4B3T stands for 4 Binary

Binary numeral system

The binary numeral system, or base-2 number system, represents numeric values using two symbols, 0 and 1. More specifically, the usual base-2 system is a positional notation with a radix of 2...

 3 (three) Ternary

Ternary signal

In telecommunication, a ternary signal is a signal that can assume, at any given instant, one of three states or significant conditions, such as power level, phase position, pulse duration, or frequency....

, a line encoding scheme used for ISDN BRI interface. 4B3T represents four binary bits using three pulses.

It uses three states:

• + (positive pulse),
• 0 (no pulse), and
• − (negative pulse).

This means we have 2⁴ = 16 input combinations to represent, using 3³ = 27 output combinations. 000 is not used to avoid long periods without a transition. To achieve an overall zero DC bias

DC bias

When describing a periodic function in the frequency domain, the DC bias, DC component, DC offset, or DC coefficient is the mean value of the waveform...

, 6 triplets are used which have no DC component (+0−, +−0, 0+−, 0−+, −+0, −0+), and the remaining 20 are grouped into 10 pairs with differing disparity (e.g. ++− and −−+). When transmitting, the DC bias is tracked and a combination chosen that has a DC component of the opposite sign to the running total.

This mapping from 4 bits to 3 ternary states is given in a table known as Modified Monitoring State 43 (MMS43).
A competing encoding technique, used for the ISDN basic rate interface

Basic rate interface

Basic Rate Interface is an Integrated Services Digital Network configuration intended primarily for use in subscriber lines similar to those that have long been used for plain old telephone service...

 where 4B3T is not used, is 2B1Q

2B1Q

Two-binary, one-quaternary is a physical layer encoding used for Integrated Services Digital Network Basic Rate Interface implementations...

.

The sync sequence used is the 11-symbol Barker code, +++−−−+−−+− or its reverse, −+−−+−−−+++.

Encoding table

Each 4-bit input group is encoded as a 3-symbol group (transmitted left to right) from the following table.
Encoding requires keeping track of the accumulated DC offset, the number of + pulses minus the number of − pulses in all preceding groups. The starting value is arbitrary; here we use the values 1 through 4, although −1.5, −0.5, +0.5 and +1.5 is another possibility.

MMS 43 coding table

Input	| Accumulated DC offset
	1	| 2	| 3	| 4
0000	+ 0 +   (+2)	0−0 (−1)
0001	0 − +   (+0)
0010	+ − 0   (+0)
0011	0 0 +   (+1)			− − 0   (−2)
0100	− + 0   (+0)
0101	0 + +   (+2)	− 0 0   (−1)
0110	− + +   (+1)		− − +   (−1)
0111	− 0 +   (+0)
1000	+ 0 0   (+1)			0 − −   (−2)
1001	+ − +   (+1)
1010	+ + −   (+1)		+ − −   (−1)
1011	+ 0 −   (+0)
1100	+ + +   (+3)	− + −   (−1)
1101	0 + 0   (+1)			− 0 −   (−2)
1110	0 + −   (+0)
1111	+ + 0   (+2)	0 0 −   (−1)

Decoding table

Decoding is simpler, as the decoder does not need to keep track of the encoder state, although doing so allows greater error detection. The 000 triplet is not a legal encoded sequence, but is typically decoded as binary 0000.

Ternary	Binary		Ternary	Binary		Ternary	Binary
0 0 0			− 0 0	0101		+ − −	1010
+ 0 +	0000		− + +	0110		+ 0 −	1011
0 − 0	0000		− − +	0110		+ + +	1100
0 − +	0001		− 0 +	0111		− + −	1100
+ − 0	0010		+ 0 0	1000		0 + 0	1101
0 0 +	0011		0 − −	1000		− 0 −	1101
− − 0	0011		+ − +	1001		0 + −	1110
− + 0	0100		− − −	1001		+ + 0	1111
0 + +	0101		+ + −	1010		0 0 −	1111

See also

Other line codes that have 3 states:

• hybrid ternary code
  Hybrid ternary code
  The hybrid ternary line code operates on a hybrid principle that combines the binary non-return-to-zero-level and the polar return-to-zero codes and thus it is called H-ternary....
  
  
• bipolar encoding
  Bipolar encoding
  In telecommunication, bipolar encoding is a type of line code . A duobinary signal is such an encoding.- Advantages :...
  
  
• MLT-3 encoding
  MLT-3 encoding
  MLT-3 encoding is a line code that uses three voltage levels...
  
  
• B3ZS