Prove that in 4B/5B encoding, a signal transition will occur at least every four bit times.
The Correct Answer and Explanation is:
Proof and Explanation:
In 4B/5B encoding, each group of 4 data bits is mapped to a 5-bit code that ensures sufficient signal transitions for reliable clock recovery. The key design rule of 4B/5B encoding is that no 5-bit code has more than three consecutive zeros. This guarantees a signal transition at least every 4 bits, which is essential for maintaining synchronization between sender and receiver.
Proof:
- Maximum Consecutive Zeros Rule:
In 4B/5B encoding, the 5-bit output codes are specifically chosen to ensure that no valid code contains more than three consecutive zeros. - No 5-bit code violates the rule:
The 4B/5B encoding table consists of 16 standard data codes and a few control codes, and all are selected such that none contains four or more consecutive zeros. - Transition occurs within every 5-bit symbol:
Since every 5-bit encoded symbol contains at most three consecutive zeros, it ensures at least one ‘1’ occurs in every 5-bit sequence, causing a voltage transition. - Transition within four bit times:
If a code contains three zeros (e.g.,0001x), the transition must occur at the fourth bit at latest, satisfying the condition that there’s a signal change at least every four bits.
Explanation:
Digital communication systems require frequent signal transitions to maintain clock synchronization between transmitter and receiver. Without enough transitions, timing drift can lead to data corruption.
Standard binary encoding (NRZ) can have long runs of zeros or ones, which causes synchronization issues. To solve this, 4B/5B encoding introduces redundancy by mapping 4 bits of data into 5 bits with rules that limit long runs of identical bits, particularly zeros.
The enforced rule that no more than three zeros appear consecutively guarantees a transition at least every four bits. This ensures the signal never stays constant too long, providing the clocking information needed for reliable data recovery.
Thus, 4B/5B encoding is a clever trade-off: it uses 25% more bandwidth (5 bits instead of 4) to achieve highly reliable and synchronized data transmission.
