Python CRC 实现指南 | AI生成和翻译

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问题：你能提供 Python 代码来演示使用生成多项式 11001 çš„ 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 =======================================================

```

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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。

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