Compact Representation of Bit and Power
Allocation Table Information for DMT Systems
Stefan Edinger and Markus Gaida
Abstract— In this paper we analyze methods to represent a
bit and power allocation table for discrete multi-tone systems in
compact form to allow for fast transmission of these important
parameters. Especially in the context of dynamic adaptation
such fast transmission is vital for fast adaptation to changed
conditions of the transmission channel.
necessary whenever the system is confronted with changed
channel conditions and simple measures, e.g. exchange of
bit swap commands [5] is not sufficient to restore reliable
communication.
I. INTRODUCTION
We use the transceiver model described in our introductory
paper about dynamic adaptive DMT modulation [6] for this
paper.
For the considerations in this paper, only additive white
Gaussian noise (AWGN) will be of interest.
During the initialization phase, the transmission channel
is estimated using a training sequence and equal reference
power pref on all sub-carriers. After this training phase, the
channel transfer function (represented by attenuation factors
gi ) as well as noise powers ni for the individual sub-carriers
are known. Signal to noise ratios (SNR) for the sub-carriers
can be computed according to the formula:
This work was partly funded by the German Research Foundation
(Deutsche Forschungsgemeinschaft, DFG)
Both authors are with the Chair of Electrical Engineering, Faculty of Mathematics & Computer Science, University of Mannheim,
68131 Mannheim, Germany {stefan.edinger|gaida (at) ti.unimannheim.de
pref · gi
.
(1)
ni
The transmission channel from [6] is reused here. SNR
for the examplary scenario are shown in Fig. 1.
SNRi =
60
55
50
45
SNR [dB]
Discrete multi-tone (DMT) modulation is an attractive
transmission scheme for environments with frequency selective transmission channels. At our chair, we have developed DMT systems for the use in industrial telecontrol
applications [1]. These applications require great robustness
of the point-to-point connection between two stations. While
conventional DMT systems provide only limited capability
to adapt themselves to changed transmission channel conditions, we focus on methods to provide extensive online adaptation capability. Transmission channels in industrial settings
are often subject to suddenly appearing disturbances, e.g.
narrow bandwidth interference. Due to such disturbances,
the signal to noise ratios (SNR) on individual or all subcarriers are decreased which leads to increased bit error
rates (BER) and in the worst case to a loss of connection.
Our DMT system detects such disturbances and can take
measures to restore the original target BER required for the
specific application [2], [3], [4].
It is not possible to guarantee a specific quality of service
(QoS) level for the connection at all times. However, it can be
shown that using our adaptation methods, the time required
for adaptation is much smaller than the time required to reestablish a lost connection. This results in less data being
lost during the adaptation process compared to the data lost
during the time to re-establish a lost connection.
An important task during the adaptation process is the
update of previously used transmission parameters. The
most important transmission parameters in DMT are the bit
allocation table (BAT) and power allocation table (PAT). The
BAT indicates the number of bits bi that is transmitted on a
specific sub-carrier i. The PAT indicates the transmit power
pi that is required to transmit the bi bits of sub-carrier i with
a given BER.
In this paper, we investigate methods to reduce the time required for updating the BAT and PAT. Such updates become
II. S YSTEM M ODEL
40
35
30
25
20
15
0
10
20
30
40
sub−carrier index
50
Fig. 1.
Exemplary transmission channel
60
70
The total transmit power of the system is limited to
ptot = 25 dBm. This power is equally distributed over
all sub-carriers during the channel estimation phase, thus
tot
pref = pM
, where M denotes the FFT length (in this paper
M = 128. The sampling frequency of the DMT system is
fS = 1024 kHz. The rather high sampling frequency and the
short FFT length effectively reduce the latency of the system
due to block oriented signal processing. The DMT symbol
rate equals rS = 6400 Hz.
# of bits
15
410 Bits
10
5
0
0
10
20
30
40
sub−carrier index
50
60
70
0
10
20
30
40
sub−carrier index
50
60
70
relative power
3
2
1
0
Fig. 2.
The above BAT could then be given as pairs (mn , bn ) for
all n:
[(4, 0), (6, 12), (6, 10), (23, 8), (9, 6), (9, 4), (2, 2), (4, 0)] .
Information about the 4 trailing zeros need not be transmitted since they can be inferred. The largest multiplier is
m = 23 which requires 5 bits in binary representation. If all
other multipliers also use 5 bits and the bi are still represented
by 4 bits, the complete BAT information fits in 7·(5+4) = 63
bits as compared to 64 · 4 = 256 bits for the conventional
encoding.
Clearly, such a large improvement can only result if large
groups of consecutive sub-carriers with the same bit load are
present.
The easiest way to make use of such improvements is to
compare conventional and alternative BAT representations
and use the one that results in smaller size. The information
which method was used can be given with one single bit as
a flag.
BAT and PAT for example channel
V. A LTERNATIVE REPRESENTATION OF PAT ENTRIES
Fig. 2 shows the BAT and PAT that maximize total bit
rate for a target BER of 10−6 according to a bit loading
algorithm such as [7].
The PAT entries ri are given as multiples of the reference
power. The transmit power pi for sub-carrier i is expressed
as
pi = ri · pref .
(2)
III. C ONVENTIONAL REPRESENTATION OF BAT AND PAT
ENTRIES
The entries of the BAT and PAT must be exchanged with
the partner station. To this end, the PAT entries must be
discretized.
Usually (for example in the ADSL standard [8]), 12 bits
are used to encode the PAT entries in a fixed-point format.
The binary point (binary equivalent to the decimal point) is
positioned after the third bit. The BAT entries are already
discretized since no fractions of bits can be transmitted.
Note that because we use only square constellations and a
maximum of 12 bits per sub-carrier, 4 bits are sufficient to
encode all possible constellation sizes inclusive 0 bits which
denotes an unused sub-carrier.
With this encoding, a total of M
2 · 16 bits are necessary to
transmit the complete BAT and PAT.
IV. A LTERNATIVE REPRESENTATION OF BAT ENTRIES
Wireline transmission channels are usually characterized
by a lowpass-shaped transfer function. As can be seen
from Fig. 2 this leads to a number of consecutive subcarriers transmitting the same number of bits and requiring
increasing amounts of transmit power to counter the effect of
channel attenuation. Instead of transmitting four bits of BAT
information for each sub-carrier, consecutive sub-carriers
with the same bi can be grouped. The BAT entries must
be rearranged to consist of a multiplier mn indicating how
many sub-carriers share the same bn and the value bn itself.
The conventional PAT representation uses 12 bits for each
sub-carrier. To determine these 12 bits, the continuous value
computed from the bit loading algorithm (depending on DSP
or processor implementation most likely a 16 or 32 bit value)
must be rounded or truncated. ADSL uses 3 bits before the
binary point limiting relative powers to the range [0 . . . 8[. We
could observe that PAT entries in our simulations are very
rarely larger than 3. Thus, a first step to increase accuracy is
to reserve only two bits before the binary point. This limits
relative powers to the range [0 . . . 4[. Moving the binary point
one digit to the left decreases the maximum rounding error
emax which can be computed according to the formula
1 −q
·2 ,
(3)
2
with q being the number of digits to the right of the
binary point. Rounding, however, can violate the total power
constraint
emax =
M/2
X
i=1
!
pi ≤
ptot
,
2
(4)
if more than half of the values are rounded up.
Thus, we propose rounding down or truncating all values
to be on the safe side. This leads to a maximum truncation
error
emax = 2−q .
(5)
Truncating, however, brings about the problem that the
target BER is not exactly reached but slightly higher than
desired.
Fig. 3 shows this effect. The PAT values from the above
example are encoded using truncation and 12 and 8 bits per
PAT entry, respectively. It can be seen that depending on
the attenuation and constellation size, the increase of BER
is different for individual sub-carriers.
−6
1.1
x 10
The bit rate per DMT symbol has only dropped by two
bits. Finally, Fig. 5 shows that the resulting BER are indeed
always below the target BER of 10−6 .
target BER
12 bits per PAT value
8 bits per PAT value
1.08
10.2
1.04
10
1.02
9.8
BER
BER
−7
1.06
1
0.98
0
10
20
30
40
sub−carrier index
50
60
x 10
9.6
9.4
70
9.2
Fig. 3.
9
The worst BER of a single sub-carrier dominates the overall mean BER over all sub-carriers. To decrease the number
of representation bits for PAT entries whithout increaseing
the resulting BER, one can compute the amount of power
necessary to round up all sub-carriers. This power ∆p can
be computed as
M
· emax .
2
∆p =
(6)
In the bit loading process the total power constraint must
be decreased by ∆p so that
M/2
X
i=1
!
pi ≤
ptot
− ∆p .
2
(7)
This modification is easily implemented and leads to only
a minimal decrease of overall bit rate.
The resulting BAT and PAT for the example channel and
8 bits used to represent PAT entries is depicted in Fig. 4.
# of bits
15
408 Bits
10
5
0
0
10
20
30
40
sub−carrier index
50
60
70
0
10
20
30
40
sub−carrier index
50
60
70
relative power
3
2
1
0
Fig. 4.
target BER
PAT values rounded up
BER with truncation
BAT and PAT with modified ptot
0
10
20
Fig. 5.
30
40
sub−carrier index
50
60
70
BER for modified ptot
Coming back to the example channel, using the conventional PAT encoding, M
2 · 12 = 768 bits are necessary to
transmit the information. Using the alternative representation
with just 8 bits per entry and leaving out all zero entries
that are known from BAT information, one can transmit the
information in (64 − 8) · 8 = 448 bits.
VI. CONCLUSIONS
We presented methods to significantly reduce the amount
of data necessary to transmit complete bit and power allocation tables. Depending on the desired accuracy, several
alternatives can be chosen from. Especially in the context
of dynamic adaptation the overall adaptation speed benefits
from the presented methods while the computational overhead is minimal.
R EFERENCES
[1] Carsten Bauer. Mehrträger-Übertragungssysteme mit dynamischer
Adaption an zeitvariante Kanaleigenschaften. Dissertation, Universität
Mannheim, 2004.
[2] Stefan Edinger, Carsten Bauer, and Norbert J. Fliege. DMT Transmission in the Context of Industrial Telecontrol Applications. In
Kleinheubacher Tagung, Miltenberg, Germany, September 2005.
[3] Stefan Edinger, Johannes Schwarz, and Norbert J. Fliege. Protected
Protocol Securing Transition Phases in Dynamically Adaptive OFDM
System. In Proc. of the International OFDM Workshop, InOWo,
Hamburg, Germany, September 2005.
[4] Stefan Edinger, Carsten Bauer, Markus Gaida, and Johannes Schwarz.
Quality of Service and Dynamic Adaptive Discrete Multitone Modulation. In Proc. IEEE International Workshop on Spectral Methods and
Multirate Signal Processing, SMMSP, Riga, Latvia, June 2005.
[5] John M. Cioffi. The Essential Merit of Bit Swapping. ANSI Contribution
T1E1.4/98-318R1, December 1998.
[6] Stefan Edinger and Carsten Bauer. Concepts of Dynamic Adaptive
DMT Modulation. In ISCCSP, Marrakech, Morocco, March 2006.
[7] Dirk Hughes-Hartogs. Ensemble Modem Structure for Imperfect Transmission Media. U.S. Patents No. 4679227 (July 1987), 4731816 (March
1988), 4833706 (May 1989), 1989.
[8] A MERICAN NATIONAL S TANDARD FOR T ELECOMMUNICATIONS :
Asymmetric Digital Subscriber Line (ADSL) Metallic Interface Specification. Technical report, Alliance for Telecommunications Industry
Solutions, 1998.