02-01-2013, 11:54 AM
Satellite Communication Systems
1Satellite Communication.ppt (Size: 2.14 MB / Downloads: 237)
What is channel coding?
Channel coding:
Transforming signals to improve communications performance by increasing the robustness against channel impairments (noise, interference, fading, ..)
Waveform coding: Transforming waveforms to better waveforms
Structured sequences: Transforming data sequences into better sequences, having structured redundancy.
“Better” in the sense of making the decision process less subject to errors.
Error control techniques
Automatic Repeat reQuest (ARQ)
Full-duplex connection, error detection codes
The receiver sends a feedback to the transmitter, saying that if any error is detected in the received packet or not (Not-Acknowledgement (NACK) and Acknowledgement (ACK), respectively).
The transmitter retransmits the previously sent packet if it receives NACK.
Forward Error Correction (FEC)
Simplex connection, error correction codes
The receiver tries to correct some errors
Hybrid ARQ (ARQ+FEC)
Full-duplex, error detection and correction codes
Channel models
Discrete memory-less channels
Discrete input, discrete output
Binary Symmetric channels
Binary input, binary output
Gaussian channels
Discrete input, continuous output
Representing codes by vectors
Code strength is measured by Hamming distance that tells how different code words are:
Codes are more powerful when their minimum Hamming distance dmin (over all codes in the code family) is large
Hamming distance d(X,Y) is the number of bits that are different between code words
(n,k) codes can be mapped into n-dimensional grid:
Convolutional codes
A Convolutional code is specified by three parameters or where is the coding rate, determining the number of data bits per coded bit.
In practice, usually k=1 is chosen and we assume that from now on.
K is the constraint length of the encoder a where the encoder has K-1 memory elements.
There is different definitions in literatures for constraint length.
Soft and hard decision decoding
In hard decision:
The demodulator makes a firm or hard decision whether one or zero is transmitted and provides no other information for the decoder such that how reliable the decision is.
In Soft decision:
The demodulator provides the decoder with some side information together with the decision. The side information provides the decoder with a measure of confidence for the decision.
Free distance of Convolutional codes
Distance properties:
Since a Convolutional encoder generates codewords with various sizes (as opposite to the block codes), the following approach is used to find the minimum distance between all pairs of codewords:
Since the code is linear, the minimum distance of the code is the minimum distance between each of the codewords and the all-zero codeword.
This is the minimum distance in the set of all arbitrary long paths along the trellis that diverge and remerge to the all-zero path.
It is called the minimum free distance or the free distance of the code, denoted by
Interleaving
Convolutional codes are suitable for memoryless channels with random error events.
Some errors have bursty nature:
Statistical dependence among successive error events (time-correlation) due to the channel memory.
Like errors in multipath fading channels in wireless communications, errors due to the switching noise, …
“Interleaving” makes the channel looks like as a memoryless channel at the decoder.