors: {data_corrupted_2bit}")
+    data_corrected_2bit = hamming_7_4_decode(data_corrupted_2bit)
+    data_corrected_2bit_str = [int.to_bytes(int(i), 1, "big").decode(
+        encoding="utf-8", errors="ignore") for i in data_corrected_2bit]
+    print(f"Recovered data from 1-bit errors: {data_corrected_2bit_str}")
+
+    data_corrupted_3bit = [data ^ (7 << (idx % 7))
+                           for idx, data in enumerate(data_encoded)]
+    # print(f"Corrupt data with 3-bit errors: {data_corrupted_3bit}")
+    data_corrected_3bit = hamming_7_4_decode(data_corrupted_3bit)
+    data_corrected_3bit_str = [int.to_bytes(int(i), 1, "big").decode(
+        encoding="utf-8", errors="ignore") for i in data_corrected_3bit]
+    print(f"Recovered data from 1-bit errors: {data_corrected_3bit_str}")