Packet-size-Controlled ECG Compression Algorithm based on

Discrete Wavelet Transform and Running Length Encoding

Asiya M. Al-Busaidi and Lazhar Khriji

Department of Electrical and Computer Engineering, College of Engineering, Sultan Qaboos University, Muscat, Oman

Keywords: Data Compression, ECG, Telecardiology, Wavelet Transform, Running Length Encoding, PRD, CR.

Abstract: This paper presents a development of new size-controlled compression algorithm for Electrocardiogram

signal (ECG). Discrete Wavelet Transform (DWT) method, Bit-Field Preserving (BFP) and Running Length

Encoding (RLE) are selected as compression tools in this work. Even though DWT-BFP-RLE is a lossy

compression method, it has shown a potential in preserving the critical (diagnostic) part of the signal.

Knowing that the size of transmitted packets of the battery-powered mobile telecardiology systems is

limited within few bytes, the current algorithm is aiming to ensure that the compressed packets fit into the

limited payload size. A parametric study of different mother wavelets and decomposition levels of DWT is

presented with an emphasize on compression ratio (CR), percentage mean-square difference (PRD) and

quality score (QS). The mother wavelet giving the best CR and QS results is then adopted to perform the

dynamic compression algorithm on ECG records from MIT-BIH arrhythmia database.

1 INTRODUCTION

The Electrocardiogram (ECG) signal is an important

biomedical signal that is widely used in diagnostic

procedures by cardiologists. The monitoring of ECG

signal can be done inside the hospitals/clinics using

sophisticated equipment or at home or outdoor by

using wearable monitoring devices that transmit the

signal via cellular network or other wireless

technologies. With the increased need of high

resolution, high sampling rate and long recording

period of the monitored ECG, the data compression

becomes more vital for storage and transmission.

Compression is the procedure of reducing the

number of digitized ECG signal without significant

loss of the diagnostic data. Many methods were

proposed for ECG compression and they can be

lossless or lossy but all of them can be grouped into

two categories: direct methods and transform

methods (Chen and Itoh, 1998). In direct methods,

compression is applied directly on the time domain

ECG signal, while in the transform methods the

ECG signal is transformed into a different domain.

In lossy methods; there is some kind of quantization

of the input data which leads to higher compression

ratio (CR) results at the expense of reversibility. But

this may be acceptable as long as no significant

clinical degradation is introduced to the encoded

signal (Moody et al., 1988). The CR levels of 2 to 1

achieved by lossless methods are too low for most

practical applications. Therefore, lossy coding

methods that introduce small reconstruction errors

are preferred in practice. In other words, the main

important factors in ECG compression are: (1) the

ability of reconstructing the important features from

the compressed ECG data, (2) the compression ratio,

(3) execution time, and (4) the amount of error

between the original and reconstructed signal.

Recently, there are some trials to combine the lossy

and lossless compression techniques specifically for

the ECG signal (Abo-Zahhad et al., 2014).

Discrete Wavelet Transform (DWT) is a

powerful time-frequency signal analysis tool that

was utilized for ECG filtering (de-noising), feature

extraction and compression (Ballesteros et al., 2012;

Ballesteros and Gaona, 2011; Chen and Itoh, 1998;

Chouakri et. al, 2011). The DWT transforms the

ECG signal into sub-bands that can be encoded

using set partitioning in hierarchal tree (SPIHT)

coding (Lu et al., 2000), vector quantization (VQ),

energy package efficiency (EPE) and other encoding

schemes. However, some of the encoding methods

can be complex to implement on FPGA’s or basic

microcontrollers and require high computational

costs, which make them unsuitable for wearable

battery-powered health monitoring devices. Chan et

246

Al-Busaidi A. and Khriji L..

Packet-size-Controlled ECG Compression Algorithm based on Discrete Wavelet Transform and Running Length Encoding.

DOI: 10.5220/0005225202460254

In Proceedings of the International Conference on Bio-inspired Systems and Signal Processing (BIOSIGNALS-2015), pages 246-254

ISBN: 978-989-758-069-7

 2015 SCITEPRESS (Science and Technology Publications, Lda.)

al. (2008) proposed an encoding scheme to compress

the DWT coefficients using bit-field preserving

(BFP) and running length encoding (RLE) and it

was tested on an FPGA system (Lee et al., 2011).

The method was simple to implement and allows

forward data processing compared to other methods

that require sorting and heavy computations.

Most of the ECG compression methods are open

loop methods that have fixed performance. On the

other hand, there are new closed loop compression

methods that were designed to check the quality of

the compressed signal by evaluating the amount of

error introduced to the reconstructed signal before

transmitting the compressed packet (Benzid et al.,

2006).

This paper introduces a dynamic compression

method that was not addressed in published

literature yet. The dynamic compression method

handles the issue of the limited payload size when

the compressed packet is exceeding the maximum

payload available. In other words, it controls the size

of the compressed packets dynamically by a closed

loop. For example, in low power wireless

technologies like Bluetooth, Bluetooth Low Energy,

6LoWPAN, and ZigBee, the payload size is not very

large and thus sending a continuous raw data will

not be efficient in terms of energy saving.

Consequently, the data have to be compressed and

the overheads have to be designed optimally to make

sure that the packet holds much more data than

headers. As a result the data rate is reduced without

a significant loss in the clinical features. The

proposed dynamic compression method was

designed based on a modified DWT-BFP-RLE

compression algorithm. The method was tested on

ECG records from MIT-BIH Arrhythmia database

after obtaining the proper compression parameters.

2 METHODS

2.1 Wavelet Decomposition and

Reconstruction

The ECG signal is a non-stationary signal that has

varying frequency components with time and the

DWT showed its powerfulness in decomposing the

different ECG waveforms. The wavelet-based

techniques fit with the standard signal filtering

methods and encoding schemes and thus produce

good compression results (Addison, 2002). The

discrete wavelet transform (DWT) method can be

done using decimation and without decimation

(redundant or shift-invariant). Here undecimated

DWT has been chosen due its better results in de-

noising (Raj and Venkateswarlu, 2011). The ECG

signal can be decomposed into J decomposition

levels as shown in Figure 1, using lowpass g(n) and

highpass h(n) FIR filter banks and then down-

sampling by a factor of 2. The decomposed signal in

each level is divided into low frequency signal (a

)

and high frequency signal (d

). The low frequency

signal a

is called the approximation signal and the

high frequency signal d

is called the detail signal.

The low frequency signal is decomposed again into

two signals and so on up to d

and a

. The filter

banks are constructed from wavelet basis functions

such as Haar, Daubechies, Biorthogonal, Coiflet,

Symmlet, Morlet, and Mexican Hat. The selection of

wavelet transform function mainly depends on the

application. The decomposed signal can be

reconstructed back again into the original signal

using reconstruction filters, which are the inverse of

the decomposition filters. In this work, Daubechies

(Db4 and Db5) and Symmlet (Sym4 and Sym6)

mother wavelets were adopted and the

decomposition level (J) was varied from 3 to 7.

Figure 1: DWT with 2 level decomposition.

2.2 Thresholding and Bit-Field

Preserving

After decomposing the signal into sub-bands using

DWT, thresholds are applied to each sub-band. The

thresholding process mainly contributes in filtering

and used for decoding as well. One of the commonly

used adaptive thresholds is provided in equation (1).

log2



 





where,  is the standard deviation of the sub-band

and N is the number of samples in the same sub-

band. However, in this work the threshold (Thres

)

was calculated based on the bit-depth (B

) of each

sub-band and the desired preserved bit-length (I

The bit-depth B

is the most significant bit of the

maximum coefficient in the sub-band. While, the

preserved-length I

is controlled according to the

desired compression performance where Sb stands

for the sub-band coefficients d

, d

,.., d

and a

h(n)

g(n)

h(n)

g(n)

↓2x

(n)

↓2 ↓2

↓2

Packet-size-ControlledECGCompressionAlgorithmbasedonDiscreteWaveletTransformandRunningLengthEncoding

247





sbsb

Thres 





A round-off mechanism is applied to the DWT

coefficients before thresholding and encoding by

adding 2

Bn-Isb

to all coefficients to reduce the

truncation error. Where, B

is the bit depth before

round-off mechanism and B

after round-off.

2.3 Encoding

Before encoding the coefficients, the mean of the

approximation coefficient a

is subtracted and it will

be added later on at the reconstruction stage. To

encode the coefficients, first they are compared to

the calculated sub-band threshold Thres

. If the

magnitude of the coefficient is greater than or equal

to the sub-band threshold, it is considered as

significant; otherwise it is considered as

insignificant. The desired bits of interest of the

significant coefficient will be sent to the bits-of-

interest (BOI) packet and a one will be sent to the

significant map (SM) stream. The SM stream

indicates the sequence of significant and

insignificant coefficients by ones and zeros,

respectively. The BOI are the extracted bits from

+1 to B

-I

+1, which represent BOI range,

including the sign bit (B

+1). In this works, each

BOI is stored into one byte and the same for BOI

range. Thus, I

is no more than 6 (i.e. bits 0 to 6

hold the extracted bits and bit 7 for the sign bit).

To reduce the redundant zeros in SM stream and

increase the compression ratio, it is divided into

bytes and then running length encoding (RLE) is

applied on the SM bytes. The RLE is well known

method that replaces the consecutive bytes with their

value followed by their number of copies (e.g. x=1 1

0 0 0 5 0 0 0 9 0 0 0 0 0 3 3 3, will be x

enc

=1 2 0 3 5

1 0 3 9 1 0 5 3 3). The SM can be easily encoded

(SMe) by encoding the consecutive zeroes. One byte

is enough to represent the number of consecutive

zeros up to 255 zeros. The last two sub-bands (a

and

) have fewer samples and less consecutive zeros

and thus RLE method was not applied to them. The

overall compression scheme is illustrated in Figure

2.4 Packetizing the Transmitted Data

To send the compressed BOI, BOI Range and SM

packets, headers are required to indicate each

segment of the compressed data. Table I shows the

headers and the sizes of each packets. First, an

indicator of the total number of samples of the ECG

signal (Ns) taken for compression is placed at the

beginning of the packet. Ns can have a value of 0, 1,

2, 3 and 4 which indicate that number of the

compressed samples of 64, 128, 256, 512 and 1024,

respectively. Then, for each transformed sub-band

by DWT, headers were created to indicate the Bits-

of-Interest Range (BOI Range), the number of bytes

that holds the Bits-of-Interest (BOI Size), the

number of bytes that holds the significant map (Size

SM) or the encoded significant map (Size SMe). The

BOI and SM follow the BOI Size and SM Size

headers, respectively. Finally, the subtracted mean

of the approximation sub-band (Mean of a

) is

divided into two bytes and placed at the end of the

packet. At the receiver side, the packets are arrived

in sequence and decompressed after decoding them

using the information arrived.

Table 1: Format of the compressed packet.

Packet Description Size Details

Number of Compressed

Samples

1 Byte 2

Samples

BOI

Range

)

The Range of Bits of

Interest of the first

detail sub-band d

1 Bytes

The 4 MSBs

for the low bit

range.

The 4 LSBs

for the high

bit range.

BOI

Size (d

)

Number of BOI in the

first detail sub-band d

2 Bytes -

BOI

)

Bits of Interest in the

first detail sub-band d

Size BOI

* 1Byte

Extracted

using Thres

SMe

Size (d

)

Number of encoded

SM in the first detail

sub-band d

1 Byte -

SMe

)

RLE Encoded

Significant Map of BOI

of the first detail sub-

band d

Size

SM *

1Byte

…

BOI

Range

)

The Range of Bits of

Interest of the approx.

sub-band a

1 Bytes -

BOI

Size (a

)

Number of BOI in the

approx. sub-band a

2 Bytes -

BOI

)

Bits of Interest of the

approx. sub-band a

Size BOI

* 1Byte

Extracted

using Thres

Size (a

)

Number of SM in the

approx. sub-band a

1 Byte -

)

Significant Map of

BOI of the approx.

sub-band a

Size SM

* 1Byte

Mean

)

The mean of the

approx. sub-band a

2 Bytes

The mean is

subtracted

from a

and

sent separately

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248

Figure 2: Compression scheme.

3 PROPOSED DYNAMIC

COMPRESSION ALGORITHM

In this study, the ECG compression scheme based on

DWT-BFP-RLE described in section 2 has been

adopted and modified for telecardiology systems by

considering the limit of the transmitted payload. The

algorithm was designed to be a closed loop

compression scheme that controls the size of the

compressed packet. A schematic diagram of the

algorithm is shown in Figure 3, which can be

summarized into the following steps:

1. Store N (2

) ECG samples into a buffer and

compress them.

2. Check the size of the compressed packet. If the

compressed packet size is less than or equal to

the maximum allowable number of bytes (M),

transmit the packet.

3. Otherwise, split the ECG data stored in the buffer

into two new packets each with size N/2.

4. Apply the compression algorithm onto each

packet separately, but in the correct sequence,

where the first half of the data is to be

compressed and transmitted first.

5. Go back to step 2 and repeat the process until all

the data are transmitted.

The efficiency of this method is investigated and

evaluated in the next section.

Figure 3: Dynamic Compression scheme.

4 SIMULATION RESULTS

To evaluate the proposed compression scheme, ECG

records from MIT-BIH Arrhythmia (mita) database

were used. The ECG signals in mita database were

sampled at 360Hz and with 11-bit resolution. Ten

different ECG records were used to evaluate the

compression scheme; 100, 102, 107, 109, 117, 118,

119, 220 and 232. To test the proposed scheme, the

first 10 minutes duration of each record was taken

Start

Compress ECG Samples

Yes

Check if the

compressed data

fits into M Bytes

Packet

Put the 1

N/2

ECG samples

from buffer into

a new buffer

Put the 2

N/2

ECG samples

from buffer into

a new buffer

Read N (2

) ECG

samples and store

into buffer

Divide Data into two equal

sets (N/2 samples)

Transmit

Data

Compress ECG Samples Compress ECG Samples

Yes

Check if the

compressed

data fits into

M Bytes

Packet

Transmit

Data

Divide Data into two

equal sets (N/2 samples)

Yes

Check if the

compressed

data fits into

M Bytes

Packet

Transmit

Data

Divide Data into two

equal sets (N/2 samples)

…

Packet-size-ControlledECGCompressionAlgorithmbasedonDiscreteWaveletTransformandRunningLengthEncoding

249

and divided into frames each contains 1024 samples

(2.84 seconds). For each record, the mother wavelet

filters Db4, Db5, Sym4 and Sym6 were applied with

varying decomposition levels between 3 and 7. The

results were evaluated using the compression

measures provided in section 4.1.

4.1 Evaluation Scheme

First, the modified compression scheme was

evaluated and then the dynamic compression scheme

was studied based on the selected parameters. To

evaluate the compression algorithm, the percentage

root-mean square difference or PRD error between

the original x

and the reconstructed signal x

was

calculated by (3). Another measure to evaluate the

compression algorithm is the compression ratio (CR)

in equation (4). The CR calculates the ratio between

the number of bits in the original signal (b

= 11 bits

1024= 11,264) and number of bits in the

compressed packet (b

comp

=8 bits  N

comp

Fira and Goras (2008) saw that the CR and PRD

are the most important compression measures in all

literature, thus they suggested a new compression

measure called “quality score” (QS) that represents

the ratio between the CR and the PRD as shown in

equation (5). The high quality score indicates a good

compression performance.



100%

or re or

PRD x x x 



(3)

comp

bCR 

(4)

PRDCRQS 

(5)

4.2 Parametric Study

Figures 4 to 7 shows the original and reconstructed

ECG signal of record 100 using different mother

wavelets and decomposition levels. Surface plots of

the average PRD and CR at different mother

wavelets and decomposition levels of the same

record are shown in Figures 8 and 9, respectively.

According to Figure 8, Sym4 and Sym6 give better

CR at the decomposition levels 4-7. However, the

best CR results are obtained by Sym4 at levels 5-7.

Figure 9 shows that levels 3 and 4 give the lowest

PRD compared to other levels. However, it is

interesting to note that Sym4 produces the lowest

PRD at all decomposition levels. The QS of record

100 is shown in Figure 10. It is clear from the figure

that Sym4 produces the best QS results at all

decomposition levels.

Figure 4: The original and reconstructed ECG of record

100 based on Db4 and J= 3 to 7.

Figure 5: The original and reconstructed ECG of record

100 based on Db5 and J= 3 to 7.

Figure 6: The original and reconstructed ECG of record

100 based on Sym4 and J= 3 to 7.

Figure 7: The original and reconstructed ECG of record

100 based on Sym6 and J= 3 to 7.

0 200 400 600 800 1000

850

900

950

1000

1050

1100

1150

1200

1250

Samples

Amplitude

Db4

J=3

J=4

J=5

J=6

J=7

ECG

0 200 400 600 800 1000

850

900

950

1000

1050

1100

1150

1200

1250

Samples

Amplitude

Db5

J=3

J=4

J=5

J=6

J=7

ECG

0 200 400 600 800 1000

850

900

950

1000

1050

1100

1150

1200

1250

Samples

Amplitude

Sym4

J=3

J=4

J=5

J=6

J=7

ECG

0 200 400 600 800 1000

850

900

950

1000

1050

1100

1150

1200

1250

Samples

Amplitude

Sym6

J=3

J=4

J=5

J=6

J=7

ECG

BIOSIGNALS2015-InternationalConferenceonBio-inspiredSystemsandSignalProcessing

250

Figure 8: CR of ECG record 100 vs. decomposition level

and wavelets.

Figure 9: PRD of ECG record 100 vs. decomposition level

and wavelets.

Figures 11 to 13 reflect the average CR, PRD

and QS of the ten ECG records. Figure 11 reveals

that the best CR value is of Sym4, which ranges

between 3.99:1 and 4.84:1. The average PRD,

shown in Figure 12, illustrates a gradual increase for

almost all of the wavelets. But the increase is found

to be a bit higher for Sym6 at higher decomposition

levels with a value of 1.46% at level 7. In terms of

the average QS, Sym4 shows the highest results

among all the decomposition level. Hence, it is

worthwhile to state that Sym4 reflects the best

compression performance.

The modified DWT-BFP-RLE performed better

compared to other well-known method as clearly shown in

Table 3. Two preserved bit-lengths I

values were tuned

to get the preferred compression performance.

Figure 10: Quality score (QS) of ECG record 100 vs.

decomposition level and wavelets. Note: surface plot axis

is rotated to provide better projection.

Figure 11: The average CR vs. decomposition level and

wavelets.

Db4

Db5

Sym4

Sym6

Levels

Wavelet

CR vs. Levels, Wavelet

Levels

Wavelet

3 4 5 6 7

Db4

Db5

Sym4

Sym6

CR vs. Levels, Wavelet

3.5

4.5

Db4

Db5

Sym4

Sym6

0.2

0.4

0.6

0.8

Levels

Wavelet

PRD %

PRD

PRD vs. Levels, Wavelet

Levels

Wavelet

3 4 5 6 7

Db4

Db5

Sym4

Sym6

PRD

PRD vs. Levels, Wavelet

0.4

0.5

0.6

0.7

0.8

0.9

Db4

Db5

Sym4

Sym6

Levels

Wavelet

QS vs. Levels, Wavelet

Levels

Wavelet

3 4 5 6 7

Db4

Db5

Sym4

Sym6

QS vs. Levels, Wavelet

Db4

Db5

Sym4

Sym6

3.5

4.5

Levels

Wavelet

CR vs. Levels, Wavelet

Levels

Wavelet

3 4 5 6 7

Db4

Db5

Sym4

Sym6

CR vs. Levels, Wavelet

3.5

4.5

Packet-size-ControlledECGCompressionAlgorithmbasedonDiscreteWaveletTransformandRunningLengthEncoding

251

Figure 12: The average PRD vs. decomposition level and

wavelets.

Figure 13: The average QS vs. decomposition level and

wavelets. Note: surface plot axis is rotated to provide

better projection.

4.3 Dynamic Compression

Sym4 mother wavelet and 4

level of decomposition

were selected to demonstrate the dynamic

compression scheme. From Figure 11, the average

CR using Sym4 wavelet and at J=4 is 4.61:1, which

corresponds to 305 of compressed samples.

Accordingly, the number of samples to be

Table

3: Performance Comparsion with Other Methods for

N=1024 and Duration of 10 Minutes (Sym4 and J=4).

Method Record CR PRD QS

SPIHT (Lu,

2000)

117

8.00:1 1.18% 6.78

Hilton (1997) 8.00:1 2.60% 3.08

Dojhon (1997) 8.00:1 3.90% 2.05

Proposed with

={1, 2, 2, 4,

8.07:1 0.95% 8.51

Proposed with

={1, 2, 2, 3,

8.30:1 1.14% 7.29

compressed was set to be Ns=256. The first 10

seconds of the ECG records 100, 117 and 119 were

used to test the dynamic compression scheme. The

available payload size (M) was assumed to be 70

bytes. Table 4 shows the number of compressed

packets generated for each record, the average CR of

these packets and the RPD between the original and

reconstructed signal. The number of packets

required to send 10 seconds of raw (un-compressed)

data is 103 packets (3,600 samples× 2 Bytes /70

Bytes), since each ECG sample is represented by 2

bytes. The efficiency of the dynamic compression

can be evaluated by calculating the percentage

amount of the packet reduction (PR) shown in (6).

%100





Raw

Compressed

Raw

(6)

where, N

Raw

and N

Compressed

are the number of raw

and compressed packets, respectively. It was found

that record 100 was segmented into 27 packets to

send 10 seconds of ECG data with an average CR of

3.02±1.65 and a high reduction of 73.79% in the

number of transmitted packets. The records and their

reconstructed signals are shown in Figure 14, where

the grid lines indicate the generated packets. The

visual results show acceptable results and confirm

the efficiency of the proposed method.

Table 4: Obtained parameters of the dynamic compression

scheme with Sym4 and J=4 (10 seconds for each record).

Record

No. of

Packets

Packet

Reduction

Average

CR ±



PRD

100 27 73.79% 3.02±1.65 0.46%

117 35 66.02% 2.62±1.09 0.47%

119 26 74.76% 3.24±1.43 0.85%

4 CONCLUSIONS

This paper presents a closed loop ECG compression

Db4

Db5

Sym4

Sym6

0.5

1.5

Levels

Wavelet

PRD

PRD vs. Levels, Wavelet

Levels

Wavelet

3 4 5 6 7

Db4

Db5

Sym4

Sym6

PRD

PRD vs. Levels, Wavelet

0.6

0.8

1.2

1.4

Db4

Db5

Sym4

Sym6

Levels

Wavelet

QS vs. Levels, Wavelet

Levels

Wavelet

3 4 5 6 7

Db4

Db5

Sym4

Sym6

QS vs. Levels, Wavelet

BIOSIGNALS2015-InternationalConferenceonBio-inspiredSystemsandSignalProcessing

252

algorithm based on modified discrete wavelet

transform (DWT), bit-field preserving (BFP) and

running-length encoding (RLE) methods. The closed

loop scheme is important for low-powered

telecardiology systems that have limited payload.

The proposed compression algorithm reveals a

dynamic scheme to subdivide the ECG data into

equal packets and apply compression on each packet

again until they fit into the provided payload. Based

on PRD, CR and QS, Sym4 and 4

level of

decomposition were adopted to implement the

dynamic

compression scheme. The proposed dynamic

scheme was tested on records 100, 117 and 119

using 10 seconds of data. The results showed that

the method can divide the ECG records to 27, 35 and

26 packets with an average CR of 3.02±1.65,

2.62±1.09 and 3.24±1.43 and PR of 73.79%, 66.02%

and 74.76% for records 100, 117 and 119,

respectively. The optimal CR and PRD can be

Moreover, a packetizing scheme of the compressed

data was proposed to have minimum headers and

more space for the compressed data. Nevertheless,

further improvement can be done on this method to

have higher CR and QS. Our future prospect is to

implement the method on ultra-low power hardware

since the initial indication shows promising results.

ACKNOWLEDGEMENTS

Authors would like to express sincere appreciation

to Qatar National Research Fund “NPRP Grant #4-

1207-2-474”and Sultan Qaboos University.

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Reconst ruct ed

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Erorr

No. Samples

OriginalReconstructed

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Error

No. Samples

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-80

Errorr

No. Samples

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BIOSIGNALS2015-InternationalConferenceonBio-inspiredSystemsandSignalProcessing

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