Download Differential encoding for a combined precoding and multiple

ITU - Telecommunications Standardization Sector
PCM00-43
Study Group 16 - Question 23
_____________________________________
V.pcm Rapporteur Meeting, Newmarket-on-Fergus, Ireland, April 25th - 28th, 2000
SOURCE:
3Com, Motorola, PCTel
CONTACT:
Richard Williams
TITLE:
Phone:
(858) 674 8591
E-mail:
[email protected]
Differential encoding for V.92 upstream
____________________
ABSTRACT
Currently there is no differential encoding defined for the V.92 upstream. This leaves a
modem open to the possibility of undetectable errors due to an inversion in the upstream
channel. This contribution proposes that the simple method of providing immunity to
channel inversions that is presented here be adopted in the V.92 standard.
Intellectual Property Statement
The individual preparing this contribution knows of patents, the use of which may be essential to
a standard resulting in whole or in part from this contribution.
Introduction
The emerging V.92 standard uses PCM modulation upstream by combining multiple
modulus conversion with precoding techniques. This leads to a problem with ensuring
180 phase shift immunity. Immunity to phase shifts that are otherwise undetectable by a
modem have been included in all recent modem standards. For V.92 the subject has not
been addressed for the upstream. This document gives a simple procedure that achieves
the required immunity using simple differential decoding techniques.
The currently agreed V.92 transmitter
The figure below is the currently agreed transmitter for the V.92 upstream.
b 0: bK-1
u(n)
Modulus
Encoder
Mi
v(n)
x(n)
prefilter
precoder
Y0
y(n)
Y1:Y4
Conv.
Encoder
Inverse
Map
A block of K bits is encoded using a modulus encoder. The output of this is then mapped
into equivalence classes in order to minimise the power coming out of the precoder. The
equivalence classes are related to each other in a simple modulo manner as in classical
Tomlinson encoding. Thus, the expanded constellations have points labelled in blocks
from 0 to Mi-1, where Mi is the modulus for the ith constellation.
Channel inversion
The modulus encoder takes in K bits as an integer R0 which is converted into 12 digits Ki.
Due to the equivalence class mapping, a symbol u(n) that is in the equivalence class of
Ki, passing through the precoder, prefilter, convolutional encoder, inverted channel and
convolutional decoder will emerge as Mi-1-u(n). This will cause errors in the output of
the modulus decoder and these errors are undetectable by the modem. It can be seen that
subtracting each digit of a modulus encoded number from one less than its respective
modulus is equivalent to subtracting the whole number from one less than its total
modulus. That is the number represented by the digits Mi-1-u(n) is N-1-R0 where N =
11
M
i 0
i
.
Differential encoding
It can be seen from the above that without a channel inversion R0 is returned but with a
channel inversion N-1-R0 is returned. To combat this a simple 'sign' differential encoder
is needed outside this operation. A 'sign' of 1 can be attributed to any frame whose value
is > (N-1)/2 a 0 to all others. The 'sign' can then be differentially encoded as d(n) = s(n) 
d(n-1), where  is modulo 2 addition. The new 'sign' is applied to the frame's value and
this is entered into the modulus encoder. The input and output of the whole scheme are
now invariant to 180 phase shifts.
The operations look like the following:
Determine the 'sign'
Differentially encode the 'sign'
Apply the 'sign' to R0
Receive the channel output
Determine the 'sign' of the output
Differentially decode the output
s(n) = 0 if R0 <= (N-1)/2, s(n) = 1 if R0 > (N-1)/2;
d(n) = s(n)  d(n-1);
D = R0 if d(n-1) = 0;
D = N-1-R0 if d(n-1) = 1;
R = D';
r(n) = 0 if R < (N-1)/2, r(n) = 1 if R > (N-1)/2;
r(n) = r(n-1) if R = (n-1)/2;
R0 = R if r(n-1) = 0;
R0 = N-1-R if r(n-1) = 1.
Conclusion
A simple differential encoding scheme that works with a combined precoding and
modulus conversion system has been described. This consists of a simple bit
manipulation between the scrambler and the modulus encoder. The corresponding receive
function is also a simple bit manipulation. The inclusion of this technique in the V.92
standard will ensure that the modem is immune to channel inversions.