4B3T

4B3T, which stands for 4 (four) Binary 3 (three) Ternary, is a line encoding scheme used for ISDN PRI interface. 4B3T represents four binary bits using three pulses.

Description

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. 4B3T uses a paired disparity code to achieve an overall zero DC bias: six 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 three 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 where 4B3T is not used, is 2B1Q.

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)			− − −   (−3)
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	N/A		− 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
• bipolar encoding
• MLT-3 encoding
• B3ZS