Python CRC 实现指南 | AI生成和翻译
问题：你能提供 Python 代码来演示使用生成多项式 11001 的 CRC (Cyclic Redundancy Check) 计算和验证过程吗？
答案：
这是一个全面的 Python 实现：```python def xor_divide(dividend: str, divisor: str) -> str: “"”Perform modulo-2 (XOR) division and return the remainder.””” div = list(dividend) divisor_len = len(divisor)
for i in range(len(dividend) - divisor_len + 1):
if div[i] == '1':
for j in range(divisor_len):
# XOR each bit
div[i + j] = '0' if div[i + j] == divisor[j] else '1'
# The remainder is the last (divisor_len - 1) bits
remainder = ''.join(div[-(divisor_len - 1):])
return remainder
def crc_calculate(message: str, generator: str) -> tuple[str, str]: “”” Calculate CRC remainder and return the transmitted frame.
Args:
message: Original information bits, e.g. '10110110'
generator: Generator polynomial bits, e.g. '11001'
Returns:
(crc_bits, transmitted_frame)
"""
r = len(generator) - 1 # degree of generator = number of zeros to append
padded = message + '0' * r # Step 1: append r zeros
print(f"\n{'='*55}")
print(f" CRC CALCULATION")
print(f"{'='*55}")
print(f" Message : {message}")
print(f" Generator : {generator} (degree = {r})")
print(f" Appended zeros : {r} zeros")
print(f" Padded message : {padded}")
crc = xor_divide(padded, generator) # Step 2: mod-2 division
crc = crc.zfill(r) # pad CRC to exactly r bits if needed
transmitted = message + crc # Step 3: append CRC to original message
print(f"\n Remainder (CRC) : {crc}")
print(f" Transmitted frame: {transmitted}")
print(f"{'='*55}")
return crc, transmitted
def crc_verify(received: str, generator: str) -> bool: “”” Verify a received frame by dividing it by the generator. Remainder == 0…0 means no error detected.
Args:
received: The full received frame (message + CRC bits)
generator: Generator polynomial bits
Returns:
True if no error detected, False otherwise
"""
r = len(generator) - 1
remainder = xor_divide(received, generator)
remainder = remainder.zfill(r)
no_error = all(b == '0' for b in remainder)
print(f"\n{'='*55}")
print(f" CRC VERIFICATION")
print(f"{'='*55}")
print(f" Received frame : {received}")
print(f" Generator : {generator}")
print(f" Remainder : {remainder}")
print(f" Result : {'✅ No error detected' if no_error else '❌ Error detected!'}")
print(f"{'='*55}")
return no_error
─── Demo ────────────────────────────────────────────────────────────────────
if name == “main”: MESSAGE = “10110110” GENERATOR = “11001” # degree 4 → append 4 zeros
# 1. Sender side: calculate CRC and build transmitted frame
crc_bits, frame = crc_calculate(MESSAGE, GENERATOR)
# 2. Receiver side — Case A: frame arrives intact
print("\n[Case A] Frame arrives with NO errors:")
crc_verify(frame, GENERATOR)
# 3. Receiver side — Case B: simulate a 1-bit error (flip bit 3)
corrupted = list(frame)
corrupted[3] = '0' if corrupted[3] == '1' else '1'
corrupted_frame = ''.join(corrupted)
print(f"\n[Case B] Frame arrives WITH a bit error (bit 3 flipped):")
print(f" Original : {frame}")
print(f" Corrupted: {corrupted_frame}")
crc_verify(corrupted_frame, GENERATOR)
# 4. Try your own values
print("\n[Custom] Try your own message and generator:")
custom_msg = "1101011011"
custom_gen = "10011"
crc_custom, frame_custom = crc_calculate(custom_msg, custom_gen)
crc_verify(frame_custom, custom_gen) ```
示例输出：
=======================================================
CRC CALCULATION
=======================================================
Message : 10110110
Generator : 11001 (degree = 4)
Appended zeros : 4 zeros
Padded message : 101101100000
Remainder (CRC) : 1110
Transmitted frame: 101101101110
=======================================================
[Case A] Frame arrives with NO errors:
=======================================================
CRC VERIFICATION
=======================================================
Received frame : 101101101110
Generator : 11001
Remainder : 0000
Result : ✅ No error detected
=======================================================
[Case B] Frame arrives WITH a bit error (bit 3 flipped):
Original : 101101101110
Corrupted: 101001101110
=======================================================
CRC VERIFICATION
=======================================================
Received frame : 101001101110
Generator : 11001
Remainder : 1001
Result : ❌ Error detected!
=======================================================
代码如何映射到理论
| 代码函数 | 理论步骤 |
|---|---|
message + '0' * r |
向消息追加 r 个零 |
xor_divide(padded, generator) |
Mod-2 (XOR) 长除法 |
message + crc |
构建传输帧 T |
xor_divide(received, generator) |
接收方重新对帧进行除法 |
remainder == '000...' |
零余数 = 无错误 |
xor_divide() 函数是核心引擎 — 它通过从左到右扫描，在看到领先的 1 位时进行 XOR 操作，从而模拟硬件 XOR 移位寄存器，完全匹配之前解释中所示的纸上长除法方法。