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Reed Solomon Encoder/Decoder on the StarCore™ SC140/SC1400 Cores, With Extended Examples

Freescale Semiconductor 

Basics of Forward Error Correction (FEC)

1 Basics of Forward Error Correction (FEC)

In an ideal communication scheme, the information received is identical to the source transmission. However, in a

typical real communication scheme, the information passes through a noisy communication channel to the receiver.

The information received at the destination is likely to contain errors due to the channel noise. The acceptable level

of transmitted signal corruption (error level) depends on the application. Voice communication, for example, is

relatively error tolerant. However, the prospect of occasionally losing a digit in communications of financial data

highlights the need for error-control mechanisms.

In 1948, C.E. Shannon proved in his classic paper [1] that a communications channel can be made arbitrarily

reliable by encoding the information so that a fixed fraction of the channel is used for redundant information. In the

years that followed, there was a rapid development in designing FEC schemes. Today, a variety of effective coding

algorithms are widely used. FEC offers a number of benefits:

• Data integrity is critical in the design of most digital communication systems and all storage devices.

Along with the design trend toward increasing bandwidths and data volumes, there is a drive to

decrease the allowed error rates. FEC enables a system to achieve high data reliability.

• FEC yields low error rates and performance gains for systems in which other options, such as

increasing the transmitted power or installing noise-limiting components, are too expensive or

impractical.

• System costs may be reduced by eliminating an expensive or sensitive component and compensating

for the lost performance by a suitable FEC scheme.

For an overview of FEC schemes, consult [2] and [3].

FEC adds carefully designed information to the transmitted data and uses this redundant information to reconstruct

the potentially corrupted data. Figure 1 depicts a typical communications scheme.

Input Source

Source Encoder FEC Encoder Modulation

Noise

Channel

Destination

Source Decoder FEC Decoder Demodulation

Figure 1. FEC Communications System

The two main type of error-control codes used in communications systems are as follows:

• Convolutional codes. Each bit depends on the current bit as well as on a number of previous bits. In

this sense, the convolutional code has a memory. The most common scheme for decoding

convolutional codes is the Viterbi algorithm.

• Block codes. A bitstream is divided into message blocks of fixed length called frames. The valid code-

word block is formed from the message bitstream by adding a proper redundant part. Each code word

is independent of the previous one, so the code is memory-less.

Reed Solomon Encoder/Decoder on the StarCore™ SC140/SC1400 Cores, With Extended Examples, Rev. 1

2

Freescale Semiconductor

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