Ungerboeck, G., "Channel Coding with Multilevel/Phase Signals", IEEE Trans. on Information Theory, vol. 28(1), pp. 55-67, Jan. 1982.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....we feel that it is more appropriate to compare the channel capacities of the three systems. This provides us with an ultimate metric as to how well these three systems will perform in a given channel. For our purpose, we calculated the capacity of the systems using the equations presented in [8] for the case of QAM transmission over an AWGN channel. This is possible since the multipath channels are effectively transformed into AWGN channels due to the presence of the DFE or multi carrier modulation [10] Figure 8 shows the CDFs of achievable channel capacities for the three systems under ....

Ungerboeck, G., "Channel Coding with Multilevel/Phase Signals", IEEE Trans. on Information Theory, vol. 28(1), pp. 55-67, Jan. 1982.

....fading channel models was mostly used only 1 Fading Channel Receive Filter Filter Modulator recovery Phase Transmit Encoder Trellis Interleaver Digital Data Source Demodulator Quantizer Decoder Trellis Deinterleaver Figure 1.1: Fading channel TCM communication system by specialists. TCM codes [5] have been widely used and Biglieri [3] summarizes many variations and its applications, extending them from Gaussian to fading channels. Most of those codes and schemes are very powerful. However, the decoding complexity is also very high. The communication system we studied in this thesis is ....

....input and giving ternary output, we essentially have a rate 1 2 code which has the same complexity as conventional circle 8 PSK with eight states. This GF(3) area has not been studied much so far as we know. The basic algebra 12 related to our work is in appendix for reference. Of course, TCM [5] code is preferred, which was a breakthrough in channel coding and provides extra coding gain without loss of bandwidth and efficiency. Therefore we need to comply with the Ungerboeck rule in set partitioning and trellis design. Besides 8 1 OOK PSK, for OOK TCM based on GF(3) there are some other ....

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G. Ungerboeck, "Channel Coding with Multilevel/Phase Signals" in IEEE Transactions On Information Theory, Vol. IT-28, No.1, 1982

....result hereof is that the use of the suboptimal metric in multistage decoding causes very little degradation in capacity compared to when optimal metric is used in each stage of the multistage decoder. I. INTRODUCTION The principle of trellis coded modulation was described by Ungerboeck in 1982 [7], and the concept of multilevel modulation was introduced by Imai and Hirakawa [5] The multilevel scheme enables the usage of a multistage decoder [5] which performs almost as well as an optimum joint maximum likelihood sequence estimator over all levels [4] but is much less complex. In previous ....

.... (block or convolutional) A set of K bits, # v (1) n) v (2) n) v (K) n) # , one bit from each of the code sequences v (1) v (2) v (K) are synchronously mapped onto one of the 2 K PSK signal points, s (n) To perform this, mapping by set partitioning [7] (Figure 2) is used. u Partition of information u (1) u (2) u (3) u (K) C1 C2 C3 CK v (1) v (2) v (3) v (K) 2 K PSK mapper s AWGN # r suboptimal decoder u Figure 1: System description of the K level modulation scheme using PSK signaling. r r r r r r r r r r r r b b b b b b ....

G. Ungerboeck, "Channel Coding with Multilevel /Phase Signals", IEEE Trans. Information Theory, vol. IT-28, 1982, pp. 55-67.

....Keywords Multilevel modulation, multistage decoding, PSK signalling, set partitioning. 1 This work was supported in part by Swedish Research Council for Engineering Sciences under Grant 95 164 1 I. INTRODUCTION The principle of trellis coded modulation was described by Ungerboeck in 1982 [7], and the concept of multilevel modulation was introduced by Imai and Hirakawa [5] The multilevel scheme enables the usage of a multistage decoder [5] which performes almost as well as an optimum joint maximum likelihood sequence estimator over all levels [4] but is much less complex. In this ....

G. Ungerboeck, "Channel Coding with Multilevel/Phase Signals," IEEE Trans. Information Theory, vol. IT-28, pp. 55-67, Jan. 1982.

....Telecommunication Theory Group, Lund University, Box 118, S 221 00 Lund, Sweden, Phone 46 46 222 3450 and 46 46 222 4460, Fax 46 46 222 4714, e mail karin it.lth.se and kamil it.lth.se 1 I. INTRODUCTION The principle of trellis coded modulation was described by Ungerboeck in his paper of 1982 [8], and the concept of multilevel modulation was introduced by Imai and Hirakawa [6] In this method the channel signal set is successively binary partitioned using the set partitioning rule where the binary labels of the branches from one level of the partition chain to the next are encoded by ....

G. Ungerboeck, "Channel Coding with Multilevel/Phase Signals," IEEE Trans. Inform. Theory, vol. IT-28, pp. 55-67, Jan. 1982. 20

....the data rate compared to that of an uncoded modulation system with the same bandwidth and energy rate. The combination of modulation, convolutional codes and soft Viterbi decoding has an especially positive effect. Further progress in this area was done by Ungerboeck in his pioneering work [1], where he suggested a principle of set partitioning of a signal constellation. The core of Ungerboeck s scheme is dividing a signal set into smaller subsets with increasing intra set Euclidean distance. Independently, Imai and Hirakawa [2] proposed a multilevel coded modulation scheme based on ....

G. Ungerboeck, "Channel coding with multilevel/phase signals," IEEE Transactions on Information Theory, vol. IT-28, pp. 55--67, Jan. 1982.

....no loss in terms of channel capacity as long as Gray mapping is used in conjunction with bit interleaving [3] B. Turbo Trellis Coded Modulation This technique, originally proposed by Robertson and Worz [9] consists of the parallel concatenation of two trellis coded modulation (TCM) schemes [10] using rate k (k 1) convolutional codes, in the same fashion as binary turbo codes (see also [11] The interleaving works on groups of bits instead of individual bits. The second encoder s output symbols are de interleaved to insure that the ordering of the computation likelihood ratio module ....

G. Ungerboeck, "Channel coding with multilevel /phase signals," in IEEE Transactions on Information Theory, Jan. 1982, vol. IT-28, pp. 55--67.

....Index Terms Demodulation, Monte Carlo methods, trellis coded modulation. I. INTRODUCTION W HEN digital data is to be transmitted across a digital microwave radio (DMR) channel, a very low bit error rate (BER) must be maintained. Due to the bandwidth limitation, trellis coded modulation (TCM) [1] has been proposed for DMR applications [2] 3] The advantage of TCM is that bandwidth expansion is not required, and coding gains are readily obtained. The DMR channel is usually characterized by a slowly time varying, frequency selective multipath fading channel model due to Rummler [4] ....

....to Fig. 1, the are input into the convolutional encoder with constraint length . The output bits are mapped into the complex valued symbols . In general, the symbols are nonlinear functions of the inputs. For example, the modulated symbols for the constraint length , rate , 8 ary PSK code, in [1], are given by (1) where denotes modulo 2 addition. The transmitted signal is given by (2) where is the symbol rate and is a bandwidth efficient (e.g. raised cosine) pulse shape. The DMR channel is usually characterized by the Rummler model [4] with frequency response in low pass equivalent ....

[Article contains additional citation context not shown here]

G. Ungerboeck, "Channel coding with multilevel/phase signals," IEEE Trans. Inform. Theory, vol. IT-28, pp. 55--67, Jan. 1982.

....we feel that it is more appropriate to compare the channel capacities of the three systems. This provides us with an ultimate metric as to how well these three systems will perform in a given channel. For our purposes, we calculated the capacity of the systems using the equations presented in [8] for the case of QAM transmission over an AWGN channel. This is possible since the multipath channels are effectively transformed into AWGN channels due to the presence of DFE or multi carrier modulation [10] Figure 8 shows the CDFs of achievable channel capacities of the three systems under ....

Ungerboeck, G., "Channel Coding with Multilevel/Phase Signals", IEEE Trans. on Information Theory, vol. 28(1), pp. 55-67, Jan. 1982.

....set partitioning, ternary signaling. 1 This work was supported in part by Swedish Research Council for Engineering Sciences under Grant 95 164 1 I. INTRODUCTION The principle of trellis coded modulation, and the concept of set partitioning was described by Ungerboeck in his paper of 1982 [7]. In [4] Imai and Hirakawa proposed a coded modulation scheme in which the labels on the branches from one level of the partition chain to the next are encoded by independent codes. This scheme enables the usage of a suboptimal multistage decoder, which demonstrates performance complexity ....

G. Ungerboeck, "Channel Coding with Multilevel/Phase Signals," IEEE Trans. Information Theory, vol. IT-28, pp. 55-67, Jan. 1982.

...., L = 1; 2; We constructed codes (block or convolutional) over the integer ring Z q modulo q, and then we mapped the q ary code symbols onto symbols of the alphabet S (I.1) 1 . In this part of the paper we study multilevel coded modulation systems, introduced independently by Ungerboeck [2] and Imai and Hirakawa [3] The multilevel scheme enables the usage of the multistage decoder, which demonstrates performance complexity advantage over the maximal likelihood decoder of the corresponding conventional coded modulation scheme. An asymptotical analysis of the multilevel modulation ....

G. Ungerboeck, "Channel coding with multilevel/phase signals," IEEE Transactions on Information Theory, vol. IT-28, pp. 55--67, Jan. 1982.

....fact implies that the codes using rate 1 2 encoder havetwo advantages: 1)better overall decoding performance and 2)less decoding complexity. key words: trellis codedmodulation, concatenatedcode,weight distribution 1. Introduction The invention of the trellis coded modulation (TCM) by Ungerboeck [1][2] 3] opened up a new field in coding theory. TCM is constructed on the basis of an expanded signal constellation (compared with an uncoded constellation at the same rate) and a binary convolutional code designed to maximize the minimum Euclidean free distance d 2 free . TCM yields an ....

....discussed in this paper is the class of rate k= k 1) feedback encoder as shown in Fig.1. Let us denote the number of memories in a feedback encoder by K. Thus,the binary trellis code generated by the encoder has 2 K states. A feedback encoder can be characterized by the paritycheck polynomials [1] H i (D) P 0 = j = K h i j D j (0 = i = k) where h j 0 = h j K = 0; j j =0; 1; j =0 (K = 2) 1) Hereafter, H i (D) is described in the octal form. We define the code complexity N c (i.e. the number of branches per 2D) by N c = 2 K 2 2 k ) L; 2) where L = 1 ....

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G. Ungerboeck: "Channel coding with multilevel/phase signals", IEEE Trans. Inform.Theory, IT-28, pp. 55--67 (1982).

....source and channel codes is implicitly chosen to force a small channel bit error probability. Other iterative design approaches to joint source and channel coding use trellis coded quantization (TCQ) a form of source coding motivated by Ungerboeck s formulation of trellis coded modulation (TCM) [22]. Ayano glu and Gray propose an iterative design for the encoder and decoder of a trellis based source code, assuming a fixed channel bit errorprobability [23] A subsequent paper [24] combines TCQ and TCM by first designing the TCQ for a noiseless channel, then matching the trellis of the TCM to ....

G. Ungerboeck, "Channel coding with multi-level/phase signals," IEEE Trans. Inform. Theory, vol. IT-28, pp. 55--67, Jan. 1982.

....8 PSK TCM schemes over the symmetric 8 PSK TCM. Index Terms Asymmetric phase shift keying, fading channels, trellis coded modulation. I. INTRODUCTION T RELLIS CODED modulation (TCM) schemes achieve good power and bandwidth efficiency for additive white Gaussian noise (AWGN) channels [1]. In recent years, TCM has increasingly been used in such channels as the mobile radio and indoor wireless channels, which are often modeled as a fading channel [2] 8] Recently, this channel is also being used for data transmission, in addition to speech. Typically, the acceptable speech error ....

....using the signal point assignments of [8] we further improve the performance using an asymmetric 8 PSK signal set shown in Fig. 1(b) Du and Vucetic [9] match the performance of Jamali and LeNgoc code with Gray code labeling of the 8 PSK signal set. The 8 state rate 2 3 8 PSK Ungerboeck code [1] has a trellis without parallel transitions. Fig. 3 shows the state transitions of the 8 state Ungerboeck code. It achieves the maximum effective length of two that is possible for an 8 state rate 2 3 8 PSK code. This code has a minimum product distance of . This is the best known 8 state rate 2 3 ....

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G. Ungerboeck, "Channel coding with multilevel/phase signals," IEEE Trans. Inform. Theory, vol. IT-28, pp. 55--67, Jan. 1982.

....Eds. Tauton, U.K. Res. Studies, 1998, pp. 121 141. Online] Available WWW: http: www.systems.caltech.edu EE Faculty rjm. 19] K. R. Narayanan and G. L. Stuber, A serial concatenation approach to iterative demodulation and decoding, IEEE Trans. Commun. vol. 47, pp. 956 961, July 1999. [20] Y. Okunev, Phase and Phase Difference Modulation Digital Communications. Norwood, MA: Artech House, 1997. 21] M. Peleg and S. Shamai (Shitz) Iterative decoding of coded and interleaved noncoherent multiple symbol detected DPSK, Electron. Lett. vol. 33, no. 12, pp. 1018 1020, June 1997. ....

.... level (i 1)of the tree can be labeled by (c1 ;c 2 ; 111;c i ) Since the subsets at the (M 1)th (last) level of the tree are exactly the elements of S, they are labeled by (c1;c 2 ; 111;c M ) This way of labeling each signal of S is known as mapping by set partitioning and is due to Ungerboeck [20]. Let C1;C 2 ; 111;C M be a set of M linear codes, each having the same length, called component codes. We shall allow an abuse of notation by also calling C i an encoder that generates the code C i : Denote by d H i the minimum Hamming distance of code C i , whose symbols are taken from the ....

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G. Ungerboeck, "Channel coding with multilevel/phase signals," IEEE Trans. Inform. Theory, vol. IT-28, pp. 55--67, Jan. 1982.

....1. INTRODUCTION The radio spectrum is a scarce resource. Therefore, one of the most important objectives in the design of a digital cellular system is the efficient exploitation of the available spectrum in order to accommodate the ever increasing traffic demands. Trellis Coded Modulation (TCM) [1], which is based on combining the functions of coding and modulation, is a bandwidth efficient scheme that has been widely recognized as an excellent error control technique suitable for applications in mobile communications [2, 3] Turbo Trellis Coded Modulation (TTCM) 4] is a more recent ....

....are 4QAM, 8PSK, 16QAM and 64QAM [14] We invoke four encoders, each adding one parity bit to each information symbol, yielding the coding rate of 1#2 in conjunction with the modulation mode of 4QAM, 2#3 for 8PSK, 3#4 for 16QAM and 5#6 for 64QAM. The TCM scheme invokes Ungerboeck s codes [1], while the TTCM scheme invokes Robertson s codes [4] The BICM scheme was constructed using Paaske s convolutional codes [15] The rate 5#6 code of the BICM scheme was constructed using Paaske s rate 1#2 code and puncturing, following the approach of [16, 17] Soft decision trellis decoding ....

G. Ungerboeck, "Channel coding with multilevel/phase signals, " IEEE Transactions on Information Theory, vol. IT-28, pp. 55--67, January 1982.

....but quite efficient, was proposed in [401] It consists of inverting the channel only for a limited number of blocks, while no power is spent to transmit the others. F. Bit Interleaved Coded Modulation Ever since 1982, when Ungerboeck published his landmark paper on trellis coded modulation [424], it has been generally accepted that modulation and coding should be combined in a single entity for improved performance. Several results followed this line of thought, as documented by a considerable body of work aptly summarized and referenced in [397] see also [361, Ch. 10] Under the ....

G. Ungerboeck, "Channel coding with multilevel/phase signals," IEEE Trans. Inform. Theory, vol. IT-28, pp. 56--67, Jan. 1982.

....can be much simpler than the inner interleaving. 2.4 TCM Encoder Decoder A proper selection of the modulation inner coding (and multiplexing) scheme has major impacts on the overall system performance. The advantages of combined coding and modulation with TCM are well known in the meantime [9, 10]. On the fading channel, TCM in connection with interleaving performs similar to a diversity scheme. Hence, minimization of the diversity factor is a major design criterion on these channels (and even more important than the free distance [11, 12, 13, 10] Stimulated by [13] we applied binary ....

....following we used the one dimensional 8 state code with uniform signal constellation (1D8SU) defined by I n =b n Gamma1 Gamma 2b n b n Gamma2 b n Gamma3 [14, 13] The asymptotic coding gain is only 3 dB (instead of 3.4 dB for nonuniform spacing [14] and 3. 6 dB for the 8 state Ungerboeck code [9]) but the diversity factor is 4 (instead of 2 for the 8 state Ungerboeck code) The interleaved bit stream is multiplexed into two parallel, independent rate 1 2 TCM encoders, as shown in Fig. 1. The 4PAM output symbols are combined into one 16QAM symbol. Note that the dimensionality of the ....

G. Ungerboeck, "Channel coding with multilevel/ phase signals," IEEE Trans. Inform. Theory, vol. IT-28, no. 1, pp. 55-67, Jan. 1982 11

....This work was supported by NSF CAREER award #97 33089 and the Xetron Corporation. fer function may be obtained using only 2 e states. These conditions are generalizations of the symmetry conditions Ungerboeck required for computing minimum free Euclidean distance using only 2 e states [6]. The technique in this paper computes the transfer function using 2 e q states where q is an integer between zero and e . For quasi regular trellis codes, q is always zero. Thus complexity in these cases is the same as achieved by the standard application of quasi regularity. However, ....

G. Ungerboeck. Channel Coding with Multilevel/Phase Signals. IEEE Trans. on Info. Th., 28(1):55-67, Jan. 1982.

....detection. Also shown in Figure 4 are simulation results for this modified QPSK scheme, giving the same results as obtained analytically. Figure 5 shows simulation results for the performance of the modified QPSK scheme together with that of three different rate 2 3, 4 state TCM 8PSK schemes [5 7] over Rayleigh fading channels. It is observed that the performance of this modified scheme is comparable to that of the coded schemes. This suggests that these coded schemes with symbol interleaving may not be optimized for the fading channel under consideration [2] That is, their performance ....

....QPSK simulation Fig. 4. Performance of uncoded QPSK scheme (regular and modified) over Rayleigh fading channels with perfect channel state information. 5 10 15 20 25 30 10 6 10 5 10 4 10 3 10 2 10 1 Eb No, dB 4 state TCM of [6] 4 state TCM of [7] modified QPSK 4 state TCM of [5] Fig. 5. Performance comparison of the modified uncoded QPSK scheme and 4 state TCM 8PSK schemes over Rayleigh fading channels, perfect channel state information. which is a function of a normalized Doppler frequency fDT s and k. The joint pdf of the two correlated Rayleigh random variables, ff n ....

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G. Ungerboeck, "Channel coding with multilevel/phase signals," IEEE Trans. Inform. Theory, vol. IT-28, No. 1, pp. 55-67, January 1982.

....a way that the minimum distance between any two sequences in a coset is made as large as possible, while maintaining symmetry among the cosets. In the following, a trellis based partitioning is considered based on convolutional codes and set partitioning rules as in Trellis Coded Modulation (TCM) [11]. Note that this is not to be confused with the Trellis Coded Quantization (TCQ) 12] framework: we still use scalar quantization but use trellises to build coset sequences. A bit stream with R bits unit time is used to partition 2 R 1 codevectors taking values in R. The set r is partitioned ....

....depends heavily on the C SNR, or the correlation structure between X and Y . Now consider the trellis coded systems as discussed in Section 3. We use 4 and 8 state trellises built on a 4 level root scalar quantizer. These trellises are designed based on setpartitioning principles as given in [11]. Since these trellises are built on a 4 level alphabet, and the rate of transmission is 1 bit per source sample, we can use rate 1 2 convolutional codes. Fig. 5(a) gives the probability of decoding failure (P df ) versus C SNR. Note that by going to coded systems, we get gains of around 3 4 dB in ....

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G. Ungerboeck, "Channel coding with multilevel/phase signals," IEEE Trans. on Inform. Theory, vol. IT-28, pp. 55--67, Jan. 1982.

....adaptive design. Let S r l ; r = 0; Delta Delta Delta ; N Gamma 1 be the r th subset of signal set i l , for some fixed number of subsets N (which is determined by the number of coded bits out of the convolutional encoder) where the subsets are found by standard Ungerboeck partitioning [8]. Let g l be the minimum intrasubset normalized Euclidean distance squared of i l , and let u m;r l ; m = 0; Delta Delta Delta ; N Gamma 1; r = 0; Delta Delta Delta ; N Gamma 1, be the minimum intersubset normalized Euclidean distance squared between signals in subsets m and r of i l . ....

G. Ungerboeck, "Channel Coding with Multilevel /Phase Signals," IEEE Trans. Inform. Theory, Vol. 28, pp. 55-67, January 1982.

....detection. Also shown in Figure 4 are simulation results for this modified QPSK scheme, giving the same results as obtained analytically. Figure 5 shows simulation results for the performance of the modified QPSK scheme together with that of three different rate 2 3, 4 state TCM 8PSK schemes [5 7] over Rayleigh fading channels. It is observed that the performance of this modified scheme is comparable to that of the coded schemes. This suggests that these coded schemes may not be optimized for the fading channel under consideration [2] Since the performance of uncoded PSK schemes can be ....

.... 6 10 5 10 4 10 3 10 2 10 1 10 0 Eb No, dB regular QPSK modified QPSK simulation Fig. 4. Performance of uncoded QPSK scheme (regular and modified) over Rayleigh fading channels with perfect channel state information. different codes. The first code known as Ungerboeck code [5] is optimum for AWGN channels but its trellis contains parallel paths and therefore does not get any diversity gain over fading channels. The two other codes [6, 7] designed for fading channels, i.e. their trellises do not contain parellel paths) perform better in fading channels however their ....

[Article contains additional citation context not shown here]

G. Ungerboeck, "Channel coding with multilevel/phase signals," IEEE Trans. Inform. Theory, vol. IT-28, No. 1, pp. 55-67, January 1982.

....current channel fading values at the transmitter is of limited utility in systems that are not delay constrained and permit high complexity decoding. However, recent work [3] 4] 5] has shown that significant gains in bandwidth efficiency are exhibited by adaptive trellis coded modulation (TCM) [6] schemes over their nonadaptive counterparts for delay constrained, low complexity decoders. Hence, while adaptive techniques may not significantly increase capacity, they may provide better performance for low complexity or delay constrained systems. The proposed adaptive TCM schemes approach ....

G. Ungerboeck, "Channel Coding with Multilevel/Phase Signals," IEEE Trans. Inform. Theory , Vol. 28, pp. 55-67, January 1982.

.... i Gamma c (2) i j 2 : 1) Trellis codes for the additive white Gaussian noise (AWGN) channel seek a large squared Euclidean distance P d i (1 2) The central trellis code design metric for AWGN channels is the minimum Euclidean distance (MED) possible between a valid pair of sequences [1]. For channels with independent fading, it is important to have d i 0 for several values of i so that a single faded symbol can t remove all the distance between a pair of sequences. For a specified pair of sequences, the number of nonzero values of d i is the effective length (EL) of the error ....

G. Ungerboeck. Channel Coding with Multilevel/Phase Signals. IEEE Trans. on Inform. Theory, 28(1):55--67, Jan. 1982.

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