# 64b/66b encoding

In data networking and transmission, **64b/66b** is a line code that transforms 64-bit data to 66-bit line code to provide enough state changes to allow reasonable clock recovery and facilitate alignment of the data stream at the receiver. It was defined by the IEEE 802.3 working group as part of the IEEE 802.3ae-2002 amendment which introduced 10 Gbit/s Ethernet.

The overhead of the 64b/66b encoding is 3.125%, which is considerably less than the 25% overhead of the previously used 8b/10b encoding scheme. At the time 64b/66b was deployed, it allowed 10 Gb Ethernet to be transmitted with the same lasers used by SONET OC-192, rather than requiring 12.5 Gbit/s lasers, which were not expected to become available for several years.

The overhead can be reduced further by doubling the block size to produce **128b/130b** encoding, as used by PCIe 3.0, and a very similar variant is the **128b/132b** encoding used by USB 3.1.

## Function

As the scheme name suggests, 64 bits of data are transmitted as a 66-bit entity.

The 66 bit entity is made by prefixing one of two possible two-bit preambles to the 64 bits to be transmitted.

- If the preamble is 01
_{2}, the 64 bits are entirely data. - If the preamble is 10
_{2}, an eight-bit type field follows, plus 56 bits of control information and/or data. - The preambles 00
_{2}and 11_{2}are not used, and generate an error if seen.

The use of the 01_{2} and 10_{2} preambles guarantees a bit transition every 66 bits, which means that a continuous stream of 0s or 1s cannot be valid data. It also allows easier clock/timer synchronization, as a transition must be seen every 66 bits.

The complete payload (consisting of either 64 data bits, or an 8-bit type and 56 data bits) is then scrambled using a self-synchronous scrambler function, with the intention of ensuring that a relatively even distribution of 1s and 0s are normally found in the transmitted data. The intention is not to encrypt the data, but to give the transmitted data useful engineering properties. The scrambler does not provide an absolute guarantee that output data will never have a long run-length of 0s or all 1s or other undesirable properties, but instead allows strong statistical bounds to be put on the probability of such events. Practical designs will choose system parameters such that a bit-error due to long run-lengths is vanishingly unlikely. This method is different from the codebook based approach of 8b/10b encoding.

The encoding and scrambling are normally done entirely in hardware, the scrambling using a linear feedback shift register. Upper layers of the software stack need not be aware that the link layer is using this code.

## Properties and application

64b/66b's design goals are clock recovery, stream alignment, DC balance, transition density and run length. Unlike 8b/10b which guarantees strict bounds on DC balance, transition density and run length, 64b/66b provides statistical bounds on these properties.

### Run length

Most clock recovery circuits designed for SONET OC-192 and 64b/66b are specified to tolerate an 80-bit run length. Such a run cannot occur in 64b/66b because transitions are guaranteed at 66 bit intervals, and in fact long runs are very unlikely. Although it is theoretically possible for a random data pattern to align with the scrambler state and produce a long run of 65 zeroes or 65 ones, the probability of such an event is equal to flipping a fair coin and having it come up in the same state 64 times in a row. At 10 Gigabits per second, the expected event rate of a 66-bit block with a 65 bit run-length, assuming random data, is 66x2^{64}/(2x10^{10}) seconds, or about once every 1900 years.

The run length statistics may get worse if the data consists of chosen specifically patterns, instead of being random. An earlier scrambler used in Packet over SONET/SDH (RFC 1619, 1994) had a short polynomial with only 7 bits of internal state which allowed a malicious attacker to create a Denial-of-service attack by transmitting patterns in all 2^{7}-1 states, one of which was guaranteed to desynchronize the clock recovery circuits. This vulnerability was kept secret until the scrambler length was increased to 43 bits (RFC 2615, 1999) making it impossible for a malicious attacker to jam the system with a short sequence.

64b/66b avoided this vulnerability by using a scrambling polynomial with enough random internal state (58 bits) so that a dedicated attacker using a crafted Ethernet packet can only create a 64 bit run-length in the scrambler output once in about 29 years.^{[1]}^{:11–13} This creates 66-bit blocks containing 65-bit runs at a rate similar to using random data.

### DC balance

The DC balance of 64b/66b is not absolutely bounded. However, it can be shown that the scrambler output closely approximates a sequence of random binary bits. Passing such a sequence through an AC-coupled circuit produces a baseline wander noise that follows a Gaussian distribution, and the impact on the system error rate can be statistically quantified. In practice, a modest coupling capacitor value of 1 nF in a 100 Ω system is sufficient to guarantee that a DC drift of more than 2.5% will occur less often than once per 10^{22} bits (about 31,700 years at 10Gbit/s). [1]:15–16

### Hamming distance

10Gbit Ethernet has a strict charter requiring a Mean Time to False Packet Acceptance (MTTFPA) to be on the order of 1 billion years for a single operating link. To achieve this at normal bit error rates requires at least a four bit hamming distance protection for all packet data. In other words, all combinations of four randomly spaced bit-flips within a packet boundary must be detected and result in an invalidated packet. Several strategies were combined to achieve the 4-bit hamming distance for 64b/66b packets: 1) strong type fields were chosen with 4-bit hamming distance, 2) the scrambler polynomial was chosen to be compatible with the CRC-32 used for packet protection and 3) protocol violations adjacent to the packet boundaries are required to invalidate the packet. The combination of CRC-32 and the chosen scrambler polynomial were evaluated by exhaustively enumerating all 4-bit bit error patterns for all possible packet sizes with an optimized C program.

### Observations

The main contribution of 64b/66b is the observation that the deterministic runlength and transition density of 8b/10b are not always worth a 25% code overhead, and that solid robust systems could be designed using statistically bounded methods. At some point, the real risk of a nuclear war, meteoric impact, or power supply failure dominate the reliability of both 8b/10b and 64b/66b systems.

### Variations

The Interlaken protocol improves the DC balance further by trading off more coding bits. Its 64b/67b encoding extends 64b/66b with explicit DC balancing. This may be beneficial for some applications, such as a using smaller on-chip coupling capacitors.

PCI Express 3.0 introduced 128b/130b encoding, which is similar to 64b/66b but has a payload of 128 bits instead of 64 bits, and uses a different scrambling polynomial: *x*^{23} + *x*^{21} + *x*^{16} + *x*^{8} + *x*^{5} + *x*^{2} + 1 . It is also not self-synchronous and so requires explicit synchronization of seed values, in contrast with 64b/66b.

USB 3.1 uses 128b/132b encoding, which is identical to 128b/130b, but duplicates each of the preamble bits to reduce the risk of undetected errors there.

## Technologies that use 64b/66b encoding

- 10 Gigabit Ethernet (most varieties)
- Fibre Channel 10GFC and 16GFC
- 100 Gigabit Ethernet
- 10G-EPON, 10 Gbit/s Ethernet Passive Optical Network
- Aurora, from Xilinx
- InfiniBand
- Thunderbolt
- Common Public Radio Interface

## Technologies that use 128b/13xb encoding

## References

- ↑ R.C. Walker; R. Dugan (18–20 January 2000). "64b/66b low-overhead coding proposal for serial links" (PDF). IEEE 802.3 High Speed Study Group.

## External links

- Note that this is the original proposal to the IEEE, and some changes were made for the final, agreed standard. The circuit diagram for the 58 bit scrambling polynomial described in the proposal is identical to the one adopted in the standard. However, the proposal numbers the registers in reverse order such that the x
^{58}+x^{19}+1 polynomial in the proposal is the same as the one labelled x^{58}+x^{39}+1 in the standard.

- US Patent/US6650638: Decoding method and decoder for 64b/66b coded packetized serial data
- US Patent/US6718491: Coding method and coder for packetized serial data with low overhead
- US Patent/US7055073: Coding method for coding packetized serial data with low overhead
- PatentView/EP1133123 Software Patent: 64b/66b decoding, for packetized serial data
- ERROR CORRECTION ON 64/66 BIT ENCODED LINKS
- Introduction to 10 Gigabit 64b/66b (Clause 49)
- A reference design by Xilinx on 64b/66b encoding and scrambling
- Aurora 64B66B IP core using 64b/66b encoding