Ungerboeck Codes Research Articles

Improving the Performance of Trellis Coded Modulation Over Rayleigh Fading Channel Using Locally Rotated Constellations

In this paper, we propose a new type of modulation technique; it is called Locally-Rotated (LR) modulation. With this new technique we are looking to optimize the channel encoding block named “Trellis-Coded Modulation with a Locally-Rotated constellation” (TCM+LR). This channel encoding block uses PSK/QAM mapping technique which takes into consideration both Ungerboeck mapping and Gray code mapping (UGM). The simulation results, over Rayleigh fading channels and Proakis B, are performed for throughput 2 and 3 bits/s/Hz with 8PSK and 16 QAM modulations, and rate 2/3, 3/4 constituent TCM encoders with memory order of 3, 4 and 5. In the Rayleigh fading channel, the results show that the proposed scheme TCM+LR-UGM with three memories produces a slight improvement in comparison to TCM+LR, by increasing the number of memories to four. It is shown that TCM+LR-UGM outperforms the TCM+LR Ungerboeck mapping by a gain of 2.5 dB and we notice a gain of 5 dB compared to the 8 state TCM+LR, moreover, a gain of 7.5 dB is achieved in comparison with the original TCM with three memories. In the selective frequency channel, the results show that the proposed scheme TCM+LR-UGM with four memories outperforms the TCM+LR Ungerboeck mapping with a gain of 1 dB and outperforms the TCM+LR with three memories with a gain of 2 dB and with a gain of 3 dB compared to the original TCM 8-states.

Bandwidth-efficient noncoherent Trellis-coded MPSK

In this letter, we propose a novel bandwidth-efficient noncoherent trellis-coded MPSK scheme, in which a particularly designed differential encoder is added in front of the trellis encoder. With this differential encoder, trellis-coded MPSK proposed by Ungerboeck is no longer noncoherently catastrophic and thus achieves better error performance. Moreover, new trellis codes which, for the proposed scheme, have better bit error rates than Ungerboeck's codes are found by computer searches.

A systematic approach to the construction of bandwidth-efficient multidimensional trellis codes

We present a unified approach to the construction of multidimensional trellis codes that have small constellation expansion ratio (CER) and small peak-to-average power ratio (PAR) and hence are of high bandwidth efficiency. In the approach, we extend Wei's (1987) construction to dimensionalities other than a power of two and propose a low-complexity encoder. We also present a general partition technique that gives geometrically uniform partitions with a good distance profile. The proposed method can generate many good codes including previously reported Ungerboeck codes, Gallager-Calderbank-Sloane codes, and Wei codes with quadrature amplitude modulation signals. Some newly discovered six-dimensional trellis codes are compared with these known codes on their CER, PAR, effective coding gain, and encoder/decoder complexities.

Source-channel optimized trellis codes for bitonal image transmission over AWGN channels

We consider the design of trellis codes for transmission of binary images over additive white Gaussian noise (AWGN) channels. We first model the image as a binary asymmetric Markov source (BAMS) and then design source-channel optimized (SCO) trellis codes for the BAMS and AWGN channel. The SCO codes are shown to be superior to Ungerboeck's codes by approximately 1.1 dB (64-state code, 10(-5) bit error probability), We also show that a simple "mapping conversion" method can be used to improve the performance of Ungerboeck's codes by approximately 0.4 dB (also 64-state code and 10 (-5) bit error probability). We compare the proposed SCO system with a traditional tandem system consisting of a Huffman code, a convolutional code, an interleaver, and an Ungerboeck trellis code. The SCO system significantly outperforms the tandem system. Finally, using a facsimile image, we compare the image quality of an SCO code, an Ungerboeck code, and the tandem code, The SCO code yields the best reconstructed image quality at 4-5 dB channel SNR.

Analysis and design of trellis codes optimized for a binary symmetric Markov source with MAP detection

We consider the problem of transmitting a binary symmetric Markov source (BSMS), over the additive white Gaussian noise (AWGN) channel. The coding technique considered is trellis-coded modulation (TCM), where we utilize decoders which implement the maximum-likelihood (ML) and maximum a posteriori (MAP) criteria. Employing 8-PSK Ungerboeck codes on a BSMS with state transition probability 0.1, we first show that the MAP decoder realizes a 0.8-2.1-dB coding gain over the ML decoder. Motivated by these gains, we consider the design of trellis codes optimized for the BSMS/AWGN/MAP system. An approximate union bound is established for this system. Using this bound, we found codes which exhibit additional 0.4-1.1-dB gains over Ungerboeck codes. Finally, we compare the proposed TCM system with a tandem coding system. At normalized signal-to-noise ratio (SNR) of 10.8 dB and below, the proposed system significantly outperforms the tandem system.

Performance analysis of a multilevel coded modulation system

A modified version of the multilevel coded modulation scheme of Imai and Hirakawa (1977) is presented and analyzed. In the transmitter, the outputs of the component codes are bit interleaved prior to mapping into 8-PSK channel signals. A multistage receiver is considered, in which the output amplitudes of the Gaussian channel are soft limited before entering the second and third stage decoders. Upper bounds and Gaussian approximations for the bit error probability of every component code, which take into account errors in previously decoded stages, are presented. Aided by a comprehensive computer simulation, it is demonstrated in a specific example that the addition of the interleaver and soft limiter in the third stage improves its performance by 1.1 dB at a bit error probability of 10/sup /spl minus/5/, and that the multilevel scheme improves on an Ungerboeck's code with the same decoding complexity. The rate selection of the component codes is also considered and a simple selection rule, based on information theoretic arguments, is provided.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Trellis coded Q2PSK signals. I. AWGN and nonlinear satellite channels

Suitable bandwidth efficient coding techniques, to be combined with Q2PSK signals, are derived and analysed on AWGN and nonlinear channels. Five new Q2PSK TCs are presented. First, an expanded Q2PSK signal constellation has been used to design new 4D RI Q2PSK TCs. Partition of the 4D expanded Q2PSK signal space into 2D subspaces has allowed the utilisation of any 8-PSK TC to be implemented along Q2PSK signals. This novel division of the Q2PSK signal space has been utilised to implement double 8-PSK TCs designed by Ungerboeck and double convolutional codes over ring modulo-8 along Q2PSK signals. Finally, an unexpanded Q2PSK signal has been considered to implement and design 2/4 and 3/4 rate Q2PSK trellis codes. Performance evaluation of coded and uncoded Q2PSK signals on nonlinear satellite channels is reported, and the results obtained from computer simulations of coded and uncoded Q2PSK on nonlinear channels are presented, where different amplifier working situations have been considered.

Some new rotationally invariant TCM schemes for multidimensional M-PSK

Trellis codes for multidimensional constellations offer a number of advantages which cannot be obtained with bidimensional constellations. Some new trellis codes for multidimensional M-PSK constellations are presented. They are all completely rotationally invariant. The performance of these codes is discussed and compared with that exhibited by Ungerboeck codes for bidimensional phase modulation with the same effective rate.

Area-efficient architectures for the Viterbi algorithm II. Applications

In part I the theoretical foundations of a new class of area-efficient architectures for the Viterbi algorithm were established. Area-efficient architectures for practical codes are presented here to illustrate the design procedures and demonstrate the favourable area-time tradeoff results. Three examples from convolutional codes, matched-spectral-null (MSN) trellis codes, and Ungerboeck codes are presented. The application of the area-efficient techniques to codes with a very large number of states, codes with time-varying trellises, and a programmable Viterbi decoder is discussed. >

Four state binary QAM trellis code better than known codes

Presents a new one-memory quaternary four-state trellis code, and its four-state binary equivalent code based on a QAM constellation which is 0.52 dB better than the four-state Ungerboeck code.

Multilevel trellis coded modulations for the Rayleigh fading channel

The authors present coded 8-phase-shift-keyed (8-PSK) modulations for the Rayleigh fading channel. The schemes are based on multilevel trellis-coded-modulation constructions and utilize maximum free Hamming distance binary convolutional codes as building blocks. A suboptimal multistage decoder that utilizes interstage interleaving and iterative decoding is proposed and evaluated. Examples are constructed to show that the proposed schemes outperform the best modified codes of the Ungerboeck type due to significantly higher implicit time diversity, yielding seven branches of built-in time diversity, whereas the Ungerboeck code yields four branches of time diversity for a 64-state system. The transmission delay is higher, however. The new schemes can provide three levels of unequal error protection when 8-PSK or 8-differential-phase-shift-keying (8-DPSK) modulations are used. They provide 10-14-dB channel signal-to-noise ratio gain over uncoded 4-DPSK at a bit error rate of 10/sup -3/ for a modest decoding complexity.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Adaptive trellis-coded modulation for bandlimited meteor burst channels

The throughput performances of three adaptive information rate techniques on the bandlimited meteor burst channel are investigated. Closed-form expressions for throughput are derived based on the channel model commonly used in the literature. The throughput performance is compared to the conventional fixed information rate modem and upper bounds on throughput improvement over the fixed rate modem are derived. It is shown that an adaptive technique that uses trellis-coded modulation (TCM) with three phase-shift keyed (PSK) signal sets can increase throughput over the conventional fixed rate modem by more than a factor of 3. Data from the US Air Force High Latitude Meteor-Scatter Test Bed confirm the superiority of the adaptive TCM technique. A practical implementation is suggested that uses a single rate 1/2 convolutional code for all three PSK signal sets. The use of this single code, versus the three best Ungerboeck codes, results in a throughput loss of less than 2%. An expression for the theoretical information capacity of the bandlimited meteor burst channel is derived. >

Trellis-coded differentially coherent (TCDC) MPSK with carrier-phase-noise

The authors consider trellis-coded M-ary phase shift keying (MPSK) when used with differentially coherent demodulation over a carrier-phase-noise dominated channel. A tight upper-bound to the probability of error is introduced. This bound shows the presence of an irreducible probability of error. When compared to coherently demodulated trellis-coded MPSK, the irreducible probability of error of the differentially coherent scheme is much lower. This improved robustness to carrier-phase-noise is obtained at the expense of signal-to-noise-ratio (SNR), coding gain. Numerical results for two Ungerboeck codes with differentially coherent MPSK demodulation show poor SNR coding gain. A modification of Ungerboeck codes which makes them more suitable for use with differentially coherent demodulation is shown to increase the SNR gain while maintaining good robustness to carrier-phase-noise.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

New detection algorithm with reduced complexity

A new algorithm for detecting and/or decoding of signals in communication system is presented. The advantage of the proposed suboptimum algorithm with respect to the classical maximum likelihood detection (MLSE) method lies in the significant reduction in computation complexity attainable by associating a reliable information to each received signal. At the same time, the error probability is maintained close to MLSE levels through the proper selection of the reliability information. We describe the application of the proposed algorithm to some interesting cases, such as the detection of continuous phase modulations with and without combined channel coding, detection of Ungerboeck codes, use in conjunction with the Viterbi algorithm. In all cases, a net reduction in computation complexity with respect to the classical MLSE algorithm is achieved.

A pragmatic approach to trellis-coded modulation

Since the early 1970s, for power-limited applications, the convolutional code constraint length K=7 and rate 1/2, optimum in the sense of maximum free distance and minimum number of bit errors caused by remerging paths at the free distance, has become the de facto standard for coded digital communication. This was reinforced when punctured versions of this code became the standard for rate 3/4 and 7/8 codes for moderately bandlimited channels. Methods are described for using the same K=7, rate 1/2 convolutional code with signal phase constellations of 8-PSK and 160PSK and quadrature amplitude constellations of 16-QASK, 64-QASK, and 256-QASK to achieve, respectively, 2 and 3, and 2, 4, and 6 b/s/Hz bandwidth efficiencies while providing power efficiency that in most cases is virtually equivalent to that of the best Ungerboeck codes for constraint length 7 or 64 states. This pragmatic approach to all coding applications permits the use of a single basic coder and decoder to achieve respectable coding (power) gains for bandwidth efficiencies from 1 b/s/Hz to 6 b/s/Hz. >

Encoded 16-PSK: a study for the receiver design

The authors present the results of a design study of the receiver in a digital transmission system using the combined coding and modulation schemes known as Ungerboeck codes. Specifically, they examine the design of the receiver for encoded 16-PSK (phase shift keying) modulation, presenting first the traditional structure for the optimum receiver and then a simpler structure. The decoding depth of the Viterbi algorithm, the quantization of the metrics inside the Viterbi processor, and the phase jitter in the recovered carrier are considered. The impact of branch and path metric quantization inside the receiver is discussed, showing that a reasonable number of bits (8) is sufficient to obtain nearly optimum performance when the code complexity is limited. The effect of imperfect carrier recovery inside the receiver is studied, providing accurate analytical estimates of the error event probability as well as an upper bound to the symbol error probability. Results of a detailed simulation, including carrier and bit timing recovery blocks, show that the effects of imperfections on the bit error probability are very small, even at low signal-to-noise ratios. On the whole, results show the robustness of the Viterbi algorithm with respect to fairly rough quantizations of the metrics and indicate that carrier recovery is not as critical as expected. >

Multilevel codes based on partitioning

Following V.V. Ginzburg (1984), a hierarchy of codes is proposed to match the geometric partitioning of a signal set. The authors show that coset codes (including Ungerboeck, lattice, and binary codes) and indeed any codes which rely on partitioning of the signal set are all subclasses of the proposed coding scheme. The combination of such codes in a multilevel scheme often leads to reduced complexity in comparison with previously published schemes. A variety of decoder structures is discussed. >

An approach to Ungerboeck coding for rectangular signal sets (Corresp.)

A method of finding good Ungerboeck codes for large rectangular [quadrature amplitude modulation (QAM)] signal sets is described. Using the concept of Euclidean weights due to Ungerboeck, we prove that a 2^{n} point basic constellation may be employed to determine exactly the free distance for an Ungerboeck-coded rectangular 2^{m} point set, when m-n-1 bits are uncoded and the remaining bits pass through a rate (n-1)/n convolutionai encoder. It is shown that rate 2/3 encoders may be used to achieve most of the theoretically possible coding gain in the proposed scheme where the effect of the error coefficient on the coding gain has been considered.

Performance of a coded 8PSK modem with a viterbi decoder using simplified metric calculation

AbstractRecently, there has been increased interest in coded octal phase‐shift keying (8PSK) modulation for satellite communications, in which convolutional encoding and Viterbi decoding are combined with 8PSK modulation and demodulation. The problem in this paper is how to simplify the process of metric calculation in a Viterbi decoder and realize reduced hardware complexity and increased operating speed of a coded 8PSK modem. An analytical expression is introduced for the performance of a coded 8PSK model with such a simplified Viterbi decoder. The expression is then applied to a typical coded 8PSK modem employing the Ungerboeck code of rate 2/3 and with constraint length ν=2. Effects of simplifications in the Viterbi decoder on the bit error rate (BER) performance of the model have been evaluated. Results in this paper would be useful in the design of future coded PSK modems, since it enables a designer to assess the tradeoffs involved in the simplifications and to realize modems with reduced hardware complexity for highspeed applications.

Ungerboeck codes do not shape the signal power spectrum (Corresp.)

Simple sufficient conditions are found for the spectrum of Ungerboeck-coded signals to be equal to the spectrum of uncoded signals. It is shown that a carefully designed Ungerboeck code does not shape the spectrum.