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BER for coded AWGN channels

The `bercoding`

function returns an upper bound or
approximation of the bit error rate (BER) for coherent BPSK or QPSK modulation over an
additive white Gaussian noise (AWGN) channel for a specified coding type, decoding
decision, code rate, and distance spectrum of the code. The results for binary PSK and
quadrature PSK modulation are the same. This function computes only modulation order 2
or 4 for *M*-ary PSK modulation. For more information, see Analytical Expressions Used in bercoding Function and Bit Error Rate Analysis App.

returns the upper bound of the BER for an the extended (24, 12) Golay code using
hard-decision decoding and coherent BPSK modulation. In accordance with [3], the Golay coding upper bound assumes only the correction of 3-error
patterns. Even though correcting approximately 19% of 4-error patterns is
theoretically possible in practice, most decoders do not have this
capability.`ber`

= bercoding(EbNo,'Golay','hard',24)

specifies a modulation type in addition to any of the previous input argument
combinations. This syntax returns an approximation of the BER for coded AWGN
channels.`ber`

= bercoding(`EbNo`

,`coding`

,___,`modulation`

)

In general, the numerical accuracy for the output BER is limited to approximately two significant digits. The numerical accuracy output by this function is limited by these restrictions.

Approximations in the analysis leading to the closed-form expressions used by the function

Approximations related to the numerical implementation of the expressions

You can configure the **Theoretical** tab in the **Bit
Error Rate Analysis** app to compute theoretical BER values instead of using the
`bercoding`

function.

[1] Proakis, John G. *Digital Communications*.
4th ed. New York: McGraw Hill, 2001.

[2] Frenger, P., P. Orten, and T. Ottosson. “Convolutional Codes with Optimum Distance Spectrum.” *IEEE Communications Letters* 3, no. 11 (November 1999): 317–19. https://doi.org/10.1109/4234.803468.

[3] Odenwalder, J. P. *Error Control Coding
Handbook*, Final Report, LINKABIT Corporation, San Diego, CA: 1976.

[4] Sklar, Bernard. *Digital Communications: Fundamentals
and Applications*. 2nd ed. Upper Saddle River, N.J: Prentice-Hall PTR,
2001.

[5] Ziemer, R. E., and R. L., Peterson.
*Introduction to Digital Communication*. 2nd ed. Prentice Hall,
2001.