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Math Help - Derive Markov chain probabilities

  1. #1
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    Derive Markov chain probabilities

    Hi all.

    I'm using a two states Markov chain to simulate a wireless channel at byte level. In the state Good the byte is well transmitted with probability 1 and in state Bad the byte is bad transmitted with probability 1. The parameters are:

    Transitions =
    [Pgg Pgb]
    [Pbg Pbb]

    Emission_probabilities =
    [1 0]
    [0 1]

    The BER is the probability of arriving to the system and find it in the Bad state: BER = Pgb/(Pgb+Pbg).
    The mean burst-error length is: Lb = 1/Pbg

    What I want to do is to derive the markov chain transistion probabilites at packet level from the markov model at byte level. Actually I don't know if the packet level transistions can be modeled with another 2-states-markov chain, but I used hmmestimate in matlab and the results were almost close.

    A packet is Good transmitted if all its bytes are Good transmitted too. A packet is bad transmitted if anyone of its bytes are bad transmitted.

    Does anyone knows the solution or where I can find it?

    Thanks in advance!
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Interlaver View Post
    Hi all.

    I'm using a two states Markov chain to simulate a wireless channel at byte level. In the state Good the byte is well transmitted with probability 1 and in state Bad the byte is bad transmitted with probability 1. The parameters are:

    Transitions =
    [Pgg Pgb]
    [Pbg Pbb]

    Emission_probabilities =
    [1 0]
    [0 1]

    The BER is the probability of arriving to the system and find it in the Bad state: BER = Pgb/(Pgb+Pbg).
    The mean burst-error length is: Lb = 1/Pbg

    What I want to do is to derive the markov chain transistion probabilites at packet level from the markov model at byte level. Actually I don't know if the packet level transistions can be modeled with another 2-states-markov chain, but I used hmmestimate in matlab and the results were almost close.

    A packet is Good transmitted if all its bytes are Good transmitted too. A packet is bad transmitted if anyone of its bytes are bad transmitted.

    Does anyone knows the solution or where I can find it?

    Thanks in advance!
    The way you have defined BER leaves this undefined (0/0), and Lb is infinite. Is that what you really intend?

    Also I think you have not explained your model in sufficient detail.

    CB
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  3. #3
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    The model I use is called Gilbert-Elliot channel and its wide used to simulate a wireless channel. The idea is that errors occurs in bursts rather than in a uniform way. A channel error means that the byte has not been correctly transmitted (the recived byte is different from the sended).

    In this model there are two states: Good and Bad. In the Good state the byte is transmitted correctly and in the Bad state no. Pgb is the probability of going to the Bad state from the Good, which is desirable to be low. Pbg is the probability of going to the Good state from the Bad, which is desirable to be high. This model is a two states markov chain.

    However what I want to study is the same channel at packet level. A packet is a group of bytes and is well transmitted if ALL its bytes are well transmitted too.

    For example supose this channel error sequence at byte level. 0 means a good byte transmission and 1 means a bad byte transmission:

    00000000000000000111110000000000000000001111111111 1000000000000

    Using Packets of for example 7 bytes, the same channel observed a packet level is

    001101110

    What I wonder is how to derivate the Pgb_packet and Pbg_packet from Pgb and Pbg if is possible. Actually I don't really know if the channel at packet level can be modeled as a gilbert-elliot channel but I think is possible.

    I simulated a Gilbert-Elliot channel at byte level in Matlab and then i computed the sequence at packet level. I calcultated the Pgb_packet and Pbg_packet (doing the mean over all the state transistions) and the results where almost close to the ones that matlab provides using the function "hmmestimate" which estimates this parameters for a markov chain.
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by Interlaver View Post
    The model I use is called Gilbert-Elliot channel and its wide used to simulate a wireless channel. The idea is that errors occurs in bursts rather than in a uniform way. A channel error means that the byte has not been correctly transmitted (the recived byte is different from the sended).

    In this model there are two states: Good and Bad. In the Good state the byte is transmitted correctly and in the Bad state no. Pgb is the probability of going to the Bad state from the Good, which is desirable to be low. Pbg is the probability of going to the Good state from the Bad, which is desirable to be high. This model is a two states markov chain.

    However what I want to study is the same channel at packet level. A packet is a group of bytes and is well transmitted if ALL its bytes are well transmitted too.

    For example supose this channel error sequence at byte level. 0 means a good byte transmission and 1 means a bad byte transmission:

    00000000000000000111110000000000000000001111111111 1000000000000

    Using Packets of for example 7 bytes, the same channel observed a packet level is

    001101110

    What I wonder is how to derivate the Pgb_packet and Pbg_packet from Pgb and Pbg if is possible. Actually I don't really know if the channel at packet level can be modeled as a gilbert-elliot channel but I think is possible.

    I simulated a Gilbert-Elliot channel at byte level in Matlab and then i computed the sequence at packet level. I calcultated the Pgb_packet and Pbg_packet (doing the mean over all the state transistions) and the results where almost close to the ones that matlab provides using the function "hmmestimate" which estimates this parameters for a markov chain.
    I don't think this will work since the probability of a bad packet being followed by a bad packet obviously depends on whether the first bad packet was preceded by a good or bad packet.


    CB
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