Channel code

When channel coding (including channel coding ) is called in communication engineering method to protect digital data for transmission over channels impaired by adding redundancy against transmission errors.

The mathematical basis for the channel coding provides the coding theory.

To distinguish the channel coding of the source code, which redundancy is reduced and the line code, which performs a spectral adaptation to the requirements of the transmission channel.

  • 2.1 source code
  • 2.2 channel codes
  • 2.3 Line Codes

Method

Channel coding adds the data to the input of a transmission channel redundancy and decodes the data to its output. If the additional information only point to an error and require a retransmission of the data, it is called backward error correction. Meets the redundancy information to correct the error, it is a forward error correction. An efficient channel coding increases the signal -to-noise ratio for bit error rate unchanged. Depending on the channel coding process, the code gain of several dB.

An essential characteristic of a channel code is its (code ) code rate, the number of symbols at the input of the encoder ( information symbols ), and the number at the output ( code symbols). Thus, information symbols are mapped to code symbols. A small rate (large ) means a higher proportion of the code symbols of the transmitted symbols, which is a smaller data transmission rate. Typically, a channel code to correct a lower code rate more errors than a comparable channel code with high code rate - so it's the trade-off between data rate and error correction capability possible.

Code concatenation

Through clever concatenating codes (eg turbo codes ), the correction capability of the resulting concatenated code can be much higher than that of the individual codes ( component codes ).

Dotting

With puncturing means the targeted strike individual code symbols so that the number of transmitted code symbols to be reduced from on. Thus results for the punctured code a higher rate. Dotting allows to use the same encoder / decoder pair for codes of different rates.

Encodings

Source code

Example of source code: Huffman code

Channel codes

Knowing the types of errors that occur in a transmission channel, one can construct various codes that may well less frequent types of errors to correct the frequent types of errors, so good. The following figure shows an overview of commonly used code classes.

  • Block codes
  • Ungerboeck code (also known as trellis coded modulation called )
  • Hamming code ( Perfect Code )
  • Reed-Solomon code (such as used in certain RAID systems )
  • Fire Code
  • BCH code
  • Golay code ( Perfect Code )
  • Low- density parity -check code
  • Convolutional codes Turbo code is known as a two-, three - or multi-dimensional general concatenation of different channel codes with multiple repeats ( feedback). The multi-dimensional entanglement of single base channel code such as a Hamming code, better overall results than conventional convolution codes can best be achieved. Turbo codes are among those channel codes which the theoretical limit of the Shannon limit come closest.
  • Viterbi code

Line codes

Example of a line code: Manchester coding

Examples

  • Channel error depending on source coding
  • For backward error correction
  • Example Rückwärts-/Vorwärtsfehlerkorrektur
  • Example, forward error correction
  • As GSM
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