An encoder of a trellis coded modulation (TCM) is composed of a linear convolutional encoder followed by a mapper to channel signals. A new condition, under which the performance evaluation of the TCM is possible base...
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An encoder of a trellis coded modulation (TCM) is composed of a linear convolutional encoder followed by a mapper to channel signals. A new condition, under which the performance evaluation of the TCM is possible based on the 2nu state error state transition diagram, is proposed, where nu is the number of delay elements in the convolutional encoder. There have been proposed three similar methods. This paper points out the restriction of the previous methods, and proposes a new method. The condition, under which the previous method is useful, is called uniformity, such as, the error weight profile is independent from the encoder state. When uniformity does not hold, we discuss to divide an error state into substates based on the coset decomposition of output vectors of the convolutional encoder. The coset is determined by the vector called coset selector. If the condition defined as equal dividing holds, the subdivided states can be merged and the performance can be evaluated based on the 2nu state transition diagram, even for the codes without uniformity. When the row rank of the transformation matrix, from the input vector of the encoder to the coset selector vector, is full, the equal dividing condition holds under the assumption of equally probable i.i.d. (independently identically distributed) input sequence. For TCM schemes without uniformity (in the case, previous methods can not be applied), upper bounds of the bit error rate are evaluated by the proposed method and compared with the simulation results. The difference is less than 10% in the range of bit error rate < 10(-4).
Asymptotic upper bounds on the minimum distance of trellis codes are derived. A universal bound and bounds specific to PSK and QAM signal sets are obtained.
Asymptotic upper bounds on the minimum distance of trellis codes are derived. A universal bound and bounds specific to PSK and QAM signal sets are obtained.
On a linear Gaussian channel with intersymbol interference (ISI), trellis precoding is a method that achieves the equalization performance of Tomlinson-Harashima (TH) precoding, the coding gain of any known lattice-ty...
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On a linear Gaussian channel with intersymbol interference (ISI), trellis precoding is a method that achieves the equalization performance of Tomlinson-Harashima (TH) precoding, the coding gain of any known lattice-type coset code, and a considerable shaping gain. trellis precoding may be viewed as a generalization of trellis shaping to Gaussian ISI channels;or, alternatively, as a generalization of TH precoding with coded modulation that achieves shaping gain. With trellis precoding channel capacity can be approached essentially as closely on any strictly band-limited, high signal-to-noise ratio Gaussian channel as on the ideal channel, using the same coding techniques. For first- or second-order FIR and IIR channels, it is shown that shaping gains close to 1 dB can be obtained with a two-dimensional 4-state trellis code. trellis precoding is quite practical whenever channel information is available at the transmitter.
trellis-coded quantization is generalized to allow noiseless coding of the trellis branch reproduction symbols. An entropy-constrained trellis-coded quantization (ECTCQ) design algorithm is presented, based on the gen...
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trellis-coded quantization is generalized to allow noiseless coding of the trellis branch reproduction symbols. An entropy-constrained trellis-coded quantization (ECTCQ) design algorithm is presented, based on the generalized Lloyd algorithm for trellis code design and the entropy-constrained vector quantization design algorithm. ECTCQ systems are designed for memoryless Gaussian and Laplacian sources, and for first- and second-order Gauss-Markov sources. With an 8-state trellis, the mean-squared error ECTCQ encoding performance for memoryless sources with smooth densities is within about 0.5 dB of the rate-distortion function. Small additional improvements are achieved with larger trellises. Similar, though not quite as good, performance is achieved for the Gauss-Markov sources by using the ECTCQ in a predictive coding structure. Extensions of the approach treat uniform and vector codebooks.
An upper bound on the minimum squared distance of trellis codes by packing Voronoi cells is derived, and we compare this bound with previously known bounds. The bound is tight to search results for coset codes with a ...
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An upper bound on the minimum squared distance of trellis codes by packing Voronoi cells is derived, and we compare this bound with previously known bounds. The bound is tight to search results for coset codes with a small number of states.
The pairwise error probability for a trellis-coded MPSK system with imperfect phase reference at high S/N is derived. These results are used to study the effect of phase offset, phase jitter and imperfect differential...
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The pairwise error probability for a trellis-coded MPSK system with imperfect phase reference at high S/N is derived. These results are used to study the effect of phase offset, phase jitter and imperfect differential detection on trellis-coded MPSK.
Different transceiver structures for the proposed high-bit-rate (800 kbit/s) digital subscriber loop transmission interface are analysed. The simulation results presented in the paper demonstrate that high-bit-rate ac...
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Different transceiver structures for the proposed high-bit-rate (800 kbit/s) digital subscriber loop transmission interface are analysed. The simulation results presented in the paper demonstrate that high-bit-rate access with a considerable performance margin is feasible if baseband transceivers with appropriate equalisation and simple trellis coding are used. Initial results also indicate that more complicated bandpass transceivers with similar equalisation and trellis coding do not provide any clear performance advantage.
trellis-coded quantization is generalized to allow a vector reproduction alphabet. Three encoding structures are described, several encoder design rules are presented, and two design algorithms are developed. It is sh...
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trellis-coded quantization is generalized to allow a vector reproduction alphabet. Three encoding structures are described, several encoder design rules are presented, and two design algorithms are developed. It is shown that for a stationary, ergodic vector source, if the optimized trellis-coded vector quantization reproduction process is jointly stationary and ergodic with the source, then the quantization noise is zero-mean and of variance equal to the difference between the source variance and the variance of the reproduction sequence. Several examples illustrate the encoder design procedure and performance.
Multi-Frequency Modulation has been the topic of several papers at NPS. In past systems the majority of time required for the generation of the MFM signal was due to the software routine used to implement the FFT. Xn ...
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Multi-Frequency Modulation has been the topic of several papers at NPS. In past systems the majority of time required for the generation of the MFM signal was due to the software routine used to implement the FFT. Xn this report a Digital Signal Processor was used to reduce the time needed to generate the FFT. The use of trellis coding and Viterbi decoding on a Digital Signal Processor was also investigated. Assembly language programs for three encoder/decoder systems were developed. The first uses a 16 QAM signal, the second uses a 2/3 rate convolutional encoder and Viterbi decoder and the third uses the V.32 convolutional encoder and a Viterbi decoder.
This article presents information related to trellis coded quantization is incorporated into a noise feedback coding structure for encoding sampled speech. A source waveform such as music or speech is sampled, then en...
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This article presents information related to trellis coded quantization is incorporated into a noise feedback coding structure for encoding sampled speech. A source waveform such as music or speech is sampled, then encoded as a sequence of hits to be transmitted through a medium to a user, where the original waveform is reconstructed from its samples. It is conceptually simpler to design each subsystem individually rather than the entire system at once. trellis coding is a source coding technique that has resulted in numerous publications and some very effective source codes. Unfortunately, the computational burden of these codes is tremendous and grows exponentially with the encoding rate. A trellis is a transition diagram for a finite state machine. The branches of the trellis represent state transitions and the labels on each branch indicate the input necessary to cause that transition and the associated output. The Viterbi algorithm is a clever application of forward dynamic programming that allows the encoding to progress from left to right through the trellis with a number of hard decisions being made at each stage.
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