Constraint Length Research Articles

Flexible constraints: An adiabatic treatment of quantum degrees of freedom, with application to the flexible and polarizable mobile charge densities in harmonic oscillators model for water

In classical molecular simulations chemical bonds and bond angles have been modeled either as rigid constraints, or as nearly harmonic oscillators. However, neither model is a good description of a chemical bond, which is a quantum oscillator that in most cases occupies the ground state only. A quantum oscillator in the ground state can be represented more faithfully by a flexible constraint. This means that the constraint length adapts itself, in time, to the environment, such that the rotational and potential forces on the constraint cancel out. An accurate algorithm for flexible constraints is presented in this work and applied to study liquid water with the flexible and the polarizable “mobile charge densities in harmonic oscillators” model. The iterations for the flexible constraints are done simultaneously with those for the electronic polarization, resulting in negligible additional computational costs. A comparison with fully flexible and rigidly constrained simulations shows little effect on structure and energetics of the liquid, while the dynamics is somewhat faster with flexible constraints.

Combined channel estimation and data decoding based on fuzzy logic

A simple method that detects the data sequence and at the same time estimates the channel condition is proposed using the Viterbi algorithm and fuzzy logic for the convolutional code. After a fixed number of decoding steps, the fuzzy logic unit reads the branch metric value of the survivor and the difference between maximum and minimum survivor path metric values at the Viterbi decoder and estimates the channel condition with the signal-to-noise ratio. The proposed method enables the channel estimation regardless of what kinds of modulator and demodulator are used. In the experiment, constraint length 7 and code rate 1/2 convolutional code that is standardized by the European Space Agency (ESA) is used. The effective movement range of the proposed channel estimation method is from 0.0 dB to 25 dB.

Sequential Decoding of Convolutional Codes for Rayleigh Fading Channels

The performance of sequential decoding of long constraint length convolutional codes is evaluated for Rayleigh fading channels. Sequential decoding is not practical below a certain theoretical signal-to-noise ratio, and these theoretical limits are calculated for a number of modulation methods and code rates. As an example, with BPSK modulation, soft decisions and code rate 1/2, the theoretical signal-to-noise ratio per information bit is 5.7 dB. Above this limit the bit error rate can be made arbitrarily small by increasing the constraint length at no significant complexity cost. Furthermore, it is shown that with carefully chosen quantization steps, 8 level uniform quantization gives a negligible loss also for sequential decoding on a Rayleigh fading channel. Simulation results using 8 level quantization correspond well with the theoretical performance bounds. Also, the performance on a correlated channel with finite interleaving has been obtained. With an interleaver depth of 50×50 and a normalized doppler frequency equal to 0.01 we are only 0.5 dB away from the performance with perfect interleaving. Finally, bit error rate results show this scheme to compete well with Turbo codes.

Multihop optical network with convolutional coding

We evaluate the bit-error-rate (BER) performance of a multihop optical ShuffleNet with and without convolutional coding. Computed results show that there is considerable improvement in network performance resulting from coding in terms of an increased number of traversable hops from a given transmitter power at a given BER. For a rate-1/2 convolutional code with constraint length K = 9 at BER = 10-9, the hop gains are found to be 20 hops for hot-potato routing and 7 hops for single-buffer routing at the transmitter power of 0 dBm. We can further increase the hop gain by increasing transmitter power.

Upper bounds on the free distance for a class of convolutional coded CPFSK signals

In this letter, we construct new encoder-independent upper bounds on the free distance for the rate (n-1)/n convolutional encoders that are formed by using rate 1/2 encoders and combined with 2/sup n/-level constant-envelope full-response CPFSK signals of single-h, by generalizing the bounding technique employed for the existing bounds. The new bounds coincide with the existing bounds for h/spl les/0.25, but are generally better for h>0.25. We also present actual encoder combinations achieving the constructed new bounds with short constraint lengths.

Distance spectra of convolutional codes over partial-response channels

This paper is concerned with the well-known coding technique that uses cosets of convolutional codes along with precoding to increase the free squared Euclidean distance at the output of a partial-response channel. The focus is on totally trellis-matched codes, for which the decoding trellis has the fewest number of states. Codes totally trellis-matched to the extended partial-response class 4 (EPR4) and the doubly extended partial-response class 4 (E/sup 2/PR4) channels for a variety of code rates and overall constraint lengths are sought for with respect to the squared Euclidean distance spectrum criterion. Furthermore, some previously published codes are shown to contain flawed codewords and are replaced with new ones.

The rate 19/20 trellis code matched to enhanced extended class-4 partial response channel

In this paper, a rate 19/20 trellis code matched to the partial response (PR) channel is presented. Our trellis rode is designed on a multidimensional Euclidean space for which the minimum free Euclidean distance is larger than conventional recording codes. By using this trellis coding, a trellis coded partial response (TCPR) system is defined for the enhanced extended class-4 partial response (E/sup 2/PR4) channel. Further, the decoding method for this TCPR system is based on the syndrome-former trellis decoding. The number of add-compare-selects (ACS's) in our system is fewer than that of conventional Viterbi decoding. The result shows that TCPR system employing this rate 19/20 trellis code with the constraint length 7 for the E/sup 2/PR4 has an excellent performance compared with the conventional 8/9 maximum transition run (MTR) coding system in high-density recording.

On asymptotically optimum rate 1/n convolutional codes for a given constraint length

The criterion used to find good convolutional codes has traditionally been the maximization of the free distance for a given constraint length and code rate. In this letter we approach convolutional code design from a different perspective. We assume no constraints in the rate of the code, and the only restriction is in the constraint length. That is, we assume we can utilize as much bandwidth as necessary but we are complexity-limited by the constraint length we can afford. The results are optimum codes for a given constraint length, which can find application, for example, in CDMA systems.

Construction of fast recovery codes using a new optimal importance sampling method

We introduce the problem of constructing good fast recovery convolutional codes. When the constraint lengths of the candidate codes are long (say more than 12), it is too computationally complex to perform the code search task. Fortunately, we can transform the code construction problem to a problem related to a transient Markov system. We then develop an optimal importance sampling (IS) method to fulfil the tasks. In this article, we also prove several propositions for optimal IS. For instance, we show analytically that the optimal IS method is unique. We prove that the optimal IS method must converge to the standard Monte Carlo (MC) simulation method when the sample path length approaches infinity. This finding shows that it is not the size of the state space of the Markov system, but the sample path length, that limits the efficiency of the IS method. Based on insights from the optimal IS method, a suboptimal IS method is then proposed to search for long fast recovery codes. The suboptimal method can achieve a substantial speedup gain. After that, several numerical results are presented to study the efficiency of the IS methods and to justify the code search procedures. Finally, we give the code search results and the application of these codes.

Comparison of convolutional and turbo codes for OFDM with antenna diversity in high-bit-rate wireless applications

This letter presents simulation results for the application of turbo coding to an OFDM system with diversity. First, results are presented for convolutional and Reed-Solomon codes. It is shown that even with short constraint lengths, convolutional codes have the potential to outperform Reed-Solomon codes, provided that sufficient precision is used in the soft decoder. We then evaluate the performance of turbo codes under slow fading conditions and study the effects of varying codeword size. Increasing codeword size theoretically provides better interleaving between the two component codes. However, this advantage is less clear when the fading rate is significantly lower than the symbol rate, which is typical of the high-data-rate systems considered here. Under such conditions, the advantage of using two component convolutional codes in turbo codes is limited. A single convolutional code with a long constraint length may be a better choice.

Multiuser decoding for multibeam systems

An iterative multiuser decoding algorithm for co-channel BPSK/QPSK users in a multibeam system is presented. The approach can be applied to the return link of multibeam satellites and to terrestrial systems with sectored base-station antennas. It allows the reuse of the same spectrum in each beam. The algorithm is based on the extension of turbo-decoding techniques to the iterative decoding of parallel users. Simulation results show one can asymptotically achieve single user performance in a high multiuser interference environment; often this includes some diversity gain. The complexity of the algorithm is approximately O(2/sup K/+2/sup /spl kappa//) operations per bit per iteration where K is the number of co-channel users and /spl kappa/ is the constraint length of the forward error correction code.

A 2-Mb/s 256-state 10-mW rate-1/3 Viterbi decoder

This paper presents a low-power bit-serial Viterbi decoder chip with the code rate r=1/3 and the constraint length K=9 (256 states) for next generation wireless communication applications. The architecture of the add-compare-select (ACS) module is based on the bit-serial arithmetic and implemented with the pass transistor logic circuit. A cluster-based ACS placement and state metric routing topology is described for the 256 bit-serial ACS units, which achieves very high area efficiency. In the trace-back operation, a power efficient trace-back scheme, allowing higher memory read access rate than memory write in a time-multiplexing method, is implemented to reduce the number of iterations required to generate a decoded output. In addition, a low-power application-specific memory suitable for the function of survivor path memory has also been developed. The chip's core, implemented using 0.5-/spl mu/m CMOS technology, contains approximately 200 K transistors and occupies 2.46 mm by 4.17 mm area. This chip can achieve the decode rate of 20 Mb/s under 3.3 V and 2 Mb/s under 1.8 V. The measured power dissipation at 2 Mb/s under 1.8 V is only about 9.8 mW. The Viterbi decoder presented here can be applied to next generation wide-band code division multiple access (W-CDMA) systems.

New rate-compatible repetition convolutional codes

The optimum rate-compatible repetition convolutional (RCRC) codes with different parent encoder rates and different constraint lengths are presented. They are constructed according to the optimum distance spectrum (ODS) criterion. The obtained codes provide, e.g., significant throughput gains compared to simple repetition codes, when applied in hybrid type II automatic repeat request (ARQ) schemes.

Metric-based node synchronization of the Viterbi decoder in satellite applications

Convolutional codes are used in digital communication systems to correct errors that occur during transmission. Their use is now commonplace, particularly in power-limited satellite and deep space communication systems. Before the decoder can correctly decode the received continuous bit sequence, however, it must establish where codewords begin and end in this sequence. The process of determining codeword boundaries is called node synchronization. In this paper we develop a node synchronization algorithm based on metric difference values with the objectives of simple implementation and reliable performance. Focusing on satellite applications, we consider the constraint length 7, rate ½ convolutional code standardized by the National Aeronautics and Space Administration (NASA) and the European Space Agency (ESA); the approach we develop can be extended to other convolutional coding systems. Through simulation, we investigate the statistics of the received sequence, and highlight correlation in the sequence of the decoder metric values. In the light of these observations, we propose a synchronization algorithm, and develop a first-order analysis of this simple up/down counter framing technique. We recommend framing parameters based on both the analytical results and the expected response of the framing algorithm to correlated metric values. Development of a simple node synchronization algorithm that accommodates correlated metric values has not been reported previously in the literature. Simulation results confirm that reliable node synchronization is possible with this very simple approach. Copyright © 2000 John Wiley & Sons, Ltd.

Two trellis coding schemes for large free distances

A trellis code encoded by using the encoder of a convolutional code C with a short constraint length followed by an additional processing unit is equivalent to a trellis code with a large constraint-length. In 1993, Hellstern proposed a trellis coding scheme for which the processing unit consists of a delay processor and a signal mapper. With Hellstern's scheme, trellis codes with large free distances can be constructed. In this paper, we propose two trellis coding schemes. For the first scheme, the processing unit is composed of multiple pairs of delay processors and signal mappers. For the second scheme, the processing unit is composed of a convolutional processor and a signal mapper, where a convolutional processor is a rate 1 convolutional code. The trellis code constructed from each of the proposed schemes can be suboptimally decoded by using the trellis of the convolutional code C with some feedback information. Either of the proposed schemes can produce a trellis code that has a larger bound on free distance and better error performance as compared to the trellis code constructed from Hellstern's scheme based on the same convolutional code C.

Code-spread CDMA using maximum free distance low-rate convolutional codes

In code division multiple-access (CDMA) systems, maximum total throughput assuming a matched filter receiver can be obtained by spreading with low-rate error control codes. Previously, orthogonal, bi-orthogonal and super-orthogonal codes have been proposed for this purpose. We present in this paper a family of rate-compatible low-rate convolutional codes with maximum free distance. The performance of these codes for spectrum spreading in a CDMA system is evaluated and shown to outperform that of orthogonal and super-orthogonal codes as well as conventionally coded and spread systems. We also show that the proposed low rate codes will give simple encoder and decoder implementations. With these codes, any rate 1/n, n/spl les/512, are obtained for constraint lengths up to 11, resulting in a more flexible and powerful scheme than those previously proposed.

New path history management circuits for Viterbi decoders

Up until now the trace back technique and the register-exchange approaches are two major techniques used for the path history management in the chip designs of Viterbi decoders. The former takes up less area but requires much more time than the latter, since it needs to search the trace of the survivor path back sequentially. We propose an alternate approach that is based on the concept of a permutation network and implements directly the trellis diagram of a given convolutional code. Instead of using registers to store the survivor path data, all information is recorded in a permutation network, and the resulting circuit has a smaller routing area than the register-exchange technique and has faster decoding speed than the trace-back method regardless of the constraint length. In addition, it is more straightforward to realize the permutation networks path history unit than the trace-forward unit.

Convolutional codes with optimum distance spectrum

New convolutional codes with rates 1/2, 1/3, and 1/4 are presented for constraint lengths ranging from 3 to 15. These new codes are maximum free-distance codes. Furthermore, the codes have optimized information error weights, resulting in a low bit-error rate for binary communication on both additive white Gaussian noise (AWGN) and Rayleigh fading channels. Improved coding gains of as much as 0.6 dB compared to previously published codes have been observed for coherent BPSK over a Rayleigh fading channel and a wide range of signal-to-noise ratios.

Asymptotic performance of ML sequence estimator using an array of antennas for coded synchronous multiuser DS-CDMA systems

The optimal joint maximum-likelihood sequence estimator using an array of antennas is derived for synchronous direct sequence-code division multiple access (DS-CDMA) systems. Each user employs a rate 1/n convolutional code for channel coding for the additive white Gaussian noise (AWGN) channel. The array receiver structure is composed of beamformers in the users' directions followed by a bank of matched filters. The decoder is implemented using a Viterbi algorithm whose states depend on the number of users and the constraint length of the convolutional code. The asymptotic array multiuser coding gain (AAMCG) is defined to encompass the asymptotic multiuser coding gain and the spatial information on users' locations in the system. We derive the upper and lower bounds of the AAMCG. As an example, the upper and lower bounds of AAMCG are obtained for the two user case where each user employes the maximum free distance convolutional code with rate 1/2. The near-far resistance property is also investigated considering the number of antenna elements and user separations in the space.

On unequal error protection using convolutional codes

This paper demonstrates the inherent unequal error protection (UEP) nature of punctured convolutional codes to develop two UEP schemes. In both schemes, the UEP level of error protection is better than the original error-control coding and modulation scheme employed. The first scheme is based on utilizing the inherent UEP capability within the columns of the puncturing matrix, without a reduction in information throughput. The second scheme reduces the effective code rate b/ v of a punctured convolutional code created from an original rate 1/ v o code. Such a UEP scheme may be of use in a communication system where it is beneficial to briefly reduce the information throughput for a much improved error protection. It is shown that the performance of a simple rate 1/2, constraint length K=3 code, when transformed to an effective rate 1/3 code, provides a coding gain of approximately 5.2 dB with the use of eight level soft-decision decoding over uncoded BPSK. In general, this UEP technique provides a coding gain of slightly greater than 10 log 10(bv o /v) dB over the performance of the original rate 1/ v o code using hard-decision Viterbi decoding. A further coding gain of approximately 1.5 dB can be expected with the use of soft-decision decoding.