Digital channels and packet networks can be modelled as a discrete two-state Elliot-Gilbert model, as shown in Figure E.1.

Figure E.1: An Elliot-Gilbert two-level error model

When the model is at the bad state, b, a bit is corrupted or a packet is received erroneously, and can be regarded as lost. The model is run for every bit (or packet) to be transmitted, and the average number of times that the model stays at the bad position is the average bit error rate, or packet loss rate, *P.* Consequently, the average number of times it stays at the good state is 1 - *P.* In the following, we show how the average bit error or packet loss rate is related to the transition probabilities *α* and β. We analyse on packet loss rate, and the same procedure can be used for the bit error rate. The model has also been accepted by the ITU-T for the evaluation of ATM networks. [1]

At each run of the model, a packet is lost in two ways. First, before the run it was at the bad state, but after the run it is also at the bad state. Second, it was in a good state, but after the run is at the bad state. Thus the probability of being at the bad

state (loss), *P,* is:

P = *P*(1 - α)+(1 - *P*)*β*

and rearranging the equation, the average packet loss rate *P* is:

(E.1) |

[1]ITU SGXV working party XV/I, Experts Group for ATM video coding, working document AVC-205, January 1992

A burst of lost packets is defined as a sequence of consecutive packets, all of which are marked as lost. The burst starts when a packet is lost after one or more packets have not been lost. Thus, the probability of a burst length of one is being at the bad state and then going to the good state. This probability is α. Similarly, the probability of a burst length of two is the probability of being at the bad state, but coming to this state at the next run. This probability is (1 - *α*)*α.* Thus in general the probability of a burst length of *k* packets is to be at the bad state for *k -* 1 times and the next run to go to the good state, which is (1 - α)(*k*--1)*α.*

The mean bust length *B* is then:

*B* = *α* + 2(1 - *α*)*α* + 3(1 *- α*)2*α*+4(l - *α)3*α *+ ...*+ *k(*1 *-α*)*k*-1*α + *...

summing this series, leads to:

(E.2) |

Rearranging eqn. E.2 gives:

(E.3) |

and rearranging eqn. E.1 and substituting for *α* from eqn. E.3 gives:

(E.4) |

For a given mean packet loss rate *P* and average burst length *B,* the transition probabilities *α* and *β* can be calculated from eqns E.3 and E.4. The model is run for as many packets as are to be served, and at each run it is decided whether the packet should be marked as lost or not. To do this, each run is equivalent to running a random number between 0 and 1, and if it is less than the relevant transition probabilities, the packet is marked lost, otherwise it is received safely.

A pseudo code to perform packet loss is given below:

PreviousPacketLost=FALSE; Readln(P,B); α=(1/B);β=P/(B× (1-P)); FOR (number of packets to be transmitted) BEGIN CASE PreviousPacketLoss OF TRUE: IFrandom<1-α THEN Packet Loss =TRUE; ELSE Packetloss=FALSE; FALSE: IFrandom<β THEN PacketLoss=TRUE; ELSE Packetloss=FALSE; END

Standard Codecs Image Compression to Advanced Video Coding

- History of Video Coding
- Video Basics
- Principles of Video Compression
- Subband and Wavelet
- Coding of Still Pictures (JPEG and JPEG2000)
- Coding for Videoconferencing (H.261)
- Coding of Moving Pictures for Digital Storage Media (MPEG-1)
- Coding of High Quality Moving Pictures (MPEG-2)
- Video Coding for Low Bit Rate Communications (H.263)
- Content-Based Video Coding (MPEG-4)
- Content Description, Search and Delivery (MPEG-7 and MPEG-21)
- Appendix A A C Program for the Fast Discrete Cosine Transform
- Appendix B Huffman Tables for the DC and AC Coefficients of the JPEG Baseline Encoder
- Appendix C Huffman Tables for Quad Tree Shape Coding
- Appendix D Frequency Tables for the CAE Encoding of Binary Shapes
- Appendix E Channel Error/Packet Loss Model
- Appendix F Solutions to the Problems
- Appendix G Glossary of Acronyms

Standard Codecs: Image Compression to Advanced Video Coding (IET Telecommunications Series)

ISBN: 0852967101

EAN: 2147483647

EAN: 2147483647

Year: 2005

Pages: 148

Pages: 148

Authors: M. Ghanbari

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