Channel Coding

Channel Coding

Channel coding has been used in digital cellular handsets and base stations for the past
10 years as a mechanism for improving transmission quality in a band-limited, noiselimited
Rayleigh faded channel. Channel encoding adds bits to the source coded data
calculated from the source coded data. The decoder uses these extra bits to detect and
correct errors. Errors are detected when the actual transmitted redundancy value fails
to match the redundancy value calculated from the transmitted data.
Two code types are used:
Block codes. Segment the message into blocks adding a parity check number,
which is a product of the information bits contained in the block.
Convolutional codes. Also known as tree codes, the encoder has memory and
the output code words depend on the current bit value and adjacent bits held
within the register.
Block codes are good for detecting bursty errors, and convolutional codes work best
with evenly distributed errors. Interleaving is used to help randomize error distribution
to ensure convolutional encoders/decoders deliver coding gain. If an error burst
lasts longer than the interleaving depth, the convolutional decoder will suffer from
error extension, making matters worse. This will hopefully be detected by the block
code parity check. The voice, image, or video sample can be discarded and the prior
sample reused. Figure 1.12 shows a simple convolutional encoder.
Each time an information bit arrives at the front end of the encoder, a branch code
word is produced. As the bit moves through the code register, it influences subsequent
branch word outputs. The objective is to increase the distance between 0s and 1s. The
memory action enables the decoder to construct and evaluate a multiple decision
process on the recovered bits. This weighted analysis provides coding gain. These
decoders are commonly described as maximum likelihood decoders. Figure 1.13 shows
how coding gain is achieved in a GSM vocoder (encoder/decoder).

A20-ms speech sample is described as a 260-bit word, which effectively contains the
speech sample frequency coefficients. The 260 bits are split into Class 1 bits, which
have parity bits added and are then convolutionally encoded. Note the 1/2 encoder
doubles the number of bits�"2 bits out for every 1 bit in. Class 2 bits are uncoded. In the
decoder, coded bits pass through the convolutional decoder. If the burst errors are
longer than the interleaving depth (40 ms in GSM), the block coded parity check
detects a parity error, the speech sample is discarded, and the prior sample is reused.
Increasing K, the length of the convolutional encoder, increases resilience against
burst errors and delivers additional coding gain (K = 7 typically delivers 5.2 dB gain,
K = 9 delivers 6 dB of gain) but requires an exponential increase in decoder complexity
(trading instructions per second against receive sensitivity). This coding gain depends
on having sufficient interleaving depth available on the air interface. Interleaving
depth in 3GPP1 (IMT2000DS/W-CDMA) is a variable: a minimum of 10 ms, a maximum
of 80 ms.
Increasing the interleaving depth from 10 to 80 ms increases coding gain by just
under 1 dB for slow mobility users (3 km/h), by just over 1 dB for medium mobility
users (20 km/h). However, increasing interleaving depth increases delay. Figure 1.14
shows how interleaving is implemented in GSM. Each 456-bit block is split into 8 × 57
sub-bit blocks and interleaved over eight time slots and eight frames (approximately
40 ms). This is an irreducible delay. You cannot reduce it by using faster processors,
because the delay is a function of the fixed frame rate.

An alternative is that careful implementation of fast power control, using the 1500 Hz
power control loop specified in 3GPP1, makes it possible to follow the fast fading envelope,
which was already partly tamed by the coherence bandwidth of the 5 MHz channel.
If the fast fading can be counteracted by the power control loop, the Rayleigh
channel becomes a Gaussian channel in which burst errors no longer occur. Fast power
control in a 5 MHz channel can therefore, theoretically, deliver additional coding gain at
least for medium-mobility users (up to 20 km/h) without the need for deep interleaving.
This shows the intricate and rather complex relationship between source rate, convolutional
encoding (the choice of 1/2 or 2/3 encoders, for example), interleaving
depth and coding gain, which in turn determines uplink and downlink sensitivity. All
the preceding parameters can be dynamically tuned to optimize handset performance. 29