CSD 2019: Turbo Product Codes
By Bill Thomson
A new class of correction codes has been developed that is a major
improvement over current error correction coding (ECC) solutions, with
performance approaching the theoretical limit for any error correction
code. These codes are called turbo codes, and have been implemented in both
software and hardware.
High-speed digital communication systems development demands the
optimization of various requirements: data transmission rate, data
reliability, transmission energy, bandwidth, system complexity,
and cost.
ECC helps meet these require- ments cost-effectively. The higher the error
correction code performance, the more flexibility the designer has to
determine the required transmission energy, bandwidth, and system
complexity.
Common codes
Signal-to-noise ratio (SNR) improvement of a communications channel depends
on the error correction code used and the channel’s characteristics.
In 1948, Claude Shannon derived the bound on the error correction
performance for all possible
codes. Unfortunately, his theorem only proves
the existence of codes with this performance. It does not supply a method
for constructing a good code. This limit on ECC performance has been termed
the Shannon limit.
Reed-Solomon (RS) and concatenated Reed-Solomon
Viterbi (RSV) are the most common error correction codes implemented today.
At a bit error rate (BER) of 10
-6
, both code types are at least
2.5 dB to 3.0 dB short of the Shannon limit in an additive white Gaussian
noise (AWGN) channel.
One step forward
Turbo codes represent the next leap forward in error correction. They have
been shown to perform within 1 dB of the Shannon limit at a BER of
10
-6
. Turbo codes break a complex decoding problem down into
simple steps, where each step is repeated until a solution is reached. The
term “turbo code” is often used to refer to turbo convolutional
codes (TCCs) — one form of turbo code. The complexity of convolutional
codes has slowed the development of
low-cost TCC decoders. On the other
hand, another type of turbo code, known as turbo product code (TPC), uses
block codes, solving multiple steps simultaneously, thereby achieving high
data throughput in hardware. TPCs have been implemented in both software
and hardware as a single integrated circuit. TPCs do not suffer from the
error floor at low BERs that have been attributed to other codes. TPCs are
also capable of providing high coding gain, even with high code rates.
Turbo product codes provide 1.5- to
3-dB bit energy-to-noise improvement
over the current standard RS and RSV error correction codes. A 1.5- to 3-dB
performance gain can allow the system developer to reduce transmitter power
and/or bandwidth and still maintain the same BER performance. Conversely, a
1.5- to 3-dB improvement can be used to boost the overall system
performance if transmitter power is not reduced. For example, the use of
TPCs can allow the systems engineer to reduce antenna size, lowering system
cost. When used to provide
improved BER performance, TPCs can also lead to
a clearer image transmission, improv- ed audio, greater range, or better
data integrity. (For more information on TPCs, go to www.aha.com or
www.eccincorp.com.)
Noisy channels
TPCs are applicable where digital data is transmitted over a noisy channel,
or when data is stored on an imperfect medium. TPCs can support the data
rates achieved with other error correction codes, while offering improved
correction capability. They can be used with
high-definition TV, digital
cellular communications, satellite communication systems, optical and
magnetic storage, and microwave point-to-point data links.
TPCs are
moving the practical performance of ECC a major step closer to the Shannon
limit. Current integrated circuit technology and improved algorithms are
making these codes cost-effective for today’s system designs. As with
RS and RSV codes, TPCs will soon find their way into many areas of wired
and wireless communications and data storage.
Bill Thomson is a senior applications engineer at Advanced Hardware
Architectures, Inc. He holds an MSEE from Washington State University. He
can be reached at
bthomson@aha.com.
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