cnp3-ebook/principles/reliability

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114 ../../principles/reliability.rst:440

	English The only solution to protect against transmission errors is to add redundancy to the frames that are sent. `Information Theory` defines two mechanisms that can be used to transmit information over a transmission channel affected by random errors. These two mechanisms add redundancy to the transmitted information, to allow the receiver to detect or sometimes even correct transmission errors. A detailed discussion of these mechanisms is outside the scope of this chapter, but it is useful to consider a simple mechanism to understand its operation and its limitations. 570/10000 · 570
115 ../../principles/reliability.rst:442

	English `Information theory` defines `coding schemes`. There are different types of coding schemes, but let us focus on coding schemes that operate on binary strings. A coding scheme is a function that maps information encoded as a string of `m` bits into a string of `n` bits. The simplest coding scheme is the (even) parity coding. This coding scheme takes an `m` bits source string and produces an `m+1` bits coded string where the first `m` bits of the coded string are the bits of the source string and the last bit of the coded string is chosen such that the coded string will always contain an even number of bits set to `1`. For example : 638/10000 · 638
116 ../../principles/reliability.rst:444

	English `1001` is encoded as `10010` 28/10000 · 28
117 ../../principles/reliability.rst:445

	English `1101` is encoded as `11011` 28/10000 · 28
118 ../../principles/reliability.rst:447

	English This parity scheme has been used in some RAMs as well as to encode characters sent over a serial line. It is easy to show that this coding scheme allows the receiver to detect a single transmission error, but it cannot correct it. However, if two or more bits are in error, the receiver may not always be able to detect the error. 330/10000 · 330
119 ../../principles/reliability.rst:449

	English Some coding schemes allow the receiver to correct some transmission errors. For example, consider the coding scheme that encodes each source bit as follows : 157/10000 · 157
120 ../../principles/reliability.rst:451

	English `1` is encoded as `111` 23/10000 · 23
121 ../../principles/reliability.rst:452

	English `0` is encoded as `000` 23/10000 · 23
122 ../../principles/reliability.rst:454

	English For example, consider a sender that sends `111`. If there is one bit in error, the receiver could receive `011` or `101` or `110`. In these three cases, the receiver will decode the received bit pattern as a `1` since it contains a majority of bits set to `1`. If there are two bits in error, the receiver will not be able anymore to recover from the transmission error. 370/10000 · 370
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

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