In data communications, the term “residual error rate” refers to which probability when an error detection scheme is employed?

Introduction:
Reliability metrics quantify how often communication systems deliver incorrect bits. “Residual error rate” specifically addresses the fraction of errors that slip past an error-detection mechanism such as parity, checksum, or CRC.

Given Data / Assumptions:

• An error detection scheme (e.g., CRC) is in use.
• Noise on the channel can flip bits or corrupt frames.
• Detection is very good but not perfect.

Concept / Approach:
Error detection codes map valid data to codewords; some error patterns may map one valid codeword into another undetectably. The residual error rate is the probability that a corrupted frame passes the detector as if it were correct, i.e., an undetected error reaches higher layers.

Step-by-Step Solution:
1) Channel introduces bit errors with some raw bit error rate (BER).2) Detector flags most corrupted frames; those are dropped/retransmitted.3) A small subset of corruptions mimic valid codewords and escape detection.4) The frequency of such escapes defines the residual error rate.

Verification / Alternative check:
CRC polynomials are selected to minimize undetected patterns (e.g., detect all single-bit errors, most burst errors up to length L). Despite this, the residual is nonzero but extremely small for strong CRCs.

Why Other Options Are Wrong:

• Bit errors per 24 hours: a time-based count, not a probability of undetected errors.
• Probability of detection: that measures success at catching errors, not misses.
• SNR divided by Eb/N0: unrelated physical-layer ratio.
• Perfect correction probability: not a standard metric and not about undetected errors.

Common Pitfalls:
Confusing BER, FER (frame error rate), and residual error rate. Residual error rate is conditional on the presence of an error detection mechanism and focuses on undetected errors that pass through as valid.

Final Answer:
Probability that one or more errors remain undetected when error detection is used