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4.1: Encoding and Framing

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  • A typical serial line is ultimately a stream of bits, not bytes. How do we identify byte boundaries? This is made slightly more complicated by the fact that, beneath the logical level of the serial line, we generally have to avoid transmitting long runs of identical bits, because the receiver may simply lose count; this is the clock synchronization problem (sometimes called the clock recovery problem). This means that, one way or another, we cannot always just send the desired bits sequentially; for example, extra bits are often inserted to break up long runs. Exactly how we do this is the encoding mechanism.

    Once we have settled the transmission of bits, the next step is to determine how the receiver identifies the start of each new packet. Ethernet packets are separated by physical gaps, but for most other link mechanisms packets are sent end-to-end, with no breaks. How we tell when one packet stops and the next begins is the framing problem.

    To summarize:

    • encoding: correctly recognizing all the bits in a stream
    • framing: correctly recognizing packet boundaries

    These are related, though not the same.

    For long (multi-kilometer) electrical serial lines, in addition to the clock-related serial-line requirements we also want the average voltage to be zero; that is, we want no DC component. We will mostly concern ourselves here, however, only with lines short enough for this not to be a major concern.

  • 4.1.1 NRZ

    NRZ (Non-Return to Zero) is perhaps the simplest encoding; it corresponds to direct bit-by-bit transmission of the 0’s and 1’s in the data. We have two signal levels, lo and hi, we set the signal to one or the other of these depending on whether the data bit is 0 or 1, as in the diagram below. Note that in the diagram the signal bits have been aligned with the start of the pulse representing that signal value.


    NRZ replaces an earlier RZ (Return to Zero) encoding, in which hi and lo corresponded to +1 and -1, and between each pair of pulses corresponding to consecutive bits there was a brief return to the 0 level.

    One drawback to NRZ is that we cannot distinguish between 0-bits and a signal that is simply idle. However, the more serious problem is the lack of synchronization: during long runs of 0’s or long runs of 1’s, the receiver can “lose count”, eg if the receiver’s clock is running a little fast or slow. The receiver’s clock can and does resynchronize whenever there is a transition from one level to the other. However, suppose bits are sent at one per µs, the sender sends five 1-bits in a row, and the receiver’s clock is running 10% fast. The signal sent is a 5-µs hi pulse, but when the pulse ends the receiver’s clock reads 5.5 µs due to the clock speedup. Should this represent five 1-bits or six 1-bits?

  • 4.1.2 NRZI

    An alternative that helps here (though not obviously at first) is NRZI, or NRZ Inverted. In this encoding, we represent a 0-bit as no change, and a 1-bit as a transition from lo to hi or hi to lo:


    Now there is a signal transition aligned above every 1-bit; a 0-bit is represented by the lack of a transition. This solves the synchronization problem for runs of 1-bits, but does nothing to address runs of 0-bits. However, NRZI can be combined with techniques to minimize runs of 0-bits, such as 4B/5B (below).

  • 4.1.3 Manchester

    Manchester encoding sends the data stream using NRZI, with the addition of a clock transition between each pair of consecutive data bits. This means that the signaling rate is now double the data rate, eg 20 MHz for 10Mbps Ethernet (which does use Manchester encoding). The signaling is as if we doubled the bandwidth and inserted a 1-bit between each pair of consecutive data bits, removing this extra bit at the receiver:


    All these transitions mean that the longest the clock has to “count” is 1 bit-time; clock synchronization is essentially solved, at the expense of the doubled signaling rate.

  • 4.1.4 4B/5B

    In 4B/5B encoding, for each 4-bit “nybble” of data we actually transmit a designated 5-bit symbol, or code, selected to have “enough” 1-bits. A symbol in this sense is a digital or analog transmission unit that decodes to a set of data bits; the data bits are not transmitted individually. (The transmission of symbols rather than individual bits is nearly universal for high-performance links, including all forms of Ethernet faster than 10Mbps and all Wi-Fi links.)

    Specifically, every 5-bit symbol used by 4B/5B has at most one leading 0-bit and at most two trailing 0-bits. The 5-bit symbols corresponding to the data are then sent with NRZI, where runs of 1’s are safe. Note that the worst-case run of 0-bits has length three. Note also that the signaling rate here is 1.25 times the data rate. 4B/5B is used in 100-Mbps Ethernet, 2.2 100 Mbps (Fast) Ethernet. The mapping between 4-bit data values and 5-bit symbols is fixed by the 4B/5B standard:

















































    There are more than sixteen possible symbols; this allows for some symbols to be used for signaling rather than data. IDLE, HALT, START, END and RESET are shown above, though there are others. These can be used to include control and status information without fear of confusion with the data. Some combinations of control symbols do lead to up to four 0-bits in sequence; HALT and RESET have two leading 0-bits.

    10-Mbps and 100-Mbps Ethernet pads short packets up to the minimum packet size with 0-bytes, meaning that the next protocol layer has to be able to distinguish between padding and actual 0-byte data. Although 100-Mbps Ethernet uses 4B/5B encoding, it does not make use of special non-data symbols for packet padding. Gigabit Ethernet uses PAM-5 encoding (2.3 Gigabit Ethernet), and does use special non-data symbols (inserted by the hardware) to pad packets; there is thus no ambiguity at the receiving end as to where the data bytes ended.

    The choice of 5-bit symbols for 4B/5B is in principle arbitrary; note however that for data from 0100 to 1101 we simply insert a 1 in the fourth position, and in the last two we insert a 0 in the fourth position. The first four symbols (those with the most zeroes) follow no obvious pattern, though.

  • 4.1.5 Framing

    How does a receiver tell when one packet stops and the next one begins, to keep them from running together? We have already seen the following techniques for addressing this framing problem: determining where packets end:

    • Interpacket gaps (as in Ethernet)
    • 4B/5B and special bit patterns

    Putting a length field in the header would also work, in principle, but seems not to be widely used. One problem with this technique is that restoring order after desynchronization can be difficult.

    There is considerable overlap of framing with encoding; for example, the existence of non-data bit patterns in 4B/5B is due to an attempt to solve the encoding problem; these special patterns can also be used as unambiguous frame delimiters.

  • HDLC

    HDLC (High-level Data Link Control) is a general link-level packet format used for a number of applications, including Point-to-Point Protocol (PPP) (which in turn is used for PPPoE – PPP over Ethernet – which is how a great many Internet subscribers connect to their ISP), and Frame Relay, still used as the low-level protocol for delivering IP packets to many sites via telecommunications lines. HDLC supports the following two methods for frame separation:

    • HDLC over asynchronous links: byte stuffing
    • HDLC over synchronous links: bit stuffing

    The basic encapsulation format for HDLC packets is to begin and end each frame with the byte 0x7E, or, in binary, 0111 1110. The problem is that this byte may occur in the data as well; we must make sure we don’t misinterpret such a data byte as the end of the frame.

    Asynchronous serial lines are those with some sort of start/stop indication, typically between bytes; such lines tend to be slower. Over this kind of line, HDLC uses the byte 0x7D as an escape character. Any data bytes of 0x7D and 0x7E are escaped by preceding them with an additional 0x7D. (Actually, they are transmitted as 0x7D followed by (original_byte xor 0x20).) This strategy is fundamentally the same as that used by C-programming-language character strings: the string delimiter is and the escape character is \. Any occurrences of or \ within the string are escaped by preceding them with \.

    Over synchronous serial lines (typically faster than asynchronous), HDLC generally uses bit stuffing. The underlying bit encoding involves, say, the reverse of NRZI, in which transitions denote 0-bits and lack of transitions denote 1-bits. This means that long runs of 1’s are now the problem and runs of 0’s are safe.

    Whenever five consecutive 1-bits appear in the data, eg 011111, a 0-bit is then inserted, or “stuffed”, by the transmitting hardware (regardless of whether or not the next data bit is also a 1). The HDLC frame byte of 0x7E = 0111 1110 thus can never appear as encoded data, because it contains six 1-bits in a row. If we had 0x7E in the data, it would be transmitted as 0111 11010.

    The HDLC receiver knows that

    • six 1-bits in a row marks the end of the packet
    • when five 1-bits in a row are seen, followed by a 0-bit, the 0-bit is removed


    Data: 011110 0111110 01111110
    Sent as: 011110 01111100 011111010 (stuffed bits in bold)

    Note that bit stuffing is used by HDLC to solve two unrelated problems: the synchronization problem where long runs of the same bit cause the receiver to lose count, and the framing problem, where the transmitted bit pattern 0111 1110 now represents a flag that can never be mistaken for a data byte.

  • B8ZS

    While insertion of an occasional extra bit or byte is no problem for data delivery, it is anathema to voice engineers; extra bits upset the precise 64 kbps DS-0 rate. As a result, long telecom lines prefer encodings that, like 4B/5B, do not introduce timing fluctuations. Very long (electrical) lines also tend to require encodings that guarantee a long-term average voltage level of 0 (versus 0.5 if half the bits are 1 v and half are 0 v in NRZ); that is, the signal must have no DC component.

    The AMI (Alternate Mark Inversion) technique eliminates the DC component by using three voltage levels, nominally +1, 0 and -1; this ternary encoding is also known as bipolar. Zero bits are encoded by the 0 voltage, while 1-bits take on alternating values of +1 and -1 volts. Thus, the bits 011101 might be encoded as 0,+1,-1,+1,0,-1, or, more compactly, 0+−+0−. Over a long run, the +1’s and the −1’s cancel out.

    Plain AMI still has synchronization problems with long runs of 0-bits. The solution used on North American T1 lines (1.544 Mbps) is known as B8ZS, for bipolar with 8-zero substitution. The sender replaces any run of 8 zero bits with a special bit-pattern, either 000+−0−+ or 000−+0+−. To decide which, the sender checks to see if the previous 1-bit sent was +1 or −1; if the former, the first pattern is substituted, if the latter then the second pattern is substituted. Either way, this leads to two instances of violation of the rule that consecutive 1-bits have opposite sign. For example, if the previous bit were +, the receiver sees


    This double-violation is the clue to the receiver that the special pattern is to be removed and replaced with the original eight 0-bits.