cnp3-ebook/principles/reliability

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123 ../../principles/reliability.rst:456

	English This simple coding scheme forces the sender to transmit three bits for each source bit. However, it allows the receiver to correct single bit errors. More advanced coding systems that allow recovering from errors are used in several types of physical layers. 258/10000 · 258
124 ../../principles/reliability.rst:458

	English Besides framing, datalink layers also include mechanisms to detect and sometimes even recover from transmission errors. To allow a receiver to notice transmission errors, a sender must add some redundant information as an `error detection` code to the frame sent. This `error detection` code is computed by the sender on the frame that it transmits. When the receiver receives a frame with an error detection code, it recomputes it and verifies whether the received `error detection code` matches the computed `error detection code`. If they match, the frame is considered to be valid. Many error detection schemes exist and entire books have been written on the subject. A detailed discussion of these techniques is outside the scope of this book, and we will only discuss some examples to illustrate the key principles. 821/10000 · 821
125 ../../principles/reliability.rst:460

	English To understand `error detection codes`, let us consider two devices that exchange bit strings containing `N` bits. To allow the receiver to detect a transmission error, the sender converts each string of `N` bits into a string of `N+r` bits. Usually, the `r` redundant bits are added at the beginning or the end of the transmitted bit string, but some techniques interleave redundant bits with the original bits. An `error detection code` can be defined as a function that computes the `r` redundant bits corresponding to each string of `N` bits. The simplest error detection code is the parity bit. There are two types of parity schemes : even and odd parity. With the `even` (resp. `odd`) parity scheme, the redundant bit is chosen so that an even (resp. odd) number of bits are set to `1` in the transmitted bit string of `N+r` bits. The receiver can easily recompute the parity of each received bit string and discard the strings with an invalid parity. The parity scheme is often used when 7-bit characters are exchanged. In this case, the eighth bit is often a parity bit. The table below shows the parity bits that are computed for bit strings containing three bits. 1172/10000 · 1172
126 ../../principles/reliability.rst:463

	English 3 bits string 13/10000 · 13
127 ../../principles/reliability.rst:463

	English Odd parity 10/10000 · 10
128 ../../principles/reliability.rst:463

	English Even parity 11/10000 · 11
129 ../../principles/reliability.rst:465 • ../../principles/reliability.rst:482

	English 000 3/10000 · 3
130 ../../principles/reliability.rst:465 • ../../principles/reliability.rst:466 • ../../principles/reliability.rst:467 • ../../principles/reliability.rst:468 • ../../principles/reliability.rst:469 • ../../principles/reliability.rst:470 • ../../principles/reliability.rst:471 • ../../principles/reliability.rst:472 • ../../principles/reliability.rst:486 • ../../principles/reliability.rst:487 • ../../principles/reliability.rst:488 • ../../principles/reliability.rst:489

	English 1 1/10000 · 1
131 ../../principles/reliability.rst:465 • ../../principles/reliability.rst:466 • ../../principles/reliability.rst:467 • ../../principles/reliability.rst:468 • ../../principles/reliability.rst:469 • ../../principles/reliability.rst:470 • ../../principles/reliability.rst:471 • ../../principles/reliability.rst:472 • ../../principles/reliability.rst:482 • ../../principles/reliability.rst:483 • ../../principles/reliability.rst:484 • ../../principles/reliability.rst:485

	English 0 1/10000 · 1
132 ../../principles/reliability.rst:466 • ../../principles/reliability.rst:483

	English 001 3/10000 · 3
133 ../../principles/reliability.rst:467 • ../../principles/reliability.rst:484

	English 010 3/10000 · 3
134 ../../principles/reliability.rst:468 • ../../principles/reliability.rst:485

	English 100 3/10000 · 3
135 ../../principles/reliability.rst:469 • ../../principles/reliability.rst:486

	English 111 3/10000 · 3
136 ../../principles/reliability.rst:470 • ../../principles/reliability.rst:487

	English 110 3/10000 · 3
137 ../../principles/reliability.rst:471 • ../../principles/reliability.rst:488

	English 101 3/10000 · 3
138 ../../principles/reliability.rst:472 • ../../principles/reliability.rst:489

	English 011 3/10000 · 3
139 ../../principles/reliability.rst:475

	English The parity bit allows a receiver to detect transmission errors that have affected a single bit among the transmitted `N+r` bits. If there are two or more bits in error, the receiver may not necessarily be able to detect the transmission error. More powerful error detection schemes have been defined. The Cyclical Redundancy Checks (CRC) are widely used in datalink layer protocols. An N-bits CRC can detect all transmission errors affecting a burst of less than N bits in the transmitted frame and all transmission errors that affect an odd number of bits. Additional details about CRCs may be found in [Williams1993]_. 620/10000 · 620
140 ../../principles/reliability.rst:477

	English It is also possible to design a code that allows the receiver to correct transmission errors. The simplest `error correction code` is the triple modular redundancy (TMR). To transmit a bit set to `1` (resp. `0`), the sender transmits `111` (resp. `000`). When there are no transmission errors, the receiver can decode `111` as `1`. If transmission errors have affected a single bit, the receiver performs majority voting as shown in the table below. This scheme allows the receiver to correct all transmission errors that affect a single bit. 542/10000 · 542
141 ../../principles/reliability.rst:480

	English Received bits 13/10000 · 13
142 ../../principles/reliability.rst:480

	English Decoded bit 11/10000 · 11

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