Differential Encoder/Decoder in GSM

Hi All,

I am looking at the Differential Encoder used in GSM. The 3GPP TS45.002
specifies that the encoder is as follows:
T(i) = D(i) xor D(i-1) where D(i) is information symbol and inputs to the
encoder, T(i) is the output.

Correspondingly at the receiver side, I am going to use a differential
decoder as below:
D(i) = R(i) xor D(i-1) where R(i) suppose to be the received bits and the
inputs to the decoder. Ideally R(i) equals T(i).

A question comes into the decoder now. One error bit in R(i) will cause
all subsequent D(i) wrong. Is it true for GSM receiver? I don't think so,
since it will cause high BER. Is there any other method that I shall use
to avoid this issue?


thank you.

On Apr 9, 9:54 am, "richard_zhang" <hardhear...@yahoo.com.cn> wrote:
> I am looking at the Differential Encoder used in GSM. The 3GPP TS45.002
> specifies that the encoder is as follows:
> T(i) = D(i) xor D(i-1) where D(i) is information symbol and inputs to the
> encoder, T(i) is the output.

hmm...as i recall, in differential encoding,
T(i) = T(i-1) xor D(i)

> Correspondingly at the receiver side, I am going to use a differential
> decoder as below:
> D(i) = R(i) xor D(i-1) where R(i) suppose to be the received bits and the
> inputs to the decoder. Ideally R(i) equals T(i).

i think it should be,
D(i) = R(i) xor R(i-1)


> A question comes into the decoder now. One error bit in R(i) will cause
> all subsequent D(i) wrong. Is it true for GSM receiver? I don't think so,
> since it will cause high BER. Is there any other method that I shall use
> to avoid this issue?

per your problem statement, the error will propagate. However, i think
that your problem
statement is incorrect.
Per the equations which i put forward, due to differential encoding
each decision error
during coherent demodulation will cause two bits to be in error.

> thank you.

Hope this helps (ofcourse, i do not have the specs with me).

Thanks,
Krishna
~ blogs @ http://www.dsplog.com

richard_zhang wrote:

> I am looking at the Differential Encoder used in GSM. The 3GPP TS45.002
> specifies that the encoder is as follows:
> T(i) = D(i) xor D(i-1) where D(i) is information symbol and inputs to the
> encoder, T(i) is the output.

> Correspondingly at the receiver side, I am going to use a differential
> decoder as below:
> D(i) = R(i) xor D(i-1) where R(i) suppose to be the received bits and the
> inputs to the decoder. Ideally R(i) equals T(i).
(snip)

Are you sure you have R and T right?  If you do it the other way
around it doesn't have that problem.

T(i) = D(i) xor T(i-1)
and
D(i) = R(i) xor R(i-1)

In this case, a received bit in error will cause two data bits
to be wrong.

Others use much more complicated scramblers, but with the same symmetry.

-- glen

>richard_zhang wrote:
>
>> I am looking at the Differential Encoder used in GSM. The 3GPP
TS45.002
>> specifies that the encoder is as follows:
>> T(i) = D(i) xor D(i-1) where D(i) is information symbol and inputs to
the
>> encoder, T(i) is the output.
>
>> Correspondingly at the receiver side, I am going to use a differential
>> decoder as below:
>> D(i) = R(i) xor D(i-1) where R(i) suppose to be the received bits and
the
>> inputs to the decoder. Ideally R(i) equals T(i).
>(snip)
>
>Are you sure you have R and T right?  If you do it the other way
>around it doesn't have that problem.
>
>T(i) = D(i) xor T(i-1)
>and
>D(i) = R(i) xor R(i-1)
>
>In this case, a received bit in error will cause two data bits
>to be wrong.
>
>Others use much more complicated scramblers, but with the same symmetry.
>
>-- glen



Krishna and Glen, Thank you for the reply.

The equation for differential encoder that I posted previously is from
3GPP specifications, please refer to the spec of 3GPP TS45.004 and the
version I am reading is V6.0.0 (2005-01).

I understand, if the encoder equation is T(i) = D(i) xor T(i-1), then the
error propagation issue will not happen at the decoder. This is what I
feel confused, why 3GPP uses the encoder of T(i) = D(i) xor D(i-1).

Am I making anything wrong ????????

thanks

richard_zhang wrote:

> Hi All,
> 
> I am looking at the Differential Encoder used in GSM. The 3GPP TS45.002
> specifies that the encoder is as follows:
> T(i) = D(i) xor D(i-1) where D(i) is information symbol and inputs to the
> encoder, T(i) is the output.
> 
> Correspondingly at the receiver side, I am going to use a differential
> decoder as below:
> D(i) = R(i) xor D(i-1) where R(i) suppose to be the received bits and the
> inputs to the decoder. Ideally R(i) equals T(i).
>
> A question comes into the decoder now. One error bit in R(i) will cause
> all subsequent D(i) wrong. Is it true for GSM receiver? I don't think so,
> since it will cause high BER. Is there any other method that I shall use
> to avoid this issue?

You have the encoder and the decoder vice versa.

Should be:

Encoder: T[i] = X[i] xor T[i-1]
Decoder: X[i] = R[i] xor R[i-1]


Vladimir Vassilevsky
DSP and Mixed Signal Design Consultant
http://www.abvolt.com

>
>
>richard_zhang wrote:
>
>> Hi All,
>> 
>> I am looking at the Differential Encoder used in GSM. The 3GPP
TS45.002
>> specifies that the encoder is as follows:
>> T(i) = D(i) xor D(i-1) where D(i) is information symbol and inputs to
the
>> encoder, T(i) is the output.
>> 
>> Correspondingly at the receiver side, I am going to use a differential
>> decoder as below:
>> D(i) = R(i) xor D(i-1) where R(i) suppose to be the received bits and
the
>> inputs to the decoder. Ideally R(i) equals T(i).
>>
>> A question comes into the decoder now. One error bit in R(i) will
cause
>> all subsequent D(i) wrong. Is it true for GSM receiver? I don't think
so,
>> since it will cause high BER. Is there any other method that I shall
use
>> to avoid this issue?
>
>You have the encoder and the decoder vice versa.
>
>Should be:
>
>Encoder: T[i] = X[i] xor T[i-1]
>Decoder: X[i] = R[i] xor R[i-1]
>
>
>Vladimir Vassilevsky
>DSP and Mixed Signal Design Consultant
>http://www.abvolt.com
>

Hi Vladimir, thanks for the reply. Please refer to the 3GPP specification
I mentioned previously and you will find that encoder/decoder equation you
put here is not the one used in GSM. 

richard_zhang wrote:


>>
>>You have the encoder and the decoder vice versa.
>>
>>Should be:
>>
>>Encoder: T[i] = X[i] xor T[i-1]
>>Decoder: X[i] = R[i] xor R[i-1]
>>
>>
> Hi Vladimir, thanks for the reply. Please refer to the 3GPP specification
> I mentioned previously and you will find that encoder/decoder equation you
> put here is not the one used in GSM. 


Well, of course you can continue to insist on your delusions :)

VLV

Vladimir Vassilevsky wrote:

(snip)
>>> Encoder: T[i] = X[i] xor T[i-1]
>>> Decoder: X[i] = R[i] xor R[i-1]

>> Hi Vladimir, thanks for the reply. Please refer to the 3GPP specification
>> I mentioned previously and you will find that encoder/decoder equation 
>> you put here is not the one used in GSM. 

> Well, of course you can continue to insist on your delusions :)

It seems that the document (though the reference is the wrong
one) uses d and d-hat.   It seems likely a typographic error
that wasn't noticed.  If it was T and X it would be much easier
to see.  Also, I don't see the decoder described, which would be
a double check on the error. Then again, which of the different 
modulation methods do people actually use?

-- glen

The 3GPP reference is here and sorry for the typo in my first post.

http://www.3gpp.org/ftp/Specs/html-info/45004.htm

Just download one 3GPP spec (e.g. the version 7.2.0) in above webpage, and
you will find the differential encoder in the spec.

>Vladimir Vassilevsky wrote:
>
>(snip)
>>>> Encoder: T[i] = X[i] xor T[i-1]
>>>> Decoder: X[i] = R[i] xor R[i-1]
>
>>> Hi Vladimir, thanks for the reply. Please refer to the 3GPP
specification
>>> I mentioned previously and you will find that encoder/decoder equation

>>> you put here is not the one used in GSM. 
>
>> Well, of course you can continue to insist on your delusions :)
>
>It seems that the document (though the reference is the wrong
>one) uses d and d-hat.   It seems likely a typographic error
>that wasn't noticed.  If it was T and X it would be much easier
>to see.  Also, I don't see the decoder described, which would be
>a double check on the error. Then again, which of the different 
>modulation methods do people actually use?
>
>-- glen
>



If it is a typo error in 3GPP spec, then I can close my case here
immediately, but who can make sure that it is an error in 3GPP?

3GPP spec here:
http://www.3gpp.org/ftp/Specs/html-info/45004.htm