10 Channel Coding and Interleaving

Independent from the modulation method used the bit error rate (BER) in general can be reduced by increasing the ratio ES/N0, i.e. the increase of transmit power (Es ~ Ps) or the decrease of the noise temperature (N0 ~ Tsys) by filtering and low noise amplifiers. Both measures in practice have limits, e.g. costs, increasing size of elements or needed current. That is why coding with error detection or even error correction and interleaving are used. By adding bits with certain procedures it is possible to reduce the BER after decoding.

Depending on the type of service coding methods with different effort are used which can be divided in two groups:

  • Automatic repeat request (ARQ)
With a simple error detecting code, it is detected if an erroneous bit has been received. If this is the case a repeated transmission is requested (cf. Figure 10-7). Therefore, the receiver sends a negative acknowledgment (NAK) to the transmitter and causes a repeated transmission of the data block. For correct reception a positive acknowledgement (ACK) is sent. If the transmitter does not receive any acknowledgment in a certain period, the transmission automatically is repeated. Because of the time needed for acknowledgement and retransmission this type of error detection is not suited for real time applications.

  • Forward error correction (FEC)
With this method the receiver cannot only detect errors but also correct them avoiding acknowledgment and retransmission. That is why more complex coding methods are used that detect errors in the received signal and their position to allow correction. The transmission time is not enlarged.

There are three different types of errors (cf. Figure 10-1):

     1) Bit error, if a single bit in the data stream is distorted,
     2) Symbol error, if a complete symbol cannot be detected correctly, and
     3) Burst error, if errors occur over multiple bits or bytes.
In this figure there is a row of attached rectangles symbolizing the transmitted bits. Every eight bits are marked as a byte. A second row symbolizes the received bits. Here the third, twelfth, sixteenth to eighteenth, twentieth, twenty-fourth to twenty-eights, thirty-fifth and thirty-seventh to thirty-ninth bits are marked in gray. Bits eight, twelve and twenty are marked as bit errors, bits 16 to 18 and 24 to 28 are indicated as burst errors, as well as the combination of bits 16 to 18 plus 20. Byte 5 with errors at 35 and 37 to 39 is indicated as symbol error.
Figure 10-1: Types of errors.

A „channel without memory“, i.e. a channel were bit errors are statistically independent, with additive white Gaussian noise (AWGN) cause statistically independent single errors (bit or symbol errors) that can be significantly reduced by the use of error correcting codes (block or convolutional codes). These codes are no longer efficient if a „channel with memory“ shows connected errors, so called burst errors. 

An example for a „channel with memory“ is the extremely time variant mobile radio channel with signal fading caused by multipath propagation with reflections extremely fluctuating in time. Deep signal drops because of multipath propagation or shadowing (attenuation) can affect the transmitted signal in a way that it drops below the noise level for a considerable moment in time so that connected transmission errors occur. To circumvent these burst errors, i.e. to make a channel memory less, so called code spreading techniques (interleaving) are used. For this purpose, at the transmitter the data stream from the external encoder is scrambled in a way that successive bits from the code words are transferred to separated positions. Then they appear as statistically independent from each other and can be removed by suited error correcting codes. Therefore, codes are used that are suited to the channel and the errors it exhibits (single bit errors, symbol errors, short or long burst errors).
The figure starts with an arrow labeled source followed by a series of blocks interconnected with arrows in the direction to the next block. The blocks are: external coder, interleaver, internal coder, channel with bit and burst errors. At this block another arrow labeled noise, fading arrives. Then the chain continuous with internal decoder, deinterleaver, and external decoder, from which an arrow labeled sink departs.
Figure 10-2: Channel coding and interleaving.

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