8b/10b encoding
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Original post：http://en.wikipedia.org/wiki/8B10B
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In telecommunications, 8b/10b is a line code that maps 8-bit symbols to 10-bit symbols to achieve DC-balance and bounded disparity, and yet provide enough state changes to allow reasonable clock recovery. This means that the difference between the count of 1s and 0s in a string of at least 20 bits is no more than 2, and that there are not more than five 1s or 0s in a row. This helps to reduce the demand for the lower bandwidth limit of the channel necessary to transfer the signal.
An 8b/10b code can be implemented in various ways, where the design may focus on specific parameters such as hardware requirements, dc-balance etc. One implementation was designed by K. Odaka for the DAT digital audio recorder.[1] Kees Schouhamer Immink designed an 8b/10b code for the DCC audio recorder.[2] Another implementation was described in 1983 by Al Widmer and Peter Franaszek.[3][4]
Contents1 How it works for the IBM code
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How it works for the IBM code
As the scheme name suggests, 8 bits of data are transmitted as a 10-bit entity called a symbol, or character. The low 5 bit of data are encoded into a 6-bit group (the 5b/6b portion) and the top 3 bits are encoded into a 4-bit group (the 3b/4b portion). These code groups are concatenated together to form the 10-bit symbol that is transmitted on the wire. The data symbols are often referred to as D.x.y where x ranges over 0–31 and y over 0–7. Standards using the 8b/10b encoding also define up to 12 special symbols (or control characters) that can be sent in place of a data symbol. They are often used to indicate start-of-frame, end-of-frame, link idle, skip and similar link-level conditions. At least one of them (i.e. a "comma" symbol) needs to be used to define the alignment of the 10 bit symbols. They are referred to as K.x.y and have different encodings from any of the D.x.y symbols.
Because 8b/10b encoding uses 10-bit symbols to encode 8-bit words, some of the possible 1024 (10 bit, 210) codes can be excluded to grant a run-length limit of 5 consecutive equal bits and grant that the difference of the count of 0s and 1s is no more than 2. Some of the 256 possible 8-bit words can be encoded in two different ways. Using these alternative encodings, the scheme is able to effect long-term DC-balance in the serial data stream. This permits the data stream to be transmitted through a channel with a high-pass characteristic, for example Ethernet's transformer-coupled unshielded twisted pair or optical receivers using automatic gain control.
Encoding tables
Note that in the following tables, for each input byte, A is the least significant bit, and H the most significant. The output gains two extra bits, i and j. The bits are sent low to high: a, b, c, d, e, i, f, g, h, and j; i.e., the 5b/6b code followed by the 3b/4b code. This ensures the uniqueness of the special bit sequence in the comma codes.
The residual effect on the stream to the number of zero and one bits transmitted is maintained as the running disparity (RD) and the effect of slew is balanced by the choice of encoding for following symbols.
The 5b/6b code is a paired disparity code, and so is the 3b/4b code. Each 6- or 4-bit code word has either equal numbers of 0s and 1s (a disparity of 0), or comes in a pair of forms, one with two more 1s than 0s (four 1s and two 0s, or three 1s and one 0, respectively) and one with two less. When a 6- or 4-bit code is used that has a non-zero disparity (count of 1s minus count of 0s; i.e., −2 or +2), the choice of positive or negative disparity encodings must be the one that toggles the running disparity. I.e., the non zero disparity codes alternate.
Running disparity
8b/10b coding is DC-free, meaning that the long-term ratio of 1s and 0s transmitted is exactly 50%. To achieve this, the difference between the number of 1s transmitted and the number of 0s transmitted is always limited to ±2, and at the end of each symbol, it is either +1 or −1. This difference is known as the running disparity (RD).
This scheme needs only two states for running disparity of +1 and −1. It starts at −1.[5]
For each 5b/6b and 3b/4b code with an unequal number of 1s and 0s, there are two bit patterns that can be used to transmit it: one with two more 1 bit and one with all bit inverted and thus two more 0s. Depending on the current running disparity of the signal, the encoding engine selects which of the two possible 6- or 4-bit sequences to send for the given data. Obviously, if the 6- or 4-bit code has equal numbers of 1s and 0s, there is no choice to make, as the disparity would be unchanged, considering the following exceptions. RD is positive at the end of the six-bit sub_block if the six-bit sub-block is 000111, and RD is positive at the end of the four-bit sub_block if the four-bit sub-block is 0011. RD is negative at the end of the six-bit sub_block if the six-bit sub-block is 111000, and RD is negative at the end of the four-bit sub_block if the four-bit sub-block is 1100.
| Previous RD | Disparity of code word | Disparity chosen | Next RD |
|---|---|---|---|
| −1 | 0 | 0 | −1 |
| −1 | ±2 | +2 | +1 |
| +1 | 0 | 0 | +1 |
| +1 | ±2 | −2 | −1 |
5b/6b
| Input | RD = −1 | RD = +1 | Input | RD = −1 | RD = +1 | |||
|---|---|---|---|---|---|---|---|---|
| EDCBA | abcdei | EDCBA | abcdei | |||||
| D.00 | 00000 | 100111 | 011000 | D.16 | 10000 | 011011 | 100100 | |
| D.01 | 00001 | 011101 | 100010 | D.17 | 10001 | 100011 | ||
| D.02 | 00010 | 101101 | 010010 | D.18 | 10010 | 010011 | ||
| D.03 | 00011 | 110001 | D.19 | 10011 | 110010 | |||
| D.04 | 00100 | 110101 | 001010 | D.20 | 10100 | 001011 | ||
| D.05 | 00101 | 101001 | D.21 | 10101 | 101010 | |||
| D.06 | 00110 | 011001 | D.22 | 10110 | 011010 | |||
| D.07 | 00111 | 111000 | 000111 | D.23 † | 10111 | 111010 | 000101 | |
| D.08 | 01000 | 111001 | 000110 | D.24 | 11000 | 110011 | 001100 | |
| D.09 | 01001 | 100101 | D.25 | 11001 | 100110 | |||
| D.10 | 01010 | 010101 | D.26 | 11010 | 010110 | |||
| D.11 | 01011 | 110100 | D.27 † | 11011 | 110110 | 001001 | ||
| D.12 | 01100 | 001101 | D.28 | 11100 | 001110 | |||
| D.13 | 01101 | 101100 | D.29 † | 11101 | 101110 | 010001 | ||
| D.14 | 01110 | 011100 | D.30 † | 11110 | 011110 | 100001 | ||
| D.15 | 01111 | 010111 | 101000 | D.31 | 11111 | 101011 | 010100 | |
| K.28 | 11100 | 001111 | 110000 | |||||
† Same code is used for K.x.7
3b/4b
| Input | RD = −1 | RD = +1 | Input | RD = −1 | RD = +1 | |||
|---|---|---|---|---|---|---|---|---|
| HGF | fghj | HGF | fghj | |||||
| D.x.0 | 000 | 1011 | 0100 | K.x.0 | 000 | 1011 | 0100 | |
| D.x.1 | 001 | 1001 | K.x.1 ‡ | 001 | 0110 | 1001 | ||
| D.x.2 | 010 | 0101 | K.x.2 ‡ | 010 | 1010 | 0101 | ||
| D.x.3 | 011 | 1100 | 0011 | K.x.3 ‡ | 011 | 1100 | 0011 | |
| D.x.4 | 100 | 1101 | 0010 | K.x.4 | 100 | 1101 | 0010 | |
| D.x.5 | 101 | 1010 | K.x.5 ‡ | 101 | 0101 | 1010 | ||
| D.x.6 | 110 | 0110 | K.x.6 ‡ | 110 | 1001 | 0110 | ||
| D.x.P7 † | 111 | 1110 | 0001 | |||||
| D.x.A7 † | 111 | 0111 | 1000 | K.x.7 † | 111 | 0111 | 1000 | |
† For D.x.7, either the Primary (D.x.P7), or the Alternate (D.x.A7) encoding must be selected in order to avoid a run of five consecutive 0s or 1s when combined with the preceding 5b/6b code. Sequences of five identical bits are used in comma codes for synchronization issues. D.x.A7 is used for only x=17, x=18, and x=20 when RD=−1 and for x=11, x=13, and x=14 when RD=+1. With x=23, x=27, x=29, and x=30, the same code forms the control codes K.x.7. Any other x.A7 code can't be used as it would result in chances for misaligned comma sequences.
‡ The alternate encoding for the K.x.y codes with disparity 0 make it possible for only K.28.1, K.28.5, and K.28.7 to be "comma" codes that contain a bit sequence which can't be found elsewhere in the data stream.
Control symbols
The control symbols within 8b/10b are 10b symbols that are valid sequences of bits (no more than six 1s or 0s) but do not have a corresponding 8b data byte. They are used for low-level control functions. For instance, in Fibre Channel, K28.5 is used at the beginning of four-byte sequences (called "Ordered Sets") that perform functions such as Loop Arbitration, Fill Words, Link Resets, etc.
Resulting from the 5b/6b and 3b/4b tables the following 12 control symbols are allowed to be sent:
| Input | RD = −1 | RD = +1 | |||
|---|---|---|---|---|---|
| DEC | HEX | HGF EDCBA | abcdei fghj | abcdei fghj | |
| K.28.0 | 28 | 1C | 000 11100 | 001111 0100 | 110000 1011 |
| K.28.1 † | 60 | 3C | 001 11100 | 001111 1001 | 110000 0110 |
| K.28.2 | 92 | 5C | 010 11100 | 001111 0101 | 110000 1010 |
| K.28.3 | 124 | 7C | 011 11100 | 001111 0011 | 110000 1100 |
| K.28.4 | 156 | 9C | 100 11100 | 001111 0010 | 110000 1101 |
| K.28.5 † | 188 | BC | 101 11100 | 001111 1010 | 110000 0101 |
| K.28.6 | 220 | DC | 110 11100 | 001111 0110 | 110000 1001 |
| K.28.7 ‡ | 252 | FC | 111 11100 | 001111 1000 | 110000 0111 |
| K.23.7 | 247 | F7 | 111 10111 | 111010 1000 | 000101 0111 |
| K.27.7 | 251 | FB | 111 11011 | 110110 1000 | 001001 0111 |
| K.29.7 | 253 | FD | 111 11101 | 101110 1000 | 010001 0111 |
| K.30.7 | 254 | FE | 111 11110 | 011110 1000 | 100001 0111 |
† Within the control symbols, K.28.1, K.28.5, and K.28.7 are "comma symbols". Comma symbols are used for synchronization (finding the alignment of the 8b/10b codes within a bit-stream). If K.28.7 is not used, the unique comma sequences 0011111 or 1100000 cannot be found at any bit position within any combination of normal codes.
‡ If K.28.7 is allowed in the actual coding, a more complex definition of the synchronization pattern than suggested by † needs to be used, as a combination of K.28.7 with several other codes forms a false misaligned comma symbol overlapping the two codes. A sequence of multiple K.28.7 codes is not allowable in any case, as this would result in undetectable misaligned comma symbols.
K.28.7 is the only comma symbol that cannot be the result of a single bit error in the data stream.
Example encoding of D31.1
| Input | RD = −1 | RD = +1 |
|---|---|---|
| HGFEDCBA | abcdei fghj | abcdei fghj |
| 00111111 | 101011 1001 | 010100 1001 |
Technologies that use 8b/10b
After the above mentioned IBM patent expired, the scheme became even more popular and is the default DC-free line code for new standards.
Among the areas in which 8b/10b encoding finds application are
- PCI Express versions prior to 3.0
- IEEE 1394b
- Serial ATA
- SAS
- Fibre Channel
- SSA
- Gigabit Ethernet (except for the twisted pair based 1000Base-T)
- InfiniBand
- XAUI
- Serial RapidIO
- DVB Asynchronous Serial Interface (ASI)
- DisplayPort Main Link
- DVI and HDMI Video Island (Transition Minimized Differential Signaling)
- HyperTransport
- Common Public Radio Interface (CPRI)
- USB 3.0
Fibre Channel
| Fibre Channel | |
|---|---|
| Layer 4. Protocol mapping | |
| LUN masking | |
| Layer 3. Common services | |
| Layer 2. Network | |
| Fibre Channel fabric Fibre Channel zoning Registered State Change Notification |
|
| Layer 1. Data link | |
| Fibre Channel 8B/10B encoding | |
| Layer 0. Physical |
The Fibre Channel FC1 data link layer implements the 8b/10b encoding and decoding of signals.
The Fibre Channel 8B/10B coding scheme is also used in other telecommunications systems. Data is expanded using an algorithm that creates one of two possible 10-bit output values for each input 8-bit value. Each 8-bit input value can map either to a 10-bit output value with odd disparity, or to one with even disparity. This mapping is usually done at the time when parallel input data is converted into a serial output stream for transmission over a fibre channel link. The odd/even selection is done in such a way that a long-term zero disparity between ones and zeroes is maintained. This is often called "DC balancing".
The 8-bit to 10-bit conversion scheme uses only 512 of the possible 1024 output values. Of the remaining 512 unused output values, most contain either too many ones or too many zeroes so are not allowed. However this still leaves enough spare 10-bit odd+even coding pairs to allow for 12 special non-data characters.
The codes that represent the 256 data values are called the data (D) codes. The codes that represent the 12 special non-data characters are called the control (K) codes.
All of the codes can be described by stating 3 octal values. This is done with a naming convention of "Dxx.x" or "Kxx.x".
Example:
- Input Data Bits: ABCDEFGH
- Data is split: ABC DEFGH
- Data is shuffled: DEFGH ABC
Now these bits are converted to decimal in the way they are paired.
Input data
C3 (HEX) = 11000011
= 110 00011
= 00011 110
= 3 6
E 8B/10B = D03.6
Digital audio
Encoding schemes 8b/10b have found a heavy use in digital audio storage applications, namely
- Digital Audio Tape, US Patent 4,456,905, June 1984 by K. Odaka.
- Digital Compact Cassette (DCC), US Patent 4,620,311, October 1986 by Kees Schouhamer Immink.
A differing but related scheme is used for audio CDs and CD-ROMs:
- Compact Disc Eight-to-Fourteen Modulation
Exceptions
For 10 Gigabit Ethernet's 10GBASE-R Physical Medium Dependent (PMD) interfaces, 64b/66b encoding is used. This scheme is considerably different in design to 8b/10b encoding, but was created with similar considerations of DC balance, maximum run length, transition density and electromagnetic emission minimization.
Note that 8b/10b is the encoding scheme, not a specific code. While many applications do use the same code, there exist some incompatible implementations; for example, Transition Minimized Differential Signaling, which also expands 8 bits to 10 bits, but it uses a completely different method to do so.
Notes
- ^ U.S. Patent 4,456,905Method and apparatus for encoding binary data, October 1984.
- ^ U.S. Patent 4,620,311Method of transmitting information, encoding device for use in the method, and decoding device for use in the method, June 1986.
- ^ Al X. Widmer, Peter A. Franaszek (1983). "A DC-Balanced, Partitioned-Block, 8B/10B Transmission Code". IBM Journal of Research and Development 27 (5): 440. http://domino.research.ibm.com/tchjr/journalindex.nsf/0/b4e28be4a69a153585256bfa0067f59a?OpenDocument.
- ^ U.S. Patent 4,486,739Byte oriented DC balanced (0,4) 8B/10B partitioned block transmission code, December 1984.
- ^ Thatcher, Jonathan (1996-04-01). "Thoughts on Gigabit Ethernet Physical". IBM. http://grouper.ieee.org/groups/802/3/z/public/presentations/mar1996/JTtgep.txt. Retrieved 2008-08-17.