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At least 19 records

Concatenated Coding Using Trellis-Coded Modulation

In the late seventies and early eighties a technique known as Trellis Coded Modulation (TCM) was developed for providing spectrally efficient error correction coding. Instead of adding redundant information in the form of parity bits, redundancy is added at the modulation stage thereby increasing bandwidth efficiency. A digital communications system can be designed to use bandwidth-efficient multilevel/phase modulation such as Amplitude Shift Keying (ASK), Phase Shift Keying (PSK), Differential Phase Shift Keying (DPSK) or Quadrature Amplitude Modulation (QAM). Performance gain can be achieved by increasing the number of signals over the corresponding uncoded system to compensate for the redundancy introduced by the code. A considerable amount of research and development has been devoted toward developing good TCM codes for severely bandlimited applications. More recently, the use of TCM for satellite and deep space communications applications has received increased attention. This report describes the general approach of using a concatenated coding scheme that features TCM and RS coding. Results have indicated that substantial (6-10 dB) performance gains can be achieved with this approach with comparatively little bandwidth expansion. Since all of the bandwidth expansion is due to the RS code we see that TCM based concatenated coding results in roughly 10-50% bandwidth expansion compared to 70-150% expansion for similar concatenated scheme which use convolution code. We stress that combined coding and modulation optimization is important for achieving performance gains while maintaining spectral efficiency.

Thompson, Michael W.↗

Multiple trellis coded modulation (MTCM)

A new trellis coded modulation technique, referred to as multiple trellis coded modulation wherein more than one channel symbol per trellis branch is transmitted and demonstrated. Simple two state trellis codes for symmetric MPSK and AM modulations, which can achieve 3 dB gain over uncoded modulation at very high signal-to-noise ratios without bandwidth expansion and without reduction in information bit rate have been found. The gain of the new trellis codes with respect to previously reported two state trellis codes is between 1 to 2 dB at very high signal-to-noise ratios, depending on the number of bits per hertz transmitted. These gains are achieved with no additional cost in complexity; while indeed additional computations per branch are needed for the multiple trellis coding scheme. This concept can be extended to higher number of states and other type of modulations; i.e., quadrature amplitude modulation.

Divsalar, D.↗

Generalized Multiple-Trellis-Coded Modulation

Generalized multiple-trellis-coded modulation technique combines multiple trellis coding (more than one channel symbol per trellis branch transmitted) with symmetrical M-ary phase-shift keying. Transmitter puts out k M-ary code symbols for every b input binary symbols. Throughout performances, b/k, of trellis-coded multiple-phase-shift-keying channels compared with computational cutoff rates, R0, of multiple-phase-shift keying. Performs better than conventional trellis-coded modulation technique, with no increase in complexity.

Divsalar, D.↗

Multiple Trellis Coded Modulation (MTCM): An MSAT-X report

Conventional trellis coding outputs one channel symbol per trellis branch. The notion of multiple trellis coding is introduced wherein more than one channel symbol per trellis branch is transmitted. It is shown that the combination of multiple trellis coding with M-ary modulation yields a performance gain with symmetric signal set comparable to that previously achieved only with signal constellation asymmetry. The advantage of multiple trellis coding over the conventional trellis coded asymmetric modulation technique is that the potential for code catastrophe associated with the latter has been eliminated with no additional cost in complexity (as measured by the number of states in the trellis diagram).

Divsalar, D.↗

Trellis coding with multidimensional QAM signal sets

Trellis coding using multidimensional QAM signal sets is investigated. Finite-size 2D signal sets are presented that have minimum average energy, are 90-deg rotationally symmetric, and have from 16 to 1024 points. The best trellis codes using the finite 16-QAM signal set with two, four, six, and eight dimensions are found by computer search (the multidimensional signal set is constructed from the 2D signal set). The best moderate complexity trellis codes for infinite lattices with two, four, six, and eight dimensions are also found. The minimum free squared Euclidean distance and number of nearest neighbors for these codes were used as the selection criteria. Many of the multidimensional codes are fully rotationally invariant and give asymptotic coding gains up to 6.0 dB. From the infinite lattice codes, the best codes for transmitting J, J + 1/4, J + 1/3, J + 1/2, J + 2/3, and J + 3/4 bit/sym (J an integer) are presented.

Pietrobon, Steven S.↗

A new description of combined trellis coding with asymmetric modulation

The combination of rate k/(k+t) trellis codes with digital modulations described by an asymmetric 2 sup k+1-point signal constellation has been recently shown to yield performance improvement over the traditional symmetric constellation combined with the same trellis code. The approach taken is to specify an underlying trellis code and then map the output code symbols into the fixed signal constellation based on a rule called mapping by set partitioning. The latter process is tantamount to assigning signals from the constellation to the trellis code transitions so as to maximize the free Euclidean distance of the code. Recently, a new description of trellis codes has been given that combines the above two steps into one. The ideas introduced are further explored, placing particular emphasis on the optimization of the signal constellation asymmetry. It can be concluded that the trellis-coded amplitude modulation (AM) designs given are very close to being optimum.

Simon, M. K.↗

The design of trellis codes for fading channels

The appropriate criterion for optimum trellis coded modulation design on the additive white Gaussian noise channel is maximization of the free Euclidean distance. When trellis coded modulation is used on a Rician fading channel with interleaving/deinterleaving, the design of the code for optimum performance is guided by other factors, in particular the length of the shortest error event path, and the product of branch distances (possibly normalized by the Euclidean distance of the path) along that path. Although maximum free distance (d sub free) is still an important consideration, it plays a less significant role the more severe the fading is on the channel. These considerations lead to the definition of a new distance measure for optimization of trellis codes transmitted over Rician fading channels. If no interleaving/deinterleaving is used, then once again the design of the trellis code is guided by maximizing d sub free. It is also shown that allowing for multiple symbols per trellis branch, i.e., multiple trellis coded modulation (MTCM), provides an additional degree of freedom for designing a code to meet the above optimization criteria on the fading channel. It is here where the MTCM technique exploits its full potential.

Divsalar, Dariush↗

Trellis coding techniques for mobile communications

A criterion for designing optimum trellis codes to be used over fading channels is given. A technique is shown for reducing certain multiple trellis codes, optimally designed for the fading channel, to conventional (i.e., multiplicity one) trellis codes. The computational cutoff rate R0 is evaluated for MPSK transmitted over fading channels. Examples of trellis codes optimally designed for the Rayleigh fading channel are given and compared with respect to R0. Two types of modulation/demodulation techniques are considered, namely coherent (using pilot tone-aided carrier recovery) and differentially coherent with Doppler frequency correction. Simulation results are given for end-to-end performance of two trellis-coded systems.

Divsalar, D.↗

Trellis coded multilevel DPSK system with doppler correction for mobile satellite channels

A trellis coded multilevel differential phase shift keyed mobile communication system. The system of the present invention includes a trellis encoder for translating input signals into trellis codes; a differential encoder for differentially encoding the trellis coded signals; a transmitter for transmitting the differentially encoded trellis coded signals; a receiver for receiving the transmitted signals; a differential demodulator for demodulating the received differentially encoded trellis coded signals; and a trellis decoder for decoding the differentially demodulated signals.

Divsalar, Dariush↗

Combined trellis coding with asymmetric modulations

The use of asymmetric signal constellations combined with optimized trellis coding to improve the performance of coded systems without increasing the average or peak power, or changing the bandwidth constraints of a system is discussed. The trellis code, asymmetric signal set, and Viterbi decoder of the system model are examined. The procedures for assigning signals to state transitions of the trellis code are described; the performance of the trellis coding system is evaluated. Examples of AM, QAM, and MPSK modulations with short memory trellis codes are presented.

Divsalar, D.↗

Bandwidth-efficient high-speed coded trellis modulation

A burst-mode coded trellis modulation system is discussed which is capable of 200-Mbit/s information rate transmission over nonlinear satellite transponders whose center frequencies are separated by 100 MHz. An overall real bandwidth efficiency of 2 bit/s per Hz of the allocated spectrum is projected. Convolutional codec and 8-PSK modulation subsystems together maximize the minimum Euclidean distance between the modulated codeword sequences in the overall coded trellis, resulting in a 4.3-dB asymptotic coding advantage over an uncoded 8-PSK system signalling at the same information rate over the same channel. The system performance has been evaluated by computer simulation.

Fang, R. J. F.↗

A hybrid M-algorithm/sequential decoder for convolutional and trellis codes

The Viterbi Algorithm (VA) is optimum in the sense of being maximum likelihood for decoding codes with a trellis structure. However, since the VA is in fact an exhaustive search of the code trellis, the complexity of the VA grows exponentially with the constraint length upsilon. This limits its application to codes with small values of upsilon and relatively modest coding gains. The M-Algorithm (MA) is a limited search scheme which carries forward M paths in the trellis, all of the same length. All successors of the M paths are extended at the next trellis depth, and all but the best M of these are dropped. Since a limited search convolutional decoder will flounder indefinitely if one of the paths in storage is not the correct one, the data are usually transmitted in blocks. It has been shown that the performance of the MA approaches the VA at high signal to noise ratios (SNR's) with an M which is far less than the 2 sup upsilon states in the full trellis. Thus the MA can be used with larger values of upsilon, making larger coding gains possible at high SNR's. However, it still requires a relatively large fixed computational effort to achieve good performance.

Wang, Fu-Quan↗

Multiple trellis coded modulation

A technique for designing trellis codes to minimize bit error performance for a fading channel. The invention provides a criteria which may be used in the design of such codes which is significantly different from that used for average white Gaussian noise channels. The method of multiple trellis coded modulation of the present invention comprises the steps of: (a) coding b bits of input data into s intermediate outputs; (b) grouping said s intermediate outputs into k groups of s.sub.i intermediate outputs each where the summation of all s.sub.i,s is equal to s and k is equal to at least 2; (c) mapping each of said k groups of intermediate outputs into one of a plurality of symbols in accordance with a plurality of modulation schemes, one for each group such that the first group is mapped in accordance with a first modulation scheme and the second group is mapped in accordance with a second modulation scheme; and (d) outputting each of said symbols to provide k output symbols for each b bits of input data.

Simon, Marvin K.↗

An algorithm for computing the distance spectrum of trellis codes

A class of quasiregular codes is defined for which the distance spectrum can be calculated from the codeword corresponding to the all-zero information sequence. Convolutional codes and regular codes are both quasiregular, as well as most of the best known trellis codes. An algorithm to compute the distance spectrum of linear, regular, and quasiregular trellis codes is presented. In particular, it can calculate the weight spectrum of convolutional (linear trellis) codes and the distance spectrum of most of the best known trellis codes. The codes do not have to be linear or regular, and the signals do not have to be used with equal probabilities. The algorithm is derived from a bidirectional stack algorithm, although it could also be based on the Viterbi algorithm. The algorithm is used to calculate the beginning of the distance spectrum of some of the best known trellis codes and to compute tight estimates on the first-event-error probability and on the bit-error probability.

Rouanne, Marc↗

The design of trellis coded MPSK for fading channels: Set partitioning for optimum code design

A previous work on criteria for designing trellis-coded MPSK modulation to achieve minimum error probability performance on the Rician fading channel is extended. It is demonstrated that allowing for multiple symbols per trellis branch, i.e., multiple trellis-coded modulation (MTCM), provides an additional degree of freedom for designing a code to meet the optimization on the fading channel. Diversities larger than those achievable with conventional trellis codes having the same number of trellis states are now attainable, it is under these conditions that MTCM achieves its full potential.

Divsalar, Dariush↗

Multiple trellis coded modulation (MTCM) performance on a fading mobile satellite channel

The author recently introduced the notion of multiple trellis coding, in which more than one channel symbol per trellis branch is transmitted. He showed that on the ideal additive white Gaussian noise (AWGN) channel, the combination of multiple trellis coding with M-ary modulation yields a performance gain with symmetric signal sets comparable to and in some cases better than that previously achieved only with signal constellation asymmetry. The combination of conventional trellis coding with multiple phase-shift-keyed (MPSK) signaling has recently been shown by the author to be a well-suited modulation/coding scheme for transmission over the fading mobile satellite channel. In particular, a rate 2/3 coded 8-PSK scheme operating at 4800 b/s is currently under development for use in NASA's Mobile Satellite Experiment (MSAT-X). The author applies the multiple trellis-coded modulation technique in the same fading mobile satellite environment, extending the analysis results previously found for its performance over the AWGN channel to the MSAT-X channel.

Simon, Marvin K.↗

Trellis coded modulation for 4800-9600 bps transmission over a fading mobile satellite channel

The combination of trellis coding and multiple phase-shift-keyed (MPSK) signalling with the addition of asymmetry to the signal set is discussed with regard to its suitability as a modulation/coding scheme for the fading mobile satellite channel. For MPSK, introducing nonuniformity (asymmetry) into the spacing between signal points in the constellation buys a further improvement in performance over that achievable with trellis coded symmetric MPSK, all this without increasing average or peak power, or changing the bandwidth constraints imposed on the system. Whereas previous contributions have considered the performance of trellis coded modulation transmitted over an additive white Gaussian noise (AWGN) channel, the emphasis in the paper is on the performance of trellis coded MPSK in the fading environment. The results will be obtained by using a combination of analysis and simulation. It will be assumed that the effect of the fading on the phase of the received signal is fully compensated for either by tracking it with some form of phase-locked loop or with pilot tone calibration techniques. Thus, results will reflect only the degradation due to the effect of the fading on the amplitude of the received signal. Also, we shall consider only the case where interleaving/deinterleaving is employed to further combat the fading. This allows for considerable simplification of the analysis and is of great practical interest. Finally, the impact of the availability of channel state information on average bit error probability performance is assessed.

Divsalar, D.↗

Trellis coded modulation for 4800-9600 bits/s transmission over a fading mobile satellite channel

The combination of trellis coding and multiple phase-shift-keyed (MPSK) signaling with the addition of asymmetry to the signal set is discussed with regard to its suitability as a modulation/coding scheme for the fading mobile satellite channel. For MPSK, introducing nonuniformity (asymmetry) into the spacing between signal points in the constellation buys a further improvement in performance over that achievable with trellis coded symmetric MPSK, all this without increasing average or peak power, or changing the bandwidth constraints imposed on the system. Whereas previous contributions have considered the performance of trellis coded modulation transmitted over an additive white Gaussian noise (AWGN) channel, the emphasis in the paper is on the performance of trellis coded MPSK in the fading environment. The results will be obtained by using a combination of analysis and simulation. It will be assumed that the effect of the fading on the phase of the received signal is fully compensated for either by tracking it with some form of phase-locked loop or with pilot tone calibration techniques. Thus, results will reflect only the degradation due to the effect of the fading on the amplitude of the received signal. Also, we shall consider only the case where interleaving/deinterleaving is employed to further combat the fading. This allows for considerable simplification of the analysis and is of great practical interest. Finally, the impact of the availability of channel state information on average bit error probability performance is assessed.

Divsalar, Dariush↗