8b/10b encoding

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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 counts of ones and zeros in a string of at least 20 bits is no more than two, and that there are not more than five ones or zeros 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] The IBM implementation was described in 1983 by Al Widmer and Peter Franaszek.[3][4]

How it works for the IBM code[edit]

As the scheme name suggests, eight bits of data are transmitted as a 10-bit entity called a symbol, or character. The low five bits of data are encoded into a 6-bit group (the 5b/6b portion) and the top three 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 zeros and ones is no more than two. Some of the 256 possible 8-bit words can be encoded in two different ways. Using these alternative encodings, the scheme is able to affect 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[edit]

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 zeros and ones (a disparity of zero), or comes in a pair of forms, one with two more zeros than ones (four ones and two zeros, or three ones and one zero, respectively) and one with two less. When a 6- or 4-bit code is used that has a non-zero disparity (count of ones minus count of zeros; i.e., −2 or +2), the choice of positive or negative disparity encodings must be the one that toggles the running disparity. In other words, the non zero disparity codes alternate.

Running disparity[edit]

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.

Rules for running disparity
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[edit]

5b/6b code
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[edit]

3b/4b code
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[edit]

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:

Control symbols
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[edit]

D31.1 for both running disparity cases
Input RD = −1 RD = +1
HGFEDCBA abcdei fghj abcdei fghj
00111111 101011 1001 010100 1001

Technologies that use 8b/10b[edit]

After the above mentioned IBM patent expired, the scheme became even more popular and was chosen as a DC-free line code for several communication technologies.

Among the areas in which 8b/10b encoding finds application are the following:

Fibre Channel (4GFC and 8GFC variants only)[edit]

Main article: Fibre Channel

The FC-0 standard defines what encoding scheme is to be used (8b/10b or 64b/66b) in a Fibre Channel system[7] – higher speed variants typically use 64b/66b to optimize bandwidth efficiency (since bandwidth overhead is 20% in 8b/10b versus approximately 3% (~ 2/66) in 64b/66b systems). Thus, 8b/10b encoding is used for 4GFC and 8GFC variants; for 10GFC and 16GFC variants, it is 64b/66b.[8] The Fibre Channel FC1 data link layer is then responsible for implementing 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[edit]

Encoding schemes 8b/10b have found a heavy use in digital audio storage applications, namely

A differing but related scheme is used for audio CDs and CD-ROMs:

Alternatives[edit]

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.

64b/66b encoding, introduced for 10-gigabit Ethernet's 10GBASE-R Physical Medium Dependent (PMD) interfaces, is a lower-overhead alternative to 10b/8b encoding, having a 2-bit overhead per 64 bits (instead of 8 bits) of encoded data. This scheme is considerably different in design from 8b/10b encoding, and does not explicitly guarantee DC balance, short run length, and transition density (these features are achieved statistically via scrambling).

References[edit]

  1. ^ U.S. Patent 4,456,905Method and apparatus for encoding binary data, October 1984.
  2. ^ 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.
  3. ^ 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. 
  4. ^ U.S. Patent 4,486,739Byte oriented DC balanced (0,4) 8B/10B partitioned block transmission code, December 1984.
  5. ^ Thatcher, Jonathan (1996-04-01). "Thoughts on Gigabit Ethernet Physical". IBM. Retrieved 2008-08-17. 
  6. ^ "Physical Layer Specifications". Mipi.org. MIPI Alliance. Retrieved 2014-04-20. 
  7. ^ Fibre Channel Framing and Signaling - 3 (FC-FS-3) Rev 1.1 Sections 5.2.1 and 5.3.1 [1]
  8. ^ FIBRE CHANNEL Physical Interface-5 (FC-PI-5) REV 6.10 Section 5.7 [2]

External links[edit]