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Principles of Mobile Communication pp 397–447Cite as

Error Control Coding

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Abstract

Channel coding and interleaving techniques have long been used for combating noise, interference, jamming, fading, and other channel impairments. The basic idea of channel coding is to introduce controlled redundancy into the transmitted signals that is subsequently exploited at the receiver for error correction. There are many different types of error correcting codes, but historically they have been classified into block codes and convolutional/trellis codes. This chapter first starts with an introduction to block codes and space-time block codes. This is followed by a introduction to convolutional codes, and decoding algorithms for convolutional codes, including the Viterbi algorithm and BCJR algorithm. The chapter then introduces trellis-coded modulation, followed the performance analysis of convolutional and trellis codes on additive white Gaussian noise (AWGN) channels. Block and convolutional interleavers are discussed that are useful for coding on fading channels. This is followed by a consideration of the design and performance analysis of trellis codes on interleaved flat fading channels. Afterwards, the performance of space-time codes and the decoding of space-time codes is considered. Finally, the chapter wraps up with a treatment of parallel and serial turbo codes.

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Notes

  1. 1.

    Here, complex low-pass vector notation is used.

  2. 2.

    The received symbol energy-to-noise ratio is γ s  = R c γ b .

  3. 3.

    The parallel concatenation of more than two component codes is possible, but only two component codes are considered for simplicity.

  4. 4.

    It is important to realize that A d is not equal to a d (in our earlier discussion of convolutional codes), since the turbo codewords can consist of multiple error events.

  5. 5.

    The case of large k is not of interest because the probability of many bad mappings is extremely small and, therefore, does not contribute significantly to the mean of the distribution.

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  1. Georgia Institute of Technology, Atlanta, GA, USA

    Gordon L. Stüber

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Stüber, G.L. (2017). Error Control Coding. In: Principles of Mobile Communication. Springer, Cham. https://doi.org/10.1007/978-3-319-55615-4_8

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  • DOI: https://doi.org/10.1007/978-3-319-55615-4_8

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