The Viterbi decoders currently used by the Deep Space Network (DSN) employ an algorithm for maintaining node synchronization that significantly degrades at bit signal-to-noise ratios (SNRs) of below 2.0 dB. In a recent report by the authors, it was shown that the telemetry receiving system, which uses a convolutionally encoded downlink, will suffer losses of 0.85 dB and 1.25 dB respectively at Voyager 2 Uranus and Neptune encounters. This report extends the results of that study to a concatenated (255,223) Reed-Solomon/(7, 1/2) convolutionally coded channel, by developing a new radio loss model for the concatenated channel. It is shown here that losses due to improper node synchronization of 0.57 dB at Uranus and 1.0 dB at Neptune can be expected if concatenated coding is used along with an array of one 64-meter and three 34-meter antennas

Deutsch, L. J.

Miller, R. L.

English

NASA Technical Reports Server

N83 14333
TDA Progress Report 42-71 July - September 1982
Viterbi Decoder Node Synchronization Losses in the
Reed-Solomon/Viterbi Concatenated Channel
L. J. Deutsch
Communications Systems Research Section
R. L. Miller
Information Systems Engineering Section
The Viterbi decoders currently used by the Deep Space Network (DSN) employ an
algorithm for maintaining node synchronization that significantly degrades at bit signal-
to-noise ratios (SNRs) of below 2.0 dB. In a recent report by the authors, it was shown
that the telemetry receiving system, which uses a convolutionally encoded downlink,
will suffer losses of 0.85 dB and 1.25 dB respectively at Voyager 2 Uranus and Neptune
encounters. This report extends the results of that study to a concatenated (255, 223)
Reed-Solomon/(7, 1/2) convolutionally coded channel, by developing a new radio loss
model for the concatenated channel. It is shown here that losses due to improper node
synchronization of 0.57 dB at Uranus and 1.0 dB at Neptune can be expected if con-
catenated coding is used along with an array of one 64-meter and three 34-meter
antennas.
I. Introduction
All planned NASA and European Space Agency (ESA)
deep space missions will have the capability of using a con-
catenated Reed-Solomon/convolutional coding scheme for
downlink telemetry (Ref. 1). Voyager 2 also has this capability
on board, and its encounter with Uranus in 1986 will be the
first use of this scheme by a space flight project. A simplified
block diagram of a concatenated coded downlink system is
shown in Fig. 1.
Although the specific details of the codes may differ among
the various missions, the basic code parameters, and hence
the overall system performances, are identical. The convolu-
tional inner code is a k = 7, rate 1/2 code. The Reed-Solomon
outer code is a (255, 223) code with 8-bit symbols. The
differences in the codes for specific missions involve differ-
ent orderings and inversions in the eonvolutional code's con-
nection vectors and different finite field representations and
generating polynomials for the Reed-Solomon code. The
baseline performance of tHis coding scene in the presence of
space loss and receiver thermal noise was determined in
Ref. 2. It is the purpose of this report to model "two additional
losses. These are noisy carrier referencing (or "radio loss")
and imperfect Viterbi decoder node synchronization. These
losses were treated for the convolutional-only channel in
Ref. 3.
Noisy carrier referencing is a degradation caused by the
effects of noise on the carrier tracking loop in the receiver
73
https://ntrs.nasa.gov/search.jsp?R=19830006062 2020-03-21T04:52:51+00:00Z
(Ref. 4). The noise causes the phase-locked loop to incor-
rectly estimate the phase of the incoming signal, which results
in a nonoptimal signal demodulation. The traditional radio
loss models do not apply in the case of concatenated coding,
since carrier phase tracking errors vary slowly compared to
the decision times in the Viterbi decoder but quickly com-
pared to the decision times in the Reed-Solomon decoder.
Thus it was necessary to develop a new model in Section II
herein called the mixed-rate model.
The node synchronization loss is a degradation caused by
the Viterbi decoder. The encoder for the (7, 1/2) convolu-
tional code outputs a pair of channel symbols for each input
bit. Conversely, the decoder must parse the received symbol
stream correctly to synchronize the symbols into pairs. When
the Viterbi decoder parses the data incorrectly, it is said to
be out of node synchronization. The current DSN Viterbi
decoders use an internal algorithm for maintaining node syn-
chronization that fails below a certain channel SNR. This
critical SNR value is called the node synchronization threshold.
Hardware tests (Ref. 5) and mathematical modeling (Ref. 3)
have demonstrated that the node synchronization threshold
of the Maximum-Likelihood Convolutional Decoders (the
DSN's Viterbi decoders, or MCDs) is about 2.0 dB.
The modeling described in Sections II and III of this report
predicts that losses to the concatenated coding system due to
poor node synchronization will amount to 0.57 dB at Voy-
ager 2 Uranus encounter and 1.0 dB at Neptune encounter.
These results assume that a perfect carrier array consisting of
one 64-meter antenna and three 34-meter antennas is used
for telemetry reception.
II. The Mixed-Rate Model
This section describes the model used to calculate the
effects of noisy carrier referencing on concatenated $oded
telemetry. Traditionally, there have been two basic models
used for radio loss calculations for coded data: the "high-rate
model" and the "low-rate model." The high-rate model
assumes that the length of time needed by the decoder for
decisions is so small that the phase estimate in the carrier
tracking loop is constant. The decoded bit error rate per-
formance is therefore given by the average of the bit error
rates caused by the different possible phase errors. This is
reflected in the equation
,
=
 J (1)
cos2 0 in SNR. The quantity p(0) is the phase error density
function and f(x) is the decoder's bit error rate as a function
of SNR in the case of perfect carrier tracking.
The low-rate model, on the other hand, assumes that the
phase errors change so much faster than the time it takes to
decode one bit that an average SNR can be used. This leads to
the equation
pb.t(x) = f ix (2)
For data rates and carrier loop bandwidths that are typical
of Voyager planetary encounters, carrier phase errors remain
relatively consant for 600 data bit times (Ref. 3). Since the
memory' length of the Viterbi decoders is only 64 bits, the
high-rate model applies to the convolutional-only channel.
Each Reed-Solomon word, however, is 2040 bits in length.
In addition, interleaving can further delay the decoding
time, so that the low-rate model applies to a Reed-Solomon-
only channel. Unfortunately, neither model applies well to
the concatenated channel.
The mixed-rate model resolves this dilemma by applying
the high-rate model to the inner convolutional code and the
low-rate model to the outer Reed-Solomon code. First, Eq. (1)
is used to calculate the Viterbi-decoded bit error probability
of the inner convolutional channel. The value x is taken to be
EV/N0 , the bit SNR of the inner convolutional channel. The
function f(x) is taken to be the ideal (no radio loss) perfor-
mance of the Viterbi decoder. The phase error density p(0) is
derived in Ref. 5 to be
exp(cos0)
In equation (1), x is the bit SNR incident upon the receiving
antenna. The effect of a phase error 0 is a degradation of
where p is the loop SNR of the carrier tracking loop, and 7Q
is the zero order modified Bessel function.
The average Reed-Solomon symbol error rate (the prob-
ability of one or more errors occurring in a string of eight
consecutive bits) TT is estimated to be 2.5 phit, where pbit is
the bit error rate of the inner convolutional channel. Figure 2
shows the ratio T/pbit for various channel and carrier loop
SNRs. A ratio of 2.5 is about average for SNRs in the 2-3 dB
range of EV/N0, where most of the mass of the integral in
(1) occurs. The overall concatenated bit error rate is then
calculated assuming that the inner channel bit error rate pbit
and the symbol error rate 11 vary quickly with respect to a
Reed-Solomon decoder decision time. The mixed-rate model
yields a concatenated bit error rate of
74
255
1=17
The bit SNR of the concatenated channel is taken to be
EJN0 = (EJNJ 255/223
due to the additional overhead of the Reed-Solomon code.
In the case of infinite carrier loop SNR, i.e., no radio loss,
Pbit = /O^v/^o)- Fi8ure 3 shows pRS as a function of Eb/N0
for this case with the assumption that Ti/pbit is 2, 2.5 or 3.
The total difference between the performances predicted by
these hypotheses at the bit error rate of 10 is less than 0.17 dB.
This implies than the assumption that this ratio is a constant
will not seriously affect the relative performance estimates
made by using the mixed-rate model.
III. Node Synchronization Model
The model of Viterbi decoder node synchronization losses
used in this study is described in Ref. 3. It is assumed that for
values of EV/N0 above the node synchronization threshold
the Viterbi decoder performs normally and in perfect syn-
chronization. For SNRs below the threshold, the decoder's
internal synchronization algorithm always believes that the
decoder is out of node synchronization. The result of this
condition is that the decoder continually oscillates between
correct and incorrect node synchronization and produces an
essentially random output.
In order to introduce the above information into the
mixed-rate model of Section II, it is only necessary to choose
a suitable Viterbi decoder performance function f(x). The
function f(x) for x larger than the node synchronization
threshold is taken to be the ideal performance function as
exhibited in Ref. 6. For values of x below the threshold,
f(x) is assumed to be equal to 1/2, a value which represents
a random decoder output.
nel with a node synchronization threshold of 2.0 dB and
carrier tracking loop SNRs of 11, 12, and 13.5 dB is shown
along with some actual hardware test data generated in the
Telecommunication Development Laboratory (TDL) (Ref. 5).
The close agreement between the actual data and the pre-
dicted performance corroborates the mixed-rate model.
Graphs of Reed-Solomon decoded bit error rate perfor-
mance for node synchronization thresholds of 0.0 and 2.0 dB
appear in Figs. 5 and 6 respectively for various loop SNRs.
These were used to generate the radio loss curves shown in
Fig. 7. Radio loss is defined to be the additional energy
per bit (in dB) needed to achieve some predetermined bit
error rate in a system with imperfect carrier tracking com-
pared to a system with ideal carrier tracking. In this case,
the ideal system is taken to be one in which the node syn-
chronization threshold of the Viterbi decoder is equal to 0
(or minus infinity dBs). The performance of this ideal system
is therefore given by the mixed-rate model with f(x) equal to
the ideal performance function of Ref. 6. The fixed bit error
rate is 10~s, the concatenated bit error rate needed for trans-
mission of compressed imaging data.
The difference between the two curves in Fig. 7 represents
the incremental SNR loss due to poor node synchronization
performance. Data from design control tables predict that for
Voyager 2 Uranus encounter at a modulation index of 76° and
90% weather, a 64-meter antenna would have an associated
loop SNR of about 13.2 dB. A four-element array consisting
of one 64-meter antenna and three 34-meter antennas would
have a combined loop SNR of 15.4 dB, provided a combined
carrier referencing scheme (Refs. 6, 7) is used. The associated
node synchronization losses for the concatenated channel
would be 0.89 dB for the 64-meter antenna alone and 0.57 dB
for the array. The arrayed loss would be slightly worse if base-
band-only combining were used. For Neptune encounter with
a 74° modulation index, the loop SNR of the 64-meter an-
tenna would be 10.8 dB while that of the array would be
about 13.6 dB. These correspond to node synchronization
losses of 1.25 dB and 1.0 dB respectively.
IV. Numerical Results
The performance of the concatenated channel with radio
losses and node synchronization losses was computed using
the mixed-rate model of Section II together with the Viterbi
decoder performance function in Section III. Performance
curves were generated for carrier loop SNRs of between
10 and 20 dB and for node synchronization thresholds of
between 0.0 and 2.5 dB. Some of the results are plotted in
Fig. 4. The predicted performance of the concatenated chan-
The losses for the concatenated channel due to poor node
synchronization performance are plotted as a function of node
synchronization threshold in Fig. 8 for various carrier tracking
loop SNRs. These represent the additional degradations over
the carrier phase tracking losses. The performance points for
the 64-meter antenna and the four-element array for Voy-
ager 2 Uranus and Neptune encounters are included in the
figure. It is evident from the figure that there is much to be
gained by improving the performance of the Viterbi decoder's
node synchronization algorithm.
75
V. Conclusions
If one compares the node synchronization losses for the
concatenated channel (Fig. 8) with those for the convolu-
tional-only channel (Ref. 3), it is clear that the concatenated
channel is more sensitive to this type of degradation. The
difference becomes more pronounced at higher carrier track-
ing loop SNRs, becoming about a 0.1-dB difference at a loop
SNR of 15 dB and a node synchronization threshold of
2.0 dB. This is not a significant additional loss. The conclusion
that must be drawn is that poor node synchronization by itself
does not degrade the concatenated channel much more than it
does the convolutional-only channel.
There are other related factors, however, that may greatly
increase the effects of poor node synchronization on the con-
catenated link. When the Viterbi decoder decides that it is out
of synchronization, it might add or delete a channel symbol
from the data stream. This could result in a loss of codeword
synchronization (or frame synchronization) in the Reed-
Solomon decoder. If frame synchronization is lost, it is likely
that several Reed-Solomon frames might be lost before resyn-
chronization occurs. This could mean that thousands of bits
would be only Viterbi decoded. The model described in this
report does not consider the effects of frame synchronization
losses.
Other sources of degradation that should be considered are
imperfect subcarrier tracking and demodulation and imperfect
symbol tracking. These effects are currently under investiga-
tion and will be the subject of a subsequent report.
References
1. Stephens, R. R., and Pellet, M. F., "Joint NASA/ESA Telemetry Channel Coding
Guideline: Issue 1," NASA/ESA Working Group (NEWG) Publication, Jan. 1982.
2. Miller, R. L., Deutsch, L. J., and Butman, S. A., "Performance of Concatenated Codes
for Deep Space Missions," IDA Progress Report 42-63, Jet Propulsion Laboratory,
Pasadena, Calif., June 15,1981.
3. Deutsch, L. J., and Miller, R. L., "The Effects of Viterbi Decoder Node Synchroniza-
tion Losses on the Telemetry Receiving System," TDA Progress Report 42-68, Jet
Propulsion Laboratory, Pasadena, Calif., Apr. 15,1982.
4. Lindsey, W. C., and Simon, M. K., Telecommunications Systems Engineering, Prentice
Hall, Inc., N.J., 1973.
5. Liu, K. Y., and Lee, J. J., "An Experimental Study of the Concatenated Reed-
Solomon/Viterbi Channel Coding System and Its Impact on Space Communications,"
Publication 81-58, Jet Propulsion Laboratory, Pasadena, Calif., Aug. 15, 1981.
6. Divsalar, D. D., and Yuen, J. H., "Improved Carrier Tracking Performance with
Coupled Phase-Locked Loops," TDA Progress Report 42-66, Jet Propulsion Labora-
tory, Pasadena, Calif., Dec. 15,1981'.
7. Deutsch, L. J., Lipes, R. G., and Miller, R. L., "Virtual Center Arraying," TDA Pro-
gress Report 42-65, Jet Propulsion Laboratory, Pasadena, Calif. Oct. 15, 1981.
76
ORIGINAL PAGE Si
OF POOR QUALITY
DATA
BITS ^~~""
1
REED-
SOLOMON
ENCODER AND
INTERLEAVER
£.c
CONVOLUTION'AL'
ENCODER
SUBCARRIER
ASSEMBLY
,-, 1
 -^SUBCARRllER' m.
MODULATOR
SPACE CHANNEL
SYMBOL
cvKk~HRDNI7FR
ASSEMBLY
CARRIER
MODULATOR
VITERBI
DECODER
TRANSMITTER
•^
^
REED-SOLOMON
DEINTERLEAVER
DECODED
DATA BITS
Fig. 1. Concatenated coding system block diagram
4 -
3 -
2 -
1 -
1
LEGEND OF
•
 f-A
 f.
0 f =
O f =
& f =
• /> =
1
1 1 1 1
LOOP SNRi
10 dB
13 dB
14 dB
15 dB A
16dB g
." £D 8
* • J
1 1 1 1
Ev/N0
Fig. 2. The relationship between Viterbi decoder bit error
rate p and Reed-Solomon symbol error rate -n
10"
10,-1
10,-2
10'
,0-7
10,-8
Eb/NQ, dB
Fig. 3. Concatenated performance assuming that
is a constant
77
ORIGINAL PAGE IS
OF POOR QUALITY
10,-3
10"
UJ
QC
QC
o
O£.
J—ea
z 10
2
o
10
-5
10',-7
DATA POINTS
OBSERVED IN
TDL TESTS
PERFORMANCE
PREDICTED BY
MIXED-RATE MODEL
J I
11 dB
2.0 2.5 3.0 3.5 4.0 4.5 5.5
Eb/NQ/ dB
Fig. 4. A comparison of the mixed-rate model with node
synchronization losses to hardware test data
10'
10
10
2.6 3.6 4.6
Eb/NQ/ dB
5.6
Fig. 5. Performance of the concatenated channel: node
synchronization threshold = 0.0 dB
78
ORIGINAL PAGE SS
OF POOR QUALITY
3.0
,0°
10',-1
,-2
2Q_
oeg
55
o
2
Q
10
10-
10-
10,-6
10,-7
10',-8
I I
f = CARRIER LOOP SNR
P = lOdB
20
1.6 2.6 3.6 4.6
Eb/NQ, dB
Fig. 6. Performance of the concatenated channel: node
synchronization threshold = 2.0 dB
5.6
12 13 14 15 16 17 18 19 20
Fig. 7. Radio loss for the concatenated channel at BER = 10~5
and node synchronization thresholds of 0.0 and 2.0 dB
79
ORIGINAL PAGE !i
OF POOR QUALITY
1.6
1.4
1.2
^ 1.0
to
IS*
2
Q 0.8
N
z
fc
o
0.6
0.4
0.2
f = 11 dB>
NEPTUNE ENCOUNTER
64-m ANTENNA
URANUS ENCOUNTER
64-m ANTENNA
NEPTUNE ENCOUNTER
4-ANTENNA ARRAY
14
15
URANUS
ENCOUNTER
4-ANTENNA
ARRAY
I I
0.5 1.0 1.5 2.0 2.5
NODE SYNCHRONIZATION THRESHOLD, dB
3.0
Fig. 8. Node synchronization losses for the concatenated
channel at various carrier tracking loop SNRs p
80


Viterbi decoder node synchronization losses in the Reed-Solomon/Veterbi concatenated channel

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