Exercise 8 Trellis-Coded Modulation in ATU · PDF file© Festo Didactic 39867-00 165 When you have completed this exercise, you will be familiar with the trellis-coded modulation.

© Festo Didactic 39867-00 165

When you have completed this exercise, you will be familiar with the trellis-coded modulation. You will be able to describe how trellis-coded modulation is implemented in ATU transmitters.

The Discussion of this Exercise covers the following points:

Introduction to the Trellis-Coded Modulation

Mapping by Set Partitioning

Selecting Points in Constellations for Each Pair of Tones

The Enhanced Immunity of TCM against Noise-Caused Errors

Trellis Encoder Block Diagram

4-D Cosets Used in ADSL Applications

Introduction to the Trellis-Coded Modulation

Convolutional coding of data is commonly used in data transmission systems to implement FEC, as mentioned earlier in this manual. This form of FEC is referred to as convolutional-coding FEC. In classic implementations of convolutional-coding FEC, the data to be transmitted is first coded using a convolutional encoder then the coded data is used directly (i.e., without any further processing) to apply digital modulation (e.g., BPSK, QPSK, QAM, etc.) to a carrier, as is shown in Figure 97. The data coding and digital modulation are thus performed independently of each other, i.e., as two separate operations with no specific relationship, in classic implementations of convolutional-coding FEC.

Figure 97. Classic implementation of convolutional-coding FEC in data transmission systems.

In 1982, the Austrian engineer Gottfried Ungerboeck published a paper describing the principles of the trellis-coded modulation (TCM). Ungerboeck’s research works demonstrated that combining coding with digital modulation in data transmission systems provides immunity against noise-caused errors that is higher than that which can be achieved in systems using classic implementations of convolutional-coding FEC. In other words, Ungerboeck demonstrated that TCM provides data transmission systems with error rates that are significantly lower than those which can be obtained in systems using classic implementations of convolutional-coding FEC.

In brief, the data coding and digital modulation are still two distinct operations in TCM, however, these operations are intimately linked to each other instead of being two unrelated operations as in classic implementations of convolutional-

Trellis-Coded Modulation in ATU Transmitters

Exercise 8

EXERCISE OBJECTIVE

DISCUSSION OUTLINE

DISCUSSION

Exercise 8 – Trellis-Coded Modulation in ATU Transmitters Discussion

166 © Festo Didactic 39867-00

coding FEC. Figure 98 is a simplified block diagram showing the implementation of TCM. The data to be transmitted is convolutionally encoded as before, but then, it is passed through an additional functional block, called constellation point selector, to obtain the data symbols that modulate the carrier (QAM is generally used in TCM). The point selection and the mapping of the data symbols to the point constellation are closely related to each other in TCM. These are the major differences between TCM and conventional implementations of convolutional-coding FEC.

Figure 98. Simplified block diagram showing the implementation of TCM.

Basically, two “active ingredients” make TCM perform better than conventional implementations of convolutional-coding FEC. First, TCM separates the point constellation into several smaller groups of points in such a way that the distance between points of a same group increases. This operation is generally referred to as mapping by set partitioning. Second, TCM applies convolutional coding to the data to be transmitted in order to limit the groups of points on the constellation that can be used at a given time to modulate tones. These aspects of TCM are further discussed in the rest of this discussion.

Mapping by Set Partitioning

a Although the number of bits allocated to each tone in ADSL applications is variable, the rest of this discussion assumes that all tones are allocated 4 bits each, thereby leading to the use of a 16-point constellation for each tone. This assumption greatly simplifies TCM analysis without detracting from a solid understanding of the underlying principles. Moreover, these principles can be applied directly to higher-order point constellations as well as cases where different numbers of bits are allocated to tones.

Figure 99 is an example that illustrates mapping by set partitioning. In this example, a 16-point constellation is divided into two groups of 8 points each then each group of 8 points is further divided into two groups to obtain 4 groups of 4 points each. The partitioning of points in this example is not arbitrary. The points are separated in such a way that the shortest distance (dmin) between points of a same group (coset) increases at each partition, thereby increasing the noise level required to cause a point in a coset to be mismatched with any other point in this coset. TCM uses this key feature of mapping by set partitioning to obtain a higher immunity against noise-caused errors in data transmission systems.

Notice that the convolutional

encoder and the constella-

tion point selector in

Figure 98 form what is usu-

ally called a trellis encoder.

Each group of points in a

constellation is commonly

referred to as a coset.



Figure 99. Mapping by set partitioning.

The 16-point constellation used in ADSL applications is shown in Figure 100. The mapping-by-set partitioning technique described above has been used to define this point constellation, as well as all other constellations employed in ADSL applications. Observe that the data symbols related to the 4 points shown in green in the constellation of Figure 100 all have the same two least significant bits (11), and that the other two bits in these data symbols form numbers whose decimal values are 0, 1, 2, and 3. These four points form a two-dimensional (2-D) coset. This coset is referred to as 2-D coset 3 (C2

3) because the decimal value defined by the 2 least significant bits of the data symbol of each point in this coset is 3.

Figure 100. Sixteen-point constellation used in ADSL applications.

Two-dimensional cosets are

often labeled C2X, where X

is the decimal value defined

by the 2 least significant bits

of the data symbols related

to each point in the coset.



The other 3 groups of 4 points shown in red, black, and blue in Figure 100 form 3 other cosets that are referred to as 2-D cosets 2, 1, and 0 (C2

2, C21, and C2

0), respectively. The four 2-D cosets in the 16-point constellation used in ADSL applications are shown on four different grids along with their labels in Figure 101. Together, these four 2-D cosets span all points in the 16-point constellation shown in Figure 100 with no overlap.

Figure 101. The four 2-D cosets in the 16-point constellation used in ADSL applications.

Close observation of the 16-point constellation shown in Figure 100 reveals that all points contiguous to a specific point in this constellation are part of 2-D cosets other than the 2-D coset in which this specific point lies. For instance, the point associated with data symbol 1010, which is part of C2

2, is surrounded by 8 points that are part of C2

0, C21, and C2

3. This observation is true for any point in any of the constellations used in ADSL. If noise is to cause occasional errors during data transmissions, these errors are more likely to be a displacement of the point received from the original point transmitted to any one of the 8 points surrounding this original point. In other words, occasional errors caused by noise are likely to cause the point received to be in a 2-D coset other than the 2-D coset in which the original point lies. This is another key feature of mapping by set partitioning which TCM uses to obtain higher immunity to errors in data transmission systems. This is covered later in this discussion.

Selecting Points in Constellations for Each Pair of Tones

The four 2-D cosets in the 16-point ADSL constellation shown in the previous section of this discussion can be matched in pair 16 different ways, i.e., C2

0 with C2

0, C20 with C2

1, C21 with C2

0, C20 with C2

2, C22 with C2

0, etc. This allows eight different four-dimensional (4-D) cosets, labeled C4

0 to C47, to be defined. Each of

these 4-D cosets consists of two pairs of 2-D cosets. Figure 102 shows 4-D coset 3 (C4

3) used in ADSL applications. This 4-D coset consists of the following two pairs of 2-D cosets: C2

2 with C20 and C2

1 with C23. The eight

4-D cosets that can be used in ADSL applications as defined by ITU-T Recommendation G.992.1 are shown at the end of this discussion.

Figure 102. Four-dimensional coset 3 (C43) used in ADSL applications.



When TCM is used in an ATU transmitter, i.e., when the trellis encoder is put to use in the constellation encoder, a single group of bits is extracted from the data frame buffer for each pair of tones. TCM uses bits u1, u2, and u3 extracted from the data frame buffer as well as the redundant check bit u0 produced by the convolutional encoder of the trellis encoder to match a pair of 2-D cosets in a 4-D coset with a pair of tones. The other bits extracted (u4 to uz) are used to select a specific point in each of the two 2-D cosets selected. For instance, let assume that the two tones in a pair are allocated 4 bits each and bits u7 to u1 extracted for this pair of tones and bit u0 calculated by the convolutional encoder are as shown in the following table.

u7 u6 u5 u4 u3 u2 u1 u0

1 0 0 0 1 1 0 1

The decimal value of bits u2, u1, and u0, is used to select one of the eight different 4-D cosets available. In the present example, 4-D coset 5 (C4

5) is selected because the decimal value of bits u2, u1, and u0 (101) is 5. This 4-D coset is shown below.

C45 = (C2

0 × C21) U (C2

3 × C22)

C20 C2

1 C23 C2

2

PAIR OF 2-D COSETS A PAIR OF 2-D COSETS B

The value of bit u3 is used to choose either one of the two pairs of the 2-D cosets in the selected 4-D coset. When bit u3 is equal to 0, the pair of 2-D cosets labeled A is selected. On the other hand, when bit u3 is equal to 1, the pair of 2-D cosets labeled B is selected. In the present example, bit u3 is equal to 1 and the pair of 2-D cosets labeled B is selected. This pair of 2-D cosets consists of C2

3 and C22, as shown below. The first 2-D coset in the selected pair (C2

3 in the present example) is associated with the first tone in a pair, and the second 2-D coset in the selected pair (C2

2 in the present example) is associated with the second tone in this pair.

C45 = (C2

0 × C21) U (C2

3 × C22)

C20 C2

1 C23 C2

2


The other bits extracted for a pair of tones, i.e., bits u4 to uz, are used to select a specific point in each of the two 2-D cosets selected for a pair of tones. In other words, these bits are used to determine the exact point that is selected for each of the two tones in a pair. Bit u4 and a certain number of the next bits extracted are used to choose a specific point in the 2-D coset selected for the first tone in a pair. The remaining extracted bits up to bit uz are used to choose a specific point in the 2-D coset selected for the second tone in this pair. In the present example,



bits u5 and u4, which are both equal to 0, are used to choose a specific point in the 2-D coset (C2

3) selected for the first tone in the pair. This selects the point shown in green in C2

3 of the 4-D coset shown below. The data symbol related to this point, according to the 16-point constellation shown in Figure 100, is 0011. Notice that the decimal value (3) of the two LSB’s in this data symbol corresponds to the index (3) of the 2-D coset (C2

3) selected for the first tone in the pair. Finally, bits u7 and u6, which are equal to 1 and 0, respectively, are used to choose a specific point in the 2-D coset (C2

2) selected for the second tone in the pair. This selects the point shown in red in C2

2 of the 4-D coset shown below. The data symbol related to this point, according to the 16-point constellation shown in Figure 100, is 1010. Notice that the decimal value (2) of the two LSB’s in this symbol corresponds to the index (2) of the 2-D coset (C2

2) selected for the second tone in the pair.

C45 = (C2

0 × C21) U (C2

3 × C22)

C20 C2

1 C23 C2

2


The Enhanced Immunity of TCM against Noise-Caused Errors

The constellation point selection described in the previous section of this discussion is directly responsible for the enhanced immunity against noise-caused errors that TCM provides to data transmission systems. In systems using TCM, the 2-D coset recognition at reception is the most at risk of being in error. This is because any point received only needs to be perceived as any one of the points contiguous to the original point transmitted to cause the 2-D coset recognized to be in error (remember that all point contiguous to a specific point in a constellation are part of 2-D cosets other than the 2-D coset in which this specific point lies). An error affecting any one of the two 2-D cosets recognized for a pair of tones automatically results in an error in the 4-D coset recognized. However, since convolutional coding is applied to bits u2, u1, and u0 used to select a 4-D coset, any error in the recognition of a 4-D coset causes a discontinuity in the path traced through the trellis diagram. This discontinuity is detected at reception, and the error can be corrected within certain limits (this is studied in the next exercise). In brief, TCM applies convolutional coding only to the bits used to select 4-D cosets because these bits are the most at risk of being incorrectly recognized at reception.

Bits u4 to uz, i.e., the bits which are used to choose a specific point in each of the two 2-D cosets selected for a pair of tones are not protected by convolutional coding. This is because these bits are less subject to noise-caused errors that can occur during transmission since the spacing between points of the same 2-D coset is twice that of contiguous points in the constellation. However, when noise is strong enough to shift the point received in such a way that it is mixed with another point of the same 2-D coset, an error occurs that cannot be corrected by the Viterbi decoder in the receiver (this is studied in the next exercise). Bit u3, like bits u4 to uz, is not protected by convolutional coding for other reasons explained below.



Bit u3 chooses a pair of 2-D cosets in the 4-D coset selected for a pair of tones. Close inspection of the eight 4-D cosets at the end of this discussion reveals that the binary numbers that represent the indices of the 2-D cosets in pair A are the complement of the binary numbers that represent the indices of the 2-D cosets in pair B. In 4-D coset 1 for instance, the indices of the 2-D cosets in pair A are 00 and 10, while the indices of the 2-D cosets in pair B are 11 and 01. Therefore, the indices of both 2-D cosets recognized at reception for a pair of tones must be complemented for the pair of 2-D cosets A to be taken for the pair of 2-D cosets B and vice versa. Furthermore, the distance between a specific point in the constellation and any contiguous point located in a 2-D coset having a complementary index is 2 times the minimum spacing (d0) between contiguous points in the constellation, as is illustrated in Figure 103. Together, these factors decrease the chances that noise causes errors on bit u3.

Figure 103. Distance between a point in the constellation and contiguous points located in complementary 2-D cosets.

Trellis Encoder Block Diagram

This section describes how, in practice, two points are selected in the constellation for each pair of tones. Figure 104 shows the block diagram of the Trellis Encoder used in the ATU-R Transmitter of our ADSL application.

a The operation of the Convolutional Encoder shown in the block diagram of Figure 104 is covered in the previous exercise.



Figure 104. Detailed block diagram of the Trellis Encoder of the ATU-R Transmitter in our ADSL application.

Bits u0 to u3 are used to select a pair of 2-D cosets in one of the eight 4-D cosets available. The 2-D Coset Selector in the Trellis Encoder converts bits u0 to u3 into a group of 2 bits labeled v1 and v0, and a second group of 2 bits labeled w1 and w0. Bits v1 and v0 form a number whose decimal value corresponds to the index of the 2-D coset selected for the first tone in a pair while bits w1 and w0 form a number whose decimal value corresponds to the index of the 2-D coset selected for the second tone in this pair. For instance, when bits u3, u2, u1, and u0, are respectively equal to 1, 0, 1, and 1, the pair of 2-D cosets B in 4-D coset 3 is selected. In other words, 2-D coset 1 is selected for the first tone in the pair and 2-D coset 3 is selected for the second tone in the pair. In this case, bits v1 and v0 are respectively equal to 0 and 1 while bits w1 and w0 are both equal to 1. Table 6 shows the relationship between bits u0 to u3 at the 2-D Coset Selector input and bits v1, v0, w1, and w0 at the 2-D Coset Selector output. The 2-D Coset Selector can be implemented using a look-up table or combinatory logic and the following linear equations:

311 uuv (2)

30 uv (3)

32101uuuuw (4)

320 uuw (5)

The 2-D Coset Selector and

Bit Concatenator in

Figure 104 form what is

called a Constellation Point

Selector in the block dia-

gram of Figure 98.



Table 6. ADSL coset conversion table.

4-D COSET u3 u2 u1 u0 v1 v0 w1 w0 PAIR OF 2-D COSETS

C40 0 0 0 0 0 0 0 0 C2

0 × C20

1 0 0 0 1 1 1 1 C23 × C2

3

C44 0 1 0 0 0 0 1 1 C2

0 × C23

1 1 0 0 1 1 0 0 C23 × C2

0

C42 0 0 1 0 1 0 1 0 C2

2 × C22

1 0 1 0 0 1 0 1 C21 × C2

1

C46 0 1 1 0 1 0 0 1 C2

2 × C21

1 1 1 0 0 1 1 0 C21 × C2

2

C41 0 0 0 1 0 0 1 0 C2

0 × C22

1 0 0 1 1 1 0 1 C23 × C2

1

C45 0 1 0 1 0 0 0 1 C2

0 × C21

1 1 0 1 1 1 1 0 C23 × C2

2

C43 0 0 1 1 1 0 0 0 C2

2 × C20

1 0 1 1 0 1 1 1 C21 × C2

3

C47 0 1 1 1 1 0 1 1 C2

2 × C23

1 1 1 1 0 1 0 0 C21 × C2

0

The Bit Concatenator combines bits v1, v0, w1, and w0 produced by the 2-D Coset Selector with the other bits extracted for a pair of tones, i.e., bits u4 to uz, to obtain the data symbol associated with each tone in the pair. For example, when each of the two tones in a pair is allocated 4 bits, 7 bits labeled u1 to u7 are extracted from the data frame buffer. The Bit Concatenator combines bits v1 and v0 with bits u5 and u4 to obtain the data symbol (u5, u4, v1, v0) for the first tone in a pair. Similarly, the Bit Concatenator combines bits w1 and w0 with bits u7 and u6 to obtain the data symbol (u7, u6, w1, w0) for the second tone in the pair. Each of these data symbols selects a specific point in the constellation for the corresponding tone in the pair.

4-D Cosets Used in ADSL Applications

4-D Coset 0

C40 = (C2

0 × C20) U (C2

3 × C23)

C20 C2

0 C23 C2

3




4-D Coset 1

C41 = (C2

0 × C22) U (C2

3 × C21)

C20 C2

2 C23 C2

1


4-D Coset 2

C42 = (C2

2 × C22) U (C2

1 × C21)

C22 C2

2 C21 C2

1


4-D Coset 3

C43 = (C2

2 × C20) U (C2

1 × C23)

C22 C2

0 C21 C2

3


4-D Coset 4

C44 = (C2

0 × C23) U (C2

3 × C20)

C20 C2

3 C23 C2

0


Exercise 8 – Trellis-Coded Modulation in ATU Transmitters Procedure Outline


4-D Coset 5

C45 = (C2

0 × C21) U (C2

3 × C22)

C20 C2

1 C23 C2

2


4-D Coset 6

C46 = (C2

2 × C21) U (C2

1 × C22)

C22 C2

1 C21 C2

2


4-D Coset 7

C47 = (C2

2 × C23) U (C2

1 × C20)

C22 C2

3 C21 C2

0


The Procedure is divided into the following sections:

Equipment Setup and Connections

Applying TCM to an Arbitrary Data Sequence

Comparing the Calculated Results with those Obtained Using the ATU-R Transmitter

Equipment Setup and Connections

1. Turn on the RTM Power Supply and the RTM and make sure the RTM power LED is lit.

2. Turn on the host computer. Make sure that the system has been installed and configured as described in the Communications Technologies Training System User Guide.

3. Start the LVCT software.

PROCEDURE OUTLINE

PROCEDURE

Exercise 8 – Trellis-Coded Modulation in ATU Transmitters Procedure


In the Application Selection dialog box, choose ADSL and click OK. This begins a new session with all settings set to their default values and with all faults deactivated. The System Diagram appears showing the ATU-R Transmitter and the ATU-C Receiver.

4. Make the Default external connections shown on the System Diagram tab of the ADSL application. For details of connections to the Reconfigurable Training Module, refer to the RTM Connections tab of the software.

Applying TCM to an Arbitrary Data Sequence

5. Display the block diagram of the ATU-R Transmitter by clicking the corresponding tab in the ADSL application.

Use the Pan and Zoom commands to display the portion of the ATU-R Transmitter shown in Figure 105.

Figure 105. Portion of the ATU-R Transmitter block diagram showing the data frame buffer and the Constellation Encoder.

Turn the Scrambler off by changing the Scrambler / Descrambler setting to Off in the ADSL Settings table.

Enable TCM in the ADSL application by setting the Trellis Encoder / Viterbi Decoder parameter in the ADSL Settings table to On.

b TCM can also be enabled by clicking the Trellis Encoder ON/OFF button in the ATU-R Transmitter or the Viterbi Decoder ON/OFF button in the ATU-C Receiver.

6. Select the Frame Step mode by clicking the Frame Step button ( ) in the ADSL application toolbar.

Click the Edit button in the Bit/Tone Table. This opens the Bit/Tone Table window. Set the number of bits allocated to all tones to 4 by entering 4 in the



data field next to the Apply to All Tones button, click this button, and click the Apply button located at the bottom of the Bit/Tone Table window.

Observe that the total number of bits allocated to all tones is equal to 96, which is equivalent to 12 bytes. However, since 16 bits are used by TCM, only 80 data bits (10 data bytes) can be extracted from the data frame buffer every data frame. It is the price to pay to implement this type of convolutional-coding FEC.

Close the Bit/Tone Table window.

7. Click the Frame Step button once to transmit a data frame.

Click the switch located just before DP2 to open the path between the Byte Multiplexer and the Scrambler.

Double click DP2 in the ATU-R Transmitter block diagram to open the corresponding data point window. This window displays the data at the Byte Multiplexer output (Scrambler input) for one data frame.

Edit the 10 data bytes in the DP2 window so that they are identical to the arbitrary data sequence shown in Figure 106. Click the Record button in the DP2 window to record the new values of the 10 data bytes. This arbitrary data sequence will be transmitted at the next data frame.

Figure 106. Arbitrary data sequence used to verify TCM in the ATU-R Transmitter.

8. Double click DP6 in the ATU-R Transmitter block diagram to open the corresponding data point window. This window displays the Ordered Tone Table.

Using the above data sequence and the information in the Ordered Tone Table, determine the values of bits u1 to u7 that will be extracted for each pair of tones. Record your result in Table 7.

a For the last two pairs of tones in the data frame, bits u1 and u2 are not extracted from the data frame buffer.



Table 7. Extracted Bit Table.

PAIR OF TONES EXTRACTED BITS

-- u7 u6 u5 u4 u3 u2 u1

1

2

3

4

5

6

7

8

9

10

11

12



9. For each of the first 10 pairs of tones, copy the values of bits u1 and u2 that you recorded in Table 7 to Figure 107.

Figure 107. Predicting how the Convolutional Encoder of the Trellis Encoder in the ATU-R Transmitter will encode the arbitrary data sequence shown in Figure 106.

For the first ten pairs of tones in the data frame, determine the successive states to which the Convolutional Encoder will step to. Record your results in the trellis diagram of Figure 107.



For the last two pairs of tones in the data frame, find the two states that the Convolutional Encoder must pass through to return to state 0h, and deduce the values of bits u0, u1, and u2. Record your results in Figure 107.

Draw the path followed by the Convolutional Encoder in the trellis diagram of Figure 107.

Indicate beside each state transition you drew in Figure 107 the value of the binary number formed by bits u2, u1, and u0 at each bit extraction (i.e., before each state transition). Also indicate at the bottom of the trellis diagram in Figure 107 the values of bits u2, u1, and u0 after each state transition.

10. Use the values of bits u0, u1, and u2 (Convolutional Encoder output) that you recorded at the bottom of the trellis diagram in Figure 107 to determine the 4-D coset that will be selected for each pair of tones. Record your results in Table 8.

Use the value of bit u3 that you recorded in Table 7 for each pair of tones to determine the pair of 2-D cosets (A or B) that will be chosen in each 4-D cosets selected. Record your results in Table 8.

Knowing the pair of 2-D coset selected in each 4-D coset, determine the index of the 2-D coset associated with each tone in a pair. Record your results in Table 8.

Table 8. Coset Selection Table.

PAIR OF TONES 4-D

COSET PAIR OF

2-D COSETS

2-D COSET INDICES

1ST TONE 2ND TONE

1

2

3

4

5

6

7

8

9

10

11

12



11. Use the values of bits u4 to u7 recorded in Table 7 and the 2-D coset indices recorded in Table 8 to determine the data symbol that will be produced for each of the two tones in each pair. Record your results in Table 9.

Table 9. Data Symbol Table.

PAIR OF

TONES

DATA SYMBOLS

1ST TONE 2ND TONE

1

2

3

4

5

6

7

8

9

10

11

12

Comparing the Calculated Results with those Obtained Using the ATU-R Transmitter

12. Double click DP5 in the ATU-R Transmitter block diagram to open the corresponding data point window. This window displays the data at the input of the Constellation Encoder for one data frame.

Display the detailed block diagram of the Bit Extractor and Trellis Encoder.

Double click DP14 and DP16 in the detailed block diagram of the Bit Extractor and Trellis Encoder to open the corresponding data point windows. These windows display the data at the outputs of the Bit Extractor and Convolutional Encoder for one data frame.

Double click DP15 in the detailed block diagram of the Bit Extractor and Trellis Encoder to open the corresponding data point window. This window displays the sequence of states followed by the Convolutional Encoder during a data frame.

13. Click the Frame Step button once to transmit one more data frame that contains the arbitrary data sequence entered in the DP2 window.

Exercise 8 – Trellis-Coded Modulation in ATU Transmitters Conclusion


For each pair of tones, compare the values of bits u1 to u7 that you recorded in Table 7 with the bits at the Bit Extractor Output (DP14). Are they identical?

Yes No

Observe the successive states which the Convolutional Encoder followed to encode the arbitrary data sequence (these states are displayed in the DP15 window). Do they match the sequence of states defined by the path you drew in the trellis diagram of Figure 107?

Yes No

For each of the pairs of tones in the data frame, compare the values of bits u2, u1 and u0 at the Convolutional Encoder Output (DP16) with the corresponding values that you recorded at the bottom of the trellis diagram in Figure 107. Are they identical?

Yes No

14. Close the DP14 and DP15 windows as well as the Ordered Tone Table (DP6 window).

Double click DP17 and DP18 in the detailed block diagram of the Bit Extractor and Trellis Encoder to open the corresponding data point windows. These windows display the data at the outputs of the 2-D Coset Selector and Bit Concatenator (Trellis Encoder Output) for one data frame.

For each pair of tones, compare the 2-D coset indices of the first and second tones that you recorded in Table 8 with those shown at the 2-D Coset Selector Output (DP17). Are they identical?

Yes No

For each pair of tones, compare the data symbols of the first and second tones that you recorded in Table 9 with those shown at the Trellis Encoder Output (DP18). Are they identical?

Yes No

15. When you have finished using the system, exit the LVCT software and turn off the equipment.

In this exercise, you learned that TCM is a form of convolutional-coding FEC used in data transmission systems to improve the immunity against noise-caused errors. You saw how TCM is implemented in ATU transmitters. You learned why TCM provides an enhanced immunity against noise-caused errors. You determined the data symbols that should be produced for all tones when an arbitrary data frame is transmitted by an ATU transmitter using TCM. You compared the data symbols you determined with those produced when the same arbitrary data frame is transmitted by the ATU-R Transmitter of our ADSL application.

CONCLUSION

Exercise 8 – Trellis-Coded Modulation in ATU Transmitters Review Questions


1. Briefly describe the main differences between TCM and classic implementations of convolutional-coding FEC.

2. Describe what is mapping by set partitioning.

3. What is the main benefit related to mapping by set partitioning? Explain briefly.

4. Briefly explain why the 2-D coset recognition at reception is the most at risk of being in error in ADSL applications using TCM.

REVIEW QUESTIONS

Exercise 8 – Trellis-Coded Modulation in ATU Transmitters Review Questions


5. Briefly explain why TCM in ADSL applications applies convolutional coding to bits u1 and u2 only.

Exercise 8 Trellis-Coded Modulation in ATU · PDF file© Festo Didactic 39867-00 165 When you have completed this exercise, you will be familiar with the trellis-coded modulation.

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