Per-survivor Based Detection of
DPSK Modulated High Rate Turbo Codes
Over Rayleigh Fading Channels
Bin Zhao and Matthew C. Valenti
Lane Dept. of Comp. Sci. & Elect. Eng.
West Virginia University
Morgantown, WV
This work funded by the Office of Naval Research under grant N00014-00-0655
Outline of Talk

Background
– Iterative channel estimation and decoding.
– Turbo DPSK (Hoeher & Lodge).

“Extended” turbo DPSK
–
–
–
–

Replace code in turbo DPSK with turbo code.
Analytical tool to predict location of “waterfall”.
Performance in AWGN and fading with perfect CSI
Performance in unknown fading channels using
PSP-based processing.
Conclusions
Iterative Channel Estimation

Pilot-symbol filtering techniques:
– Valenti and Woerner – “Iterative channel estimation and decoding
of pilot symbol assisted turbo codes over flat-fading channels,”
JSAC, Sept. 2001.
– Li and Georghiades, “An iterative receiver for turbo-coded pilotsymbol assisted modulation in fading channels,” Comm. Letters,
April 2001.

Trellis-based techniques:
– Komninakis and Wesel, “Joint iterative channel estimation and
decoding in flat correlated Rayleigh fading channels,” JSAC, Sept.
2001.
– Hoeher and Lodge, “Turbo DPSK: Iterative differential PSK
demodulation and channel decoding,” Trans. Comm., June 1999.
– Colavolpe, Ferrari, and Raheli, “Noncoherent iterative (turbo)
decoding,” Trans. Comm., Sept. 2000.
Turbo DPSK Structure
input
channel
Interleaver
RSC
D
P
S
K
output
Channel
+
convolutional
decoder
Deint
-
+






channel
Interleaver
APP
Demod
extrinsic
infomation
From Hoeher/Lodge.
K=6 convolutional code.
Block interleaver: 20 frames.
Trellis-based APP demodulation of DPSK with perfect CSI.
In flat fading channels, per-survivor processing and linear
prediction are applied to estimate the channel information.
Iterative decoding and APP demodulation.
APP Demodulator for DPSK

Can use BCJR algorithm to coherently detect
trellis-based DPSK modulation.
– Only 2 state trellis when perfect CSI available.

With unknown CSI apply linear prediction and
per-survivor processing to estimate the channel
information.
– Requires an expansion of the DPSK code-trellis.
– Complexity of APP demodulator is exponentially
proportional to the order of linear prediction.
– PSP algorithm must be modified to produce softoutputs.
Construction of Super-Trellis
0
S0
0
1
0
S1
Window 1
0
S0

1
0
Window 2
S0
1
S1
S2
0
0
S1
S2
1
S3
0
S3
Use a sliding window to
combine multiple
adjacent stages of simple
DPSK trellis to construct
the super-trellis of APP
demodulator.
 Number of adjacent
stages equals the order of
the linear predictor.
 Complexity of supertrellis is exponentially
proportional to the order
of linear prediction.
Branch Metric of APP Demodulation in
Correlated Fading Channel with PSP
R
|| y  b  p y b
|| z  2  1   p r
|
(b )  S
|| y  b  p y b
||
|T 2  1   p r
N
~
~
k
k
n
k n
k n
1
k
k
N
2
n
~
2
~
ak = 1
n n
1
k
N
~
k
k
2
~
n
k n
k n
1
N
2
n
~
ak = 0
n n
1



~
Channel LLR y and estimated channel input b k  n
Prediction coefficient pnNand Gaussian noise 2 2n
Prediction residue 1   pn rn
1
Extended Turbo DPSK Structure
RSC
turbo
interlea ver
RSC
P
U
N
T
Channel
Interleaver
Turbo Encoder
D
P
S
K


Channel


Turbo
decoder
APP
Demod
Deint
+
+

Channel
Interleaver
extrinsic
infomation

Code polynomials (1,23/35)
UMTS interleaver for turbo
code.
Rate compatible puncturing
pattern.
Block channel interleaver.
Per-survivor based APP
demodulation for correlated
fading channels.
Iterative decoding and
demodulation.
Performance in AWGN Channel
with Perfect CSI
0
10

Framesize 1024 bits
 The energy gap between
turbo code and extended
turbo DPSK:
extended turbo DPSK
turbo code (coherent BPSK)
-1
10
-2
10
-3
BER
10
-4
10
4/7
4/5
8/9
1/3

-5
10
-6
10
10
1 dB
2.5 dB
-4
Energy Gap
8/9
2 dB
4/5
1 dB
4/7
1.5 dB
1/3
2.5 dB
The energy gap decreases
as the rate increases
except for the rate 8/9
case.
– Why?
-7
-6
Rate
-2
0
2
Es/No in dB
4
6
8
Analytical Tool: Convergence Box

0
10
Similar to the “tunnel theory”
analysis.
–
Threshold box
-1
10
Non converge
c
b
d
2 a
1
BER
-2
r =⅓
turbo code
–

4
-3
10

-2
0
2
Es/No in dB
4
6
8
Turbo Code  BPSK
Convergence box shows
minimum SNR required for
converge.
–
10
1
iterations iteration
DPSK  BPSK
Turbo code decoder
•
Converge
-4
APP demodulator
•
BPSK
3
-6
Suppose Turbo decoder and APP
demodulator ideally transform
input Es/No into output Es/No.
–
coherent
DPSK
0
10

S. Ten Brink, 1999.
corresponds to the threshold
SNR in the tunnel theory.
convergence box location:
rate
Es/No
Eb/No
1/2
0.5 dB 3.5 dB
1/3 -1.3 dB 3.5 dB
Performance in Fading Channel:
r = 4/5 case






BT=0.01
Block interleaver
improves the
performance of turbo
code by about 1.5 dB.
With perfect CSI, the
energy gap between
turbo code and extended
turbo DPSK is 3 dB.
For extended turbo
DPSK, differential
detection works better
than per-survivor based
detection
Reason A: 1 local
iteration of turbo
decoding is sub-optimal.
Reason B: the punctured
outer turbo code is too
weak.
Performance in Fading Channel:
r = 1/3 case



Per-survivor based
detection loses about
1 dB to perfect CSI
case.
Per-survivor based
detection has 1 dB
gain over extended
turbo DPSK with
differential detection.
Increasing the trellis
size of APP
demodulator provides
a decreasing
marginal benefit.
Performance in Fading Channel:
r = 4/7 case




With perfect CSI, the
energy gap between
turbo code and extended
turbo DPSK is around
2.5 dB.
Per-survivor based
detection loses about 1
dB to perfect CSI case.
Per-survivor based
detection has 1 dB gain
over extended turbo
DPSK with differential
detection.
Increasing the trellis size
of APP demodulator
provides a decreasing
marginal benefit.
Conclusions

“Extended turbo” DPSK = turbo code + DPSK modulation.
– Performs worse than turbo codes with BPSK modulation and
coherent detection.
– However, the gap in performance depends on code rate.
– Large gap if code rate too low or too high.
– “Convergence box” predicts performance.

Extended turbo DPSK suitable for PSP-based detection.
– PSP about 1 dB worse than extended DPSK with perfect CSI.
– For moderate code rates, PSP is 1 dB better than differential
detection.
– However, if code rate too high, PSP can be worse than diff. detection.
• Performance can be improved by executing multiple local iterations of
turbo decoding per global iteration (future work).
Future Work



Search for optimal puncturing patterns for extended turbo DPSK.
Search for a better modulation structure for turbo codes with a
convergence region comparable or even better than that of BPSK
modulated turbo codes.
Further develop analytical tools that leverage the concepts of
Gaussian density evolution and convergence boxes of extended
turbo DPSK in the error-cliff region.