Editing Orthogonal frequency-division multiplexing (section)

=== Channel coding and interleaving ===
OFDM is invariably used in conjunction with [[channel coding]] ([[forward error correction]]), and almost always uses frequency and/or time [[Bit interleaving|interleaving]].

Frequency (subcarrier) [[Bit interleaving|interleaving]] increases resistance to frequency-selective channel conditions such as [[fading]]. For example, when a part of the channel bandwidth fades, frequency interleaving ensures that the bit errors that would result from those subcarriers in the faded part of the bandwidth are spread out in the bit-stream rather than being concentrated. Similarly, time interleaving ensures that bits that are originally close together in the bit-stream are transmitted far apart in time, thus mitigating against severe fading as would happen when travelling at high speed.

However, time interleaving is of little benefit in slowly fading channels, such as for stationary reception, and frequency interleaving offers little to no benefit for narrowband channels that suffer from flat-fading (where the whole channel bandwidth fades at the same time).

The reason why interleaving is used on OFDM is to attempt to spread the errors out in the bit-stream that is presented to the error correction decoder, because when such decoders are presented with a high concentration of errors the decoder is unable to correct all the bit errors, and a burst of uncorrected errors occurs. A similar design of audio data encoding makes compact disc (CD) playback robust.

A classical type of error correction coding used with OFDM-based systems is [[convolutional code|convolutional coding]], often [[concatenated error correction codes|concatenated]] with [[Reed–Solomon error correction|Reed-Solomon]] coding. Usually, additional interleaving (on top of the time and frequency interleaving mentioned above) in between the two layers of coding is implemented. The choice for Reed-Solomon coding as the outer error correction code is based on the observation that the Viterbi decoder used for inner convolutional decoding produces short error bursts when there is a high concentration of errors, and Reed-Solomon codes are inherently well suited to correcting bursts of errors.

Newer systems, however, usually now adopt near-optimal types of error correction codes that use the turbo decoding principle, where the decoder iterates towards the desired solution. Examples of such error correction coding types include [[turbo code]]s and [[LDPC]] codes, which perform close to the [[Shannon limit]] for the Additive White Gaussian Noise ([[Additive white Gaussian noise|AWGN]]) channel. Some systems that have implemented these codes have concatenated them with either Reed-Solomon (for example on the [[MediaFLO]] system) or [[BCH code]]s (on the [[DVB-S2]] system) to improve upon an [[error floor]] inherent to these codes at high [[signal-to-noise ratio]]s.<ref name="bookMPLC">{{cite book|title= MIMO Power Line Communications: Narrow and Broadband Standards, EMC, and Advanced Processing |series= Devices, Circuits, and Systems |date=February 2014|editor= Berger, Lars T. |editor2=Schwager, Andreas |editor3=Pagani, Pascal |editor4=Schneider, Daniel M|publisher= CRC Press |page=25|doi=10.1201/b16540-1|isbn=978-1-4665-5753-6|chapter= Introduction to Power Line Communication Channel and Noise Characterisation }}</ref>