Forward error correction

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Forward error correction

1 Introduction
2 Convolutional Code with Viterbi
- 2.1 r=1/3 k=3 Conv Code
- 2.2 r=1/2 k=7 Conv Code
3 Reed-Solomon Code
4 Turbo
5 Hardware Devices
6 Books
7 Documents

[edit] Introduction

In telecommunication, forward error correction (FEC) is a system of error control for data transmission, whereby the sender adds redundant data to its messages, which allows the receiver to detect and correct errors (within some bound) without the need to ask the sender for additional data. The advantage of forward error correction is that retransmission of data can often be avoided, at the cost of higher bandwidth requirements on average, and is therefore applied in situations where retransmissions are relatively costly or impossible. See Wikipedia: Forward Error Correction for more details.

The reason for FEC is the high probability of data bits received which are in error. Any bit flip during transmissions ruins the information. Any chance of correcting the error bits allows the system to perform the same for a longer distance or send more information with out corruption. The following graph shows the probability of receiving bits in error. Notice the small chance of receiving a "110" when a "0" bit was transmitted.

Different block codes and their associated Eb/No graph.

When FEC is used, the energy per bit Eb to have the same bit error rate (BER) is alot less.

Since microcontrollers with around 40MHz speeds are used on board the satellite for any data processing, careful consideration must be taken in order to implement an FEC that is efficient. The algorithm needs to be able to perform a significant level of error correcting without taking too much time. If either are lacking, then the design is undesirable for space communication.

Since the link between stations improves, a gain can be calculated. The FEC gain, usually known as a coding gain, is generally defined as the following:

See the FEC Log File for current CAPE research.

[edit] Convolutional Code with Viterbi

Some convolutional codes in space

Convolutional codes with Viterbi algorithms are one option for implementing FEC. However, on the receive end, path (data) history must be stored somewhere in memory. In memory, a trellis is drawn of every possible path the information could take, which is eventually narrowed down to only the most probable paths. Therfore, significant memory must be allocated to storing the data which has been received before decoding can begin. See Wikipedia: Convolutional Code and Wikipedia: Viterbi Algorithm for more details.

[edit] r=1/3 k=3 Conv Code

This actually is one of the most simple of convolutional codes. Beginners can relatively easily build this in software to get the basic understanding of encoding.

[edit] r=1/2 k=7 Conv Code

This is the popular "Voyager" code, first used extensively on the Voyager space missions. Today, this code is popular among many systems including the AO-40 spacecraft. See Wikipedia: AO-40.