HDB3 Code

Long runs of zeros in AMI

The AMI code suppresses the DC component when binary 1s use alternating positive and negative pulses. A long, uninterrupted sequence of zeros ($000000...$) produces a constant zero-voltage interval.

The receiver uses signal transitions to align its clock with the transmitter timing. During a zero-voltage run, the absence of transitions can increase timing error. HDB3 replaces selected runs of zeros with bipolar pulses while preserving the AMI balance rule.

HDB3: high-density bipolar code with a three-zero limit

HDB3 is a modified AMI code specified by ITU-T G.703 for the 2048 kbit/s interface used in $E1$ systems. It represents ordinary binary 1s with alternating pulses and applies substitutions to runs of four zeros. The recommendation defines the signal as pseudo-ternary: zeros remain zero outside substitution blocks, while 1s alternate as positive and negative marks.

• High-density bipolar: It uses +V, 0, and -V, with substitution rules for runs of zeros.
• Three-zero limit: A substitution prevents more than three consecutive zero symbols in the output signal.

Outside a four-zero run, HDB3 follows AMI. The substitution determines the inserted B pulse and the AMI violation V.

HDB3 substitution rules

When the encoder encounters four consecutive zeros ($0000$), it replaces the block with one of two four-symbol patterns: 000V or B00V. The fourth symbol is always V, so the decoder can identify the replacement and restore four zeros.

The B and V pulses

• V (Violation) pulse: This non-zero pulse (+V or -V) breaks the alternating polarity rule of AMI. A V pulse has the same polarity as the immediately preceding non-zero pulse. The decoder recognizes it as part of a zero substitution.
• B (Bipolar) pulse: This non-zero pulse (+V or -V) substitutes for the first zero in the $B00V$ sequence. The B pulse follows the alternating polarity rule of AMI and contributes to the balance used to select substitutions.

Choosing a substitution to limit DC

The encoder selects 000V or B00V so consecutive V pulses have alternating polarities. The HDB3 rule keeps the number of B pulses between consecutive violations odd.

The rule: After an earlier V, the encoder tracks the parity of the regular non-zero pulses before the next zero block. An odd count selects 000V; an even count selects B00V. The first block also depends on the encoder's initial substitution state; this example assumes 000V. The inserted B pulse keeps the number of pulses between successive V pulses odd.

HDB3 example: step by step

Encode the following binary stream: $1010000110000$

1. Input $1$: Last pulse was none. Start with $+$. The initial polarity is a convention; reversing it reverses every non-zero symbol without changing the decoded bits.
   Encoded: +
2. Input $0$: No substitution needed.
   Encoded: + 0
3. Input $1$: Last pulse was $+$. Alternate to $-$.
   Encoded: + 0 -
4. Input $0000$: Apply the first substitution.
   Initial block convention: use the pattern $000V$, which ends in $V$.
   The previous non-zero pulse is $-$.
   The violation repeats that polarity.
   Encoded: + 0 - 0 0 0 -
5. Input $1$: Last pulse was $V$, which had $-$ polarity. Alternate to $+$.
   Encoded: + 0 - 0 0 0 - +
6. Input $1$: Last pulse was $+$. Alternate to $-$.
   Encoded: + 0 - 0 0 0 - + -
7. Input $0000$: Another substitution.
   Count since the last substitution ($000V$): the previous $V$ has negative polarity, followed by 2 regular pulses ($+$ and $-$).
   This is an EVEN number.
   Pattern: use $B00V$. The $B$ pulse alternates from the last pulse $-$; therefore $B$ is $+$.
   The $V$ polarity repeats $B$, so $V$ is $+$.
   Encoded: + 0 - 0 0 0 - + - + 0 0 +

Final encoded signal: + 0 - 0 0 0 - + - + 0 0 +