TRELLIS CODED MODULATION

Seminar report On Trellis coded modulation

SUBMITTED TO: Nisha Gupta ELECTRONICS & COMMUNICATION DEPT. NIT KURUKSHETRA SUBMITTED BY: RAMNEEK BANSAL 107440 ECE-4 ELECTRONICS & COMMUNICATION DEPT.

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ABSTRACT This report describes basic framework of TCM, which have very good performance as comparison to conventional coding in case of bandlimited channels by just increasing the number of symbols instead of increasing symbol rate. And it also explain that in TCM coding and modulation occurs simultaneously while in conventional and convolutional coding first coding is done then modulation occurs. QAM and PSK are also briefly explained as TCM is widely used with them. There is a practical example of TCM in the end which briefly explains all key aspects of  TCM that is trellis encoding, trellis decoding, mapper and set partitioning

ABBREVIATIONS

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1. TCM –Trellis Code Modulation 2. ACG – Asymptotic Coding Gain 3. AWGN –Additive white Gaussian Noise 4.

SED – Squared Euclidian Distance

5.

MSED – Minimum Squared Distance

6.

SSED – Sum of Squared Euclidean Distance

7.

SNR – Signal To Noise Ratio

8. QAM – Quadrature Amplitude modulation 9. PSK – Phase Shift Key 10. BPSK – Binary Phase Shift Key 11. QPSK – Quadrature Phase Shift Key 12. ASK – Amplitude Shift Key 13. FSK – Frequency Shift Key 14. BER – Bit Error Rate

INDEX 3

1 Introduction…………………………………………........................................5 1.1 Features of Channel Coding…………………………………………5 1.2 TCM Introduction…………………………………………………...6 2 TCM…………………………………………………………………………....8 2.1 History of TCM……………………………………………………….8 2.2 Basic Concepts………………………………………………..…...…9 2.2.1 Euclidean Distance…………………………………………9 2.2.2 Hamming Distance…………………………………………9 2.3 Basics Principles of TCM…………………………………………....11 2.4QAM………………………………………………..………………..12 2.5 PSK………………………………………………………………….13 2.5.1 Binary Phase Shift Keying (BPSK) ………..……………..13 2.5.2 Quadrature Phase Shift Keying (QPSK) ……………….....15 2.6 TCM in QAM and PSK……………………………………………..16 2.7 Coding Gain…………………………………………………………18 3 Implementation………………………………………………………………...19 3.1 Basic Philosophy…………………………………………………….19 3.2 Trellis Encoding 3.2.1 Trellis Encoder…………………………………………….19 3.2.2 Trellis State Diagram………………………………………20 3.2.3 Set Partitioning……………………………………………..21 3.2 Trellis Decoding……………………………………………………..22 3.2.1 Viterbi Decoding…………………………………………..24 4. Applications of Trellis Coded Modulation…………………………………...25 4.1 Applications in Wireline Communications………………………….25 4.1.1 Adsl………………………………………………………..25 4.1.2 Data/Fax Modem…………………………………………..25 4.1.3 Cable Modem………………………………………………25 4.1.4 Ethernet…………………………………………………….25 4.2 Applications In Wireless Communications………………………….26 4.2.1 Wi-Fi………………………………………………………..26 4.2.2 Wimax………………………………………………………26 4.2.3 Wpan………………………………………………………..26 4.2.4 Uwb………………………………………………………...26 4.2.5 Satellite Communications…………………………………..26 5 Conclusion……………………………………………………………………...27 6 References……………………………………………………………………...28

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1 INTRODUCTION The aim of channel encoding theory is to find codes which transmit quickly, contain many valid code words and can correct or at least detect many errors. These aims are mutually exclusive however, so different codes are optimal for different applications. The needed properties of this code mainly depend on the probability of errors happening during transmission.[1] The term algebraic coding theory denotes the sub-field of coding theory where the  properties of codes are expressed in algebraic terms and then further researched. Algebraic Coding theory, is basically divided into two major types of codes 1. Linear block codes 2. Convolution codes 1.1 FEATURES OF CHANNEL CODING

• Information theory tells us that for optimal communications we should design long sequences of signals, with maximum separation among them; and at the receiver we should perform decision making over such long signals rather than individual bits or  symbols. • If this process is done properly, then the message error probability will decrease exponentially with sequence length, n provided that the rate R is less than R0, which in turn is less than the Shannon Capacity. −

 P e

≈

e

2

d min 2

2σ  

…………. 1.1

• This is the idea behind coding. In conventional coding, the coding is separate from modulation . Coding occurs at the digital level, before modulation and generally involves adding bits to the input sequence. The resultant redundancy requires added bandwidth. • At the receiver, hard decoding occurs after demodulation. The decoding operation is based on hard decisions, since a digital bit (or symbol) stream fees the decoder and is either in error or not. Decoding can also be done based on the analog received samples, and this is called soft decoding. The theoretical loss due to hard [vs. soft] decoding leads to a ~2dB performance loss.[5]

1.2 TCM INTRODUCTION

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TCM uses many diverse concepts from signal processing. In simplest terms it is a combination of coding and modulation, hence it name TCM where the word trellis stands for the use of trellis (also called convolutional) codes. Whereas we normally talk about coding and modulation as two independent aspects of the communications link, in TCM they are combined. TCM is a complex concept to understand particularly due to the nonlinear nature of the performance. It uses ideas from modulation and coding as well as dynamic programming, lattice structures and matrix math. A convolutional code that has optimum performance when used independently may not be optimum in TCM. Gray coding is helpful in uncoded signaling and constellation mapping, but not always so in TCM.[3] It uses concepts of convolutional codes, trellis, lattice, cossets, and cosset generators. Communications theory says that it is best to design codes in long sequences of  messages. The allowed sequences should be very different from each other. The receiver  can then make a decision between sequences using their statistics rather than on symbol by-symbol basis. When decoding this way, the probability of error is an inverse function of the sequence length. In general form the probability of error between sequences is given by the expression

−

 P e

≈

e

2

d min 2

2σ  

………….1.2

where dmin is the sequence Euclidean distance between sequences and is ó2 the noise  power. We measure the performance of TCM (and many other schemes) by ACG. This is the gain obtained over some baseline performance at high SNR in a Gaussian environment. ACG is not achievable in practice because we do not transmit signals at high SNRs, have hardware and channel imperfections that depart from AWGN assumptions. So recognize that all gains quoted herein are maximum possible only in theory.[3]

The functions of a TCM consist of a Trellis code and a constellation mapper as shown in Figure TCM combines the functions of a convolutional coder of rate and a M-ary signal mapper  that maps input points into a larger constellation of constellation points.[3]

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FIGURE 1.1 A general trellis coded modulation

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2 TCM 2.1 HISTORY OF TCM

FIGURE 2.1 History of TCM

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2.2 BASIC CONCEPTS 2.2.1 EUCLIDEAN DISTANCE While representing two signals in the Euclidean space as linear combination of M orthonormal basis functions.[4] A straight line distance between any two points is called the Euclidean distance. For a  point p1 at (x1, y1) and another point p2 at (x2, y2), the Euclidean distance is given by the familiar formula 2

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…………….2.1 It is implicit that this distance is the shortest distance between these points. The Euclidean distance is an analog concept, the very concept of distance that we normally use day-to-day in the world of real numbers. For signals, we define this distance in the IQ plane. In Figure 1 we have a 8PSK signal constellation. The radius is equal to 1 and represents the maximum amplitude. Each point of the constellation is a certain combination of a particular  amplitude and phase. The distance between these points is can be measured in the manner  described above and these are given in the Figure below. The distances given in Figure 1 are squared and are called SED. The smallest of these distances is called the MSED, designated as for a particular constellation.[3] ( X  1

−  X  2

)

+

(Y 1

− Y 2

)

FIGURE 2.2 8 PSK constellation and squared Euclidean distances between symbols

2.2.2 HAMMING DISTANCE

Just as real numbers have a concept of distance, so do the binary numbers. Take two  binary numbers, 011011 and 101101. The distance between these is the number of places these two numbers differ. And that number is 4. This distance is called the Hamming distance  between these numbers. The distance would be zero, if these two numbers were the same. A zero distance means the numbers are the same, same interpretation as in Euclidean concept of distance. We distinguish these two types of distances by recognizing that one belongs to the analog world of real numbers and the other to the  binary world. Both concepts are useful in signal processing.

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In coding Hamming distance is most often used as a performance metric whereas it is Euclidean distance in the analog world.[3]

Distance between sequences We can also talk about Euclidean distances between sequences  by comparing distances  between corresponding points of the sequences. Let’s take for example an 8PSK signal that consists of a sequence of these symbols.[3] S0 S3 S2 S1 S0 In bits, we can map these as: 000 011 010 101 100 000

FIGURE 2.3 Euclidean and sequence Hamming distance

The Euclidean distance for this sequence is the distance between each symbol in this sequence and a reference sequence. If we designate the all-zero-symbols as the reference sequence, then the squared Euclidean distance (SED) is the distance between each one of these symbols and the symbol S0. s0 to s0 = 0.0, s0 to s1 = .586, s0 to s2 = 2.0, s0 to s3 = 3.414 The SSED, also called d2 free of this sequence, from the all zero sequence is 3.414 + 2.0 + 0.586 = 6.0 This cumulative distance gives a feeling of how easy or difficult it would be to mistake one sequence for another. For the reference sequence we could have used any other  sequence than the all zero, and the results would be the same. However using an all-zero sequence is convenient and conventional.[3]

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2.3 BASIC PRINCIPLES OF TCM

• The key idea is that the operations of [baseband] modulation and coding are combined. • The bandwidth is not expanded: same symbol rate, but redundancy is introduced by using a constellation with more points than wo uld be required without coding.  – Typically, the number of points is doubled  – The symbol rate is unchanged  – The power spectrum is unchanged • Since there are more possible points per symbol, it may appear that the error probability would increase for a given S/N. • As in conventional coding, dependencies are introduced among different symbols ---only certain sequences of successive constellation points are allowed. • By properly making use of these constraints during reception, the error probability actually decreases. • A measure of performance improvement is the coding gain, which is the difference in S/N between a coded and uncoded system of the same information rate that produces the same error probability. • It can be shown for the Gaussian channel that there is an input discrete alphabet that has capacity very close to the capacity with continuous inputs • As shown on the next chart, an eight- level system can achieve a capacity of  2 bits/symbol • This suggests that it is only necessary to double the signal constellation to get good coding gains (increasing the signal alphabet will not improve the coding gain) • The bandwidth has not been expanded (same symbol rate)[5]

FIGURE 2.4 TCM

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2.4 QAM

Quadrature amplitude modulation (QAM) is a modulation scheme in which two sinusoidal carriers, one exactly 90 degrees out of phase with respect to the other, are used to transmit data over a given physical channel. Because the orthogonal carriers occupy the same frequency band and differ by a 90 degree phase shift, each can be modulated independently, transmitted over the same frequency band, and separated by demodulation at the receiver. For a given available bandwidth, QAM enables data transmission at twice the rate of standard pulse amplitude modulation (PAM) without any degradation in the bit error rate (BER). QAM and its derivatives are used in both mobile radio and satellite communication systems. You can use the numerically controlled oscillator (NCO) Compiler to design a dualoutput oscillator that accurately generates the in-phase and quadrature carriers used by a QAM modulator. The carrier frequency of each sinusoid can be set to any precision by defining the phase increment input to the NCO. A block diagram of the QAM modulator  is shown Figure 1. A raised cosine finite impulse response (FIR) filter is used to filter the data streams before modulation onto the quadrature carriers. When passed through a  band-limited channel, rectangular pulses suffer from the effects of time d ispersion and tend to smear into one another. This pulse shaping filter eliminates inter-symbol interference by ensuring that at a given sampling instance, the contribution to the response from all other symbols is zero.[6]

FIGURE 2.5 quadrature modulator 

The motivation for QAM comes from the fact that a DSBSC signal occupies twice the   bandwidth of the message from which it is derived. This is considered wasteful of  resources. QAM restores the balance by placing two independent DSBSC, derived from 12

message #1 and message #2, in the same spectrum space as one DSBSC. The bandwidth imbalance is removed. In digital communications this arrangement is p opular. It is used because of its bandwidth conserving (and other) properties. The QAM modulator is so named because, in analog applications, the messages do in fact vary the amplitude of each of the DSBSC signals. In QPSK the same modulator is used, but with binary messages in both the I and Q channels, as describe above. Each message has only two levels, ±V volt. For a non-bandlimited message this does not vary the amplitude of the output DSBSC. As the message changes polarity this is interpreted as a 1800 phase shift, given to the DSBSC.

2.5 PSK  Phase-shift keying (PSK) is a digital modulation scheme that conveys data by changing, or modulating, the phase of a reference signal (the carrier wave). Any digital modulation scheme uses a number of distinct signals to represent digital data. In the case of PSK, a finite number of phases are used. Each of these phases is assigned a unique pattern of binary bits. Usually, each phase encodes an equal number of bits. Each   pattern of bits forms the symbol that is represented by the particular phase. The demodulator, which is designed specifically for the symbol-set used by the modulator, determines the phase of the received signal and maps it back to the symbol it represents, thus recovering the original data. This requires the receiver to be able to compare the  phase of the received signal to a reference signal — such a system is termed coherent.[7] 2.5.1 BPSK  There are three major classes of digital modulation techniques used for transmission of  digitally represented data: • ASK  • FSK  • PSK  All convey data by changing some aspect of a base signal, the carrier wave, (usually a sinusoid) in response to a data signal. In the case of PSK, the phase is changed to represent the data signal. There are two fundamental ways of utilizing the phase of a signal in this way: • By viewing the phase itself as conveying the information, in which case the demodulator must have a reference signal to compare the received signal's phase against; or  • By viewing the change in the phase as conveying information — differential schemes, some of which do not need a reference carrier (to a certain extent). A convenient way to represent PSK schemes is on a constellation diagram. This shows the points in the Argand plane where, in this context, the real and imaginary axes are termed the in-phase and quadrature axes respectively due to their 90° separation. Such a representation on perpendicular axes lends itself to straightforward implementation. The

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amplitude of each point along the in-phase axis is used to modulate a cosine (or sine) wave and the amplitude along the quadrature axis to modulate a sine (or cosine) wave. In PSK, the constellation points chosen are usually positioned with uniform angular  spacing around a circle. This gives maximum phase-separation between adjacent points and thus the best immunity to corruption. They are positioned on a circle so that they can all be transmitted with the same energy. In this way, the moduli of the complex numbers they represent will be the same and thus so will the amplitudes needed for the cosine and sine waves. Two common examples are BPSK which uses two phases, and QPSK which uses four phases, although any number of phases may be used. Since the data to be conveyed are usually binary, the PSK scheme is usually designed with the number of  constellation points being a power of 2.

FIGURE 2.6 Constellation diagram for BPSK.

BPSK is the simplest form of PSK. It uses two phases which are separated by 180° and so can also be termed 2-PSK. It does not particularly matter exactly where the constellation points are positioned, and in this figure they are shown on the real axis, at 0° and 180°. This modulation is the most robust of all the PSKs since it takes serious distortion to make the demodulator reach an incorrect decision. It is, however, only able to modulate at 1bit/symbol (as seen in the figure) and so is unsuitable for high data-rate applications.

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2.5.2 QPSK 

FIGURE 2.7 Constellation diagram for QPSK with Gray coding.

Sometimes known as quaternary or quadriphase PSK or 4-PSK, QPSK uses four points on the constellation diagram, equispaced around a circle. With four phases, QPSK can encode two bits per symbol, shown in the diagram with Gray coding to minimize the BER — twice the rate of BPSK. Analysis shows that this may be used either to double the data rate compared to a BPSK system while maintaining the bandwidth of the signal or to maintain the data-rate of BPSK but halve the bandwidth needed. can be viewed as a quaternary modulation, it is easier to see it as two independently modulated quadrature carriers. With this interpretation, the even (or odd) bits are used to modulate the in-phase component of the carrier, while the odd (or even) bits are used to modulate the quadrature-phase component of the carrier. BPSK is used on both carriers and they can be independently demodulated. As a result, the probability of bit-error for QPSK is the same as for BPSK:

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2.6 TCM IN QAM AND PSK 

• Given a channel with a bandwidth limitation, first determine the maximum symbol rate that can be transmitted. • Determine the size of the alphabet, which is needed to produce the desired bit rate. • Double the size of the constellation and introduce a channel coder that produces one extra bit • The coder need not code all the incoming bits • There are many ways to map the coded bits into symbols. The choice of mapping will drastically affect the performance of the code. • Ungerboeck produced a good heuristic technique called mapping by set partitioning   – The encoding philosophy is to first partition the larger constellation into smaller subsets   – The Euclidean distance between sequences of signal points in different subsets is substantially increased (and may be on the order of the distance between points in the same subset)  – Performance will be determined by the distance between sequences in different subsets. • Trellis coding produces a dramatic increase in the Euclidean (free) distance between sequences of signal points and the Viterbi Algorithm is used to detect the signal • Results also hold for 2-dimensional modulation.[3] Let’s say that we intend to transmit a QPSK signal. Figure 2.8 shows the constellation of  a QPSK signal of amplitude = 1. The minimum Euclidean distance between the four  constellation points is min which is a trivial case.[5]

now we draw the trellis of this QPSK signal

FIGURE 2.8 QPSK signal constellation and its trellis (a) Four constellation points of QPSK, (b) the signal trellis of a QPSK signal which allows all transitions at each time period.

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So if original signal is BPSK, then a TCM encoder will put out a QPSK, a QPSK will  become 8PSK and if 8PSK was chosen, it becomes a 16QAM signal. As constellation expands but the signal energy is kept the same, the distance between the symbols decreases. That implies a worsening of a performance, not improving. So where is the improvement coming from? We start with a given bandwidth B, because in real life this is a big constraint. From this  bandwidth, we determine the maximum possible symbol rate, which is never more than 2B but usually less. Now determine the size of the alphabet that can deliver the needed signal BER at the given available power. The MSED, is the minimum squared distance between all points of a constellation and is usually the distance between any two adjacent points. The decoder on the receive side makes the decision about which symbol was sent based on which decision region the signal falls in sort like a dartboard.[3]

FIGURE 2.9 General trellis coded modulation (a) BPSK, code rate 1/2, output QPSK (b) QPSK, code rate = 2/3, output 8PSK  (c) 8PSK, code rate = 3/4, output 16QAM

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2.8 CODING GAIN

The coding gain of a coded signal is given by

where dfree/coded is equal to the coded sequence Euclidean distance and dmin/uncoded is minimum distance between the signals in the uncoded constellation as previously defined. This coding gain is referenced to the baseline signal. How do you measure the Euclidean distance of a coded signal when in fact, its constellation Euclidean distance is smaller than dmin. Now we need to talk about distances between sequences rather than distances between signals. dfree is defined as the Euclidean distance of a coded signal in terms of the smallest possible distance between all allowed sequences. Instead of checking all possible combinations, this distance is measured from the all-zero sequence, same as the measurement of Hamming distance and Hamming weight, which are both referenced to an all-zero code word. Let say that we transmit an all-zero message. During decoding, errors occur and wrong trellis path is followed by the decoder. The only way, the decoder can get depart and then  back to the correct path, which is the all-zero path, is by diverging and then remerging. Remember that each sequence is a set of demodulated symbols. When two paths diverge, it means, there was an error and the decoder made a wrong decision. Assuming that the  probability of such error is small, at subsequent junctions, the further decisions should take the path back to the correct one. A small allowed path which incorrect is more likely than a long one, so the distance of this small path is a measure of the error correcting capability of the code. This is the same concept as when a receiver is most likely to pick  neighboring signal points because they are most like the correct signal, rather than  picking one that is quite different, as such the fundamental idea behind MLD.[3]

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3 IMPLEMENTATION 3.1 BASIC PHILOSOPHY

• Form an expanded constellation, with double the number of points • Partition that constellation into subsets. The points within each subset are far  apart in Euclidean distance, and are made to correspond to the uncoded bits. • The remaining bits determine the choice of the subset. Only certain sequences of subsets are allowed. Typically, the allowed sequences correspond to a simple convolutional code. • In order to keep the allowed sequences far apart, choose subsets that correspond to branching in and out of each state to have maximum distance separation. • At the receiver, we find the allowed sequence which is closest in Euclidean distance to the received sequence of signals. • After the output sequence is decoded, the receiver decides between the uncoded points based on the Euclidean distance to the nearest signal point --thus the distance between uncoded pairs and closest sequences should be ~ the same. 3.2 TRELLIS ENCODING 3.2.1 TRELLIS ENCODER  Even though the minimum distance between signal points in the enlarged constellation is reduced from the original constellation (for the same average power), TCM succeeds in increasing the distance between the transmitted sequences. • Finding good TCM codes does not follow from knowing how to find good codes with good hamming distances (i.e. conventional convolutional codes) • The mapping to analog signals is critical • Recall that the output of the coder is determined by the new input and the current state and the state evolves to a (possibly) new state.[5]

FIGURE 3.1 trellis encoder 

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3.2.2 TRELLIS STATE DIAGRAM The bits are encoded in accordance with the trellis state diagram. Every state has two  paths coming out of it. The two paths corresponds to the two of the partitioned sets with maximum Euclidean between two state vectors.

FIGURE 3.2 TCM does not  protect parallel branches Receiver trellis strives to generate (i.e. “estimate”) the transmit path through the trellis

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3.2.3 SET PARTITIONING

FIGURE 3.3 Partitioning of 16-Point Constellation

This Figure shows how the 8 points of 8PSK are successively portioned into disjoint cosets such that the SEDs are increasing at each level. There are total of four partitions counting the first unpartitioned set. At top-most level, the MSED is 0.586. At the next level, where there are only four points in each of the two cosets, the MSED has increased to 2.0 and at the last level, the MSED is 4.0. Each subset is also called a coset and by the lattice terminology, we can show the partition with its coset generators in this way. Since the top two levels have smaller distances, these errors are more likely, we will use the coded bits to traverse through this part. b3 to and b2 which are coded can be used to decide which partition (or coset) to choose and then we can use the uncoded bit at the last level to pick the signal transmitted. The most significant bit b1, used at the last level, has a large Euclidean distance from its complement and would require an error of 180 degrees to be corrupted.[3]

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3.3 TRELLIS DECODING Several algorithms exist for decoding convolutional codes. For relatively small values of  k , the Viterbi algorithm is universally used as it provides maximum likelihood  performance and is highly parallelizable.[2] As with decoding of convolutional codes, the Viterbi Algorithm (VA) is an application of dynamic programming that finds “shortest  paths” [here maximum likelihood sequences]. A critical feature is that complexity grows linearly with time , rather than exponentially with time (i.e., the number of symbols transmitted). The VA finds the sequence at a = minimum Euclidean distance from the received signal ---or equivalently the accumulated squared error is minimized.

1. Keep track of n possible sequences, each terminating in one of the n states. 2. For each new received symbol, calculate the new error value for each allowed continuation of each sequence, and add it to the accumulated error of the sequence up to that time. 3. For each new state, keep only the one sequence with minimum accumulated error. Discard the other sequences. Keep track of the new error and the bits associated with these n survivor sequences. 4. Depend on “merges”, and enough delay, to output the past history of the sequence. The operation of the algorithm is best described by a trellis diagram, which shows the  possible sequences of states.[5]

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FIGURE 3.4 trellis diagram

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3.3.1 VITERBI ALGORITHM

FIGURE 3.5 Viterbi algorithm

• Compare (rk-Asolid)2 vs (rk - Adashed)2 to determine survivor for each state. We show only the survivors. • Note that “00” is a merged node at k (evident at k+2); similarly “00” is a merged node at k+1 (evident at k+3). “11” merged at k+3 bold segment is part of max. likelihood sequence.[5]

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4. APPLICATIONS OF TRELLIS CODED MODULATION This coding scheme has been used in many application such as Asymmetric Digital Subscriber Line (ADSL), Data/Fax modem, Cable modem, Ethernet, Wi-Fi, WiMAX / Wireless MAN, WPAN, UWB, Satellite and IP Core. 4.1 APPLICATIONS IN WIRELINE COMMUNICATIONS

Wireline communication (or fixed line communication) refers to computer networks where there is a physical connection (either copper or fiber cables) between sender and receiver. 4.1.1 ADSL

ADSL (Asymmetric Digital Subscriber Line) is a technology for transmitting digital information at a high bandwidth on existing phone lines (also known as "twisted copper   pairs") to homes and businesses for ultra-fast Internet access. 4.1.2 DATA/FAX MODEM

A combination of fax and data modem, which is either an external unit that plugs into the serial port or an expansion board that is installed internally. It includes a switch that routes the call to the fax or data modem. The data/fax modem is like a regular modem except that it is designed to transmit documents to a fax machine or to another fax modem. The data/fax modem makes it possible to fax a document straight from the computer, but cannot scan documents which are not in the computer. 4.1.3 CABLE MODEM

A cable modem is a device that enables you to hook up your PC to a local cable TV line and receive data at about 1.5 Mbps. This data rate far exceeds that of the prevalent 28.8 and 56 Kbps telephone modems and the up to 128 Kbps of Integrated Services Digital  Network (ISDN) and is about the data rate available to subscribers of Digital Subscriber  Line (DSL) telephone service. A cable modem can be added to or integrated with a settop box that provides your TV set with channels for Internet access. 4.1.4 ETHERNET

Ethernet is the most widely-installed local area network (LAN) technology. Specified in a standard, IEEE 802.3, Ethernet was originally developed by Xerox from an earlier  specification called Alohanet (for the Palo Alto Research Center Aloha network) and then developed further by Xerox, DEC, and Intel.

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4.2 APPLICATIONS IN WIRELESS COMMUNICATIONS

Wireless communication is fundamentally the art of communicating information without wires. A wireless network is an infrastructure for communication “through the air”, in other words, no cables are needed to connect from one point to another. These connections can be used for speech, e-mail, surfing on the Web and transmission of audio and video. The most widespread use is mobile telephones. Wireless networks are also used for communication between computers. 4.2.1 Wi-Fi

Wi-Fi (short for "Wireless Fidelity") is a term for certain types of wireless local area network (WLAN) that use specifications in the IEEE 802.11 family. The term Wi-Fi was created by an organization called the Wi-Fi Alliance, which oversees tests that certify  product interoperability. 4.2.2 WiMAX

WiMAX is a wireless industry coalition whose members organized to advance IEEE 802.16 standards for broadband wireless access (BWA) networks. WiMAX 802.16 technology is expected to enable multimedia applications with wireless connection and, with a range of up to 30 miles, enable networks to have a wireless last mile solution. 4.2.3 WPAN

“A wireless personal area network (WPAN) is a personal area network- a network for  interconnecting devices centered around an individual person's workspace - in which the connections are wireless. Typically, a wireless personal area network uses some technology that permits communication within about 10 meters - in other words, a very short range. One such technology is Bluetooth, which was used as the basis for a new standard, IEEE 802.15. 4.2.4 UWB

“Ultra wideband (also known as UWB or as digital pulse wireless) is a wireless technology for transmitting large amounts of digital data over a wide spectrum of  frequency bands with very low power for a short distance. Ultra wideband radio not only can carry a huge amount of data over a distance up to 230 feet at very low power (less than 0.5 milliwatts), but has the ability to carry signals through doors and other obstacles that tend to reflect signals at more limited band widths and a higher power. 4.2.5 SATELLITE COMMUNICATIONS

A communications satellite is a spacecraft that orbits the Earth and relays messages, radio, telephone and television signals.

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CONCLUSION

Just as for Gaussian channels, trellis-coded modulation is shown to be power-efficient and bandwidth-efficient modulation technique for fading channels. A large amount of  coding gain on the order of 10 dB can be easily obtained in this case. Using two-fold antenna diversity can improve the performance of trellis-coded modulation by another 8 dB.It has an edge over other coding techniques in band limited channels.It is widely used in space telecommunications.[5]

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REFERENCES [1] www.wikipedia.org [2] www.rfmd.com/DataBooks/db97/an0001.pdf  [3] www.complextoreal.com/chapters/tcm.pdf  [4] Communication Systems by Simon Haykin [5] www.mjtele.com/pds/mjtele_pds/Trellis_coded_modulation.pdf  [6] www.altera.com/products/ip/altera/t-alt-qam.html [7] www.eefocus.com/html/dict_83754_db8aed07fa1928147037f5a3608e2176.html

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