4B3T

The principle of forming 4B3T code

4B3T (4 Binary 3 Ternary, when 4 binary characters are transmitted using 3 ternary characters) - one of the methods of linear coding ^[1] ( physical coding , channel coding, pulse-code modulation ^[1] ^[2] , signal manipulation ). A method of converting data presented in digital form, in the form of a signal, with the aim of transmitting data through a physical communication channel (such as optical fiber , twisted pair , coaxial cable , infrared radiation ). The signal at the output of the encoder, according to the code 4B3T, is three-level, i.e. at the output of the encoder, a signal with three potential levels is formed. The code is generated, for example, according to the MMS43 coding table. Every four bit combinations are represented by a three-level (with three different potentials) combination.

Content

Coding Table

Each input sequence is represented by 4 data bits. Total incoming combinations consisting of 4 bits can be represented $2^{4}=16$ ${\ displaystyle 2 ^ {4} = 16}$ ${\ displaystyle 2 ^ {4} = 16}$ . When using a three-level data transmission system, represented by 3 significant intervals, you can imagine a total $3^{3}=27$ ${\ displaystyle 3 ^ {3} = 27}$ ${\ displaystyle 3 ^ {3} = 27}$ various combinations.

MMS43 Encoding Table ^[3]
entrance	Accumulated DC offset
entrance	one	2	3	four
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)

To encode, for example, sequence 1111, you can, in principle, use either of two options. But 4B3T has an interesting feature - it allows you to keep the average current through the communication channel approximately zero: if many positive trits are transmitted, it starts to transmit many negative ones. It is done like this.

We set the accumulated DC offset variable to some initial value (for example, 2). Having encoded 1111 as 00−, we subtract from adder 1, we get 1. And the next four 1111 will be encoded ++ 0, and the adder will take the value 3.

Decoding Table

The decoding table is as follows:

Ternary code	Binary code	Ternary code	Binary code	Ternary code	Binary code
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

Upon receipt at the input device of the receiver, the data is fed to the decoding device, according to the decoding table, a four-bit sequence of source data is generated. A combination of 000 is not valid.

Example

On the transmitting side is transmitted information presented in digital form, in binary code: 0100101010011101

According to the 4B3T encoding rule, every 4 bits of data are represented by 3 potential levels (see MMS43 encoding table):

The combination "0100" is represented as "- + 0", ie: lower potential level (-), upper potential level (+) and average potential level (0)
The combination "1010" is represented as "++ -", i.e.: upper potential level (+), upper potential level (+) and lower potential level (-)
The combination "1001" is represented as "+ - +", that is: the upper potential level (-), the lower potential level (+) and the upper potential level (0)
The combination "1101" is represented as "0 + 0", ie: average potential level (0), upper potential level (+) and average potential level (0)

Those. at the output of the encoder, a signal is generated with the potentials: "- + 0 ++ - + - + 0 + 0" (see figure)

On the receiving side, data is restored according to the decoding table, i.e. upon receipt of a combination of potential changes "- + 0 ++ - + - + 0 + 0" the decoder converts:

The combination "- + 0" is converted to data: "0100"
The combination "++ -" is converted to data: "1010"
The combination "+ - +" is converted to data: "1001"
The combination "0 + 0" is converted to data: "1101"

Accordingly, the receiver receives the data: "0100101010011101" and restores the information presented in digital form.

Benefits

Data rate per cycle is higher than NRZ
Code redundancy compared to binary coding (three ternary characters give 27 combinations, and four binary 16 combinations)
Redundant combinations can be used for special functions. ^[four]
It can maintain the average current through the communication channel in the region of zero: if a lot of “+” trits have passed through the channel, the code starts sending more “-” trits there, and vice versa.
In this mode, it transfers no more than four trit with the same value, this simplifies synchronization.

Weaknesses

Not self-synchronizing

Scope

ISDN BRI

Notes

↑ ¹ ² Berlin A. N. Switching in communication systems and networks. - M .: Eco-Trends, 2006 .-- 344 p. - ISBN 5-88405-073-9 .
↑ Dansmore, Brad, Scanner, Toby. Handbook of telecommunications technology. - M .: Williams, 2004 .-- 640 p. - ISBN 5-8459-0562-1 .
↑ "Wired Communications T-SMINTO 4B3T Second Gen. Modular ISDN NT (Ordinary)" (PDF) (Data sheet). Version 1.1. Infineon November 2001. PEF 80902. (neopr.) .
↑ Goldstein Boris Solomonovich. Access network protocols. - BHV-Petersburg. - 2005.

Literature

Wired Communications T-SMINTO 4B3T Second Gen. Modular ISDN NT (Ordinary) ". Version 1.1. Infineon. November 2001. PEF 80902
Discrete messaging: Textbook for universities / V.P. Shuvalov, N.V. Zakharchenko, V.O. Shvartsman and others; Ed. V.P. Shuvalova. - M .: Radio and communications, —1990-464 ISBN: 5-256-00852-8

[:0-1] ¹ ² Berlin A. N. Switching in communication systems and networks. - M .: Eco-Trends, 2006 .-- 344 p. - ISBN 5-88405-073-9 .

[2] Dansmore, Brad, Scanner, Toby. Handbook of telecommunications technology. - M .: Williams, 2004 .-- 640 p. - ISBN 5-8459-0562-1 .

[3] "Wired Communications T-SMINTO 4B3T Second Gen. Modular ISDN NT (Ordinary)" (PDF) (Data sheet). Version 1.1. Infineon November 2001. PEF 80902. (neopr.) .

[4] Goldstein Boris Solomonovich. Access network protocols. - BHV-Petersburg. - 2005.