In this study the authors derive a formula to compute the optimal signal constellation, bit error probabilities and decision thresholds for M-ASK (amplitude shift keying) with non-equal symbol probabilities. The resulting signal constellation is not equally spaced. The authors demonstrate the importance of assigning lower energy signals to symbols with higher probabilities. The authors show that the optimal system has a lower error probability than a conventional system, that is, a system with source coding, equiprobable symbols and equal space constellation. In several cases presented in this study the error probability of the optimal system is significantly lower than in the conventional system. The authors show that even with equal symbol probabilities the equal space constellation is only asymptotically optimal, not optimal for M≥4. However in the several cases that the authors have studied the difference in the error probabilities between ASK with optimal constellation and equal space constellation is insignificant in practice. The authors further extend our results in M-ASK to M-QASK (quadrature ASK) and similar improvements can be obtained.

Can a device that can perform hyperacuity vision tasks be built? In this paper, a feasibility study based on separation discrimination is conducted. Two types of ideal detectors are considered. The first is the stimulus defined statistically (SDS) detector by Geisler and Davilla. The second is one that estimates the uncertainty and then takes out its effect. In the first method, an array of many ideal stimulus defined exactly (SDE) detectors covers uncertainties and forms the ideal SDS detector. When the separation distance between the SDE detectors is around 1 arcmin, the SDS detector can achieve nearly optimal performance. To cover the motion uncertainty with nearly optimal performance, the SDE detector at each position needs to cover 16 directions, and at each direction, it needs to cover speeds with an increment of 0.5 degrees/s. Typically, the SDS detector needs 7776 SDE detectors to deal with a speed up to 2 degrees/s stimulus movement with a randomly selected direction and a 9 min x 9 min position uncertainty region. This ideal observer can achieve a hyperacuity threshold of 2-4 arcsec. Its threshold is almost constant over the range of speeds covered by the SDS detector. Using the second method, position estimation and motion tracking capability is examined. With perfect position estimation and motion tracking, the SDS detector can be reduced to a single SDE detector that is tuned to correct position and motion direction and speed. Two lower bounds on the estimation variance are examined, namely: 1) the Cramer-Rao bound and 2) the Ziv-Zakai bound. The results showed that if an estimation algorithm that can achieve the performance of bounds can be found, then the second method could achieve a hyperacuity capability of 1 s or less. The human visual system may more likely adopt the first method, but the second is simpler to use in building up a device using microprocessors. In this paper, dot-pair templates are used, which precisely match to dot-pair stimuli, to compute the likelihood and make a decision. The main difference between this paper and that of Geisler and Davilla lies in using a discrete sum over an array of SDE detectors to closely approximate continuous integration over the uncertain region, which makes it much easier in hardware implementation.

The aim of this paper is to investigate the effect of impulsive noise on the performance of the turbo TCM coded OFDM system. We construct a punctured parity-concatenated trellis code which functions as a turbo TCM code but with much lower complexity and explore their application in OFDM systems using 64QAM constellation to offer higher spectral efficiency. The conventional iterative bit MAP decoding algorithm is modified to catch up the corresponding impulsive noise statistical characteristics. The bit error rate (BER) performance of the TTCM coded OFDM systems over both AWGN channel and UWB channel with impulsive noise is evaluated through simulation. The study shows several essential requirements to achieve high data rate transmission for non-Gaussian channels

How could human vision system differentiate a small misalignment of two short lines up to 1/10-th of photoreceptor size (better than the Nyquist rate) when the retina is moving constantly? Over the last twenty years, detection theory has played essential role in explaining this hyper-acuity phenomenon. These principles may be useful for us to develop new communication systems. In this paper, we investigate the optimal detection theory for a retinal-like device. We model the fixational eye movement and point spread as a two-dimensional first-order Markov process. Due to the movement and point spread, a single dot stimulus will produce a center-surround opponent reception field at the output of photoreceptor. We develop an optimal statistic matched filter receiver to detect the presence of the moving dot. We show that the movement and spread are essential to the eye hyper-acuity function. Our detector can differentiate a small mismatch (just 10% of the size of photoreceptor) between two short lines. The mean values of output from photoreceptor do not contribute to the optimal receiver. However, without the mean values, the ON-center and work OFF-center pathways are essential to differentiate a black object in a white background from a white object in a black background.

One of UWB proposal in IEEE P802.15 WPAN project is to use OFDM system and punctured convolutional codes for UWB channels supporting data rate up to 480 Mb/s. We apply a TTCM encoder to examine the possible improvement for UWB/OFDM. We construct punctured parity-concatenated trellis codes in which a TCM code is used as the inner code and a simple parity-check code is used as the outer code. The bit MAP algorithm is used in iterative decoding. The code performance is examined when applied to OFDM systems in UWB channel environments. The study shows that the system can offer much higher spectral efficiency up to 1 Gbps over UWB channel

We propose a new type of secure communication systems, called amorphous communication systems, in which the message is embedded in the statistics of the random pulse waveforms. We further apply the principle of statistical matched filters to construct an optimal receiver. We show how the system works and then analyze its performance based on density evolution and Gaussian approximation. We also compare it with BPSK and DBPSK signals with random spreading waveforms and present numerical results. The amorphous system shall support large M-ary communications. When M changes from 2 to 20, the performance is slightly degraded (less than 1 dB)

This paper proposes a finite length serial concatenation of SPC (single parity check) codes with convolutional codes. The analytical and numerical results explain the convergence of the proposed codes.

In this paper, we present several properties on minimum distance(d/sub min/) and girth(G/sub min/) in Tanner graphs for low-density parity-check (LDPC) codes with small left degrees. We show that the distance growth of (2, 4) LDPC codes is too slow to achieve the desired performance. We further give a tight upper bound on the maximum possible girth. The numerical results show that codes with large G/sub min/ could outperform the average performance of regular ensembles of the LDPC codes over binary symmetric channels. The same codes perform about 1.5 dB away from the sphere-packing bound on additive white Gaussian noise channels.

We address several issues for implementing the iterative Viterbi decoder. We show that 3-bit branch metric quantization, 7- or 8-bit state metric precision, and a survivor length of five times the constraint length yields little degradation for the iterative Viterbi algorithm (IVA). Our results show that without changing the VA hardware (except adding some additional circuits), the error performance of several standard systems can be significantly improved.

A novel compound code is designed for the multidimensional (M-D) Wei (1987) trellis code combined with a simple parity-check code. Using the iterative Viterbi decoding algorithm, we can achieve a remarkable performance improvement with low computational complexity. Simulation results show that at a bit error rate (BER) of 3.7 /spl times/ 10/sup -6/ about 2.2-dB additional net gain has been obtained over the conventional scheme of the 4-D 16-state Wei code at a spectral efficiency of 6.7871 bit/T.

We define and apply a new algorithm called the iterative Viterbi decoding algorithm (IVA) to decode a high-rate parity-concatenated TCM system in which a trellis code is used as the inner code and a simple parity-check code is used as the outer code. With trellis shaping, the IVA can achieve a performance 1.25 dB away from the Shannon limit at a BER of 3/spl times/10/sup -5/ with low complexity. By augmenting the system with a binary BCH code, the error floor can be reduced to 10/sup -9/ with very little additional cost.

The Viterbi algorithm (1967) and conventional serial concatenated codes (CSCC) have been widely applied in digital communication systems over the last 30 years. We show that the Shannon capacity of additive white Gaussian noise (AWGN) channels can be approached by CSCCs and the iterative VA (IVA). We firstly study the algebraic properties of CSCCs. We then present the IVA to decode these codes. We also analyze the performance of the IVA and conclude that a better performance can be achieved if we replace the powerful block codes by some simple parity codes. One of the key results in this paper shows that by using a proper design for the decoding method, codes with small loops can be very efficiently decoded using a min-sum type algorithm. The numerical results show that the IVA can closely approach the Shannon sphere-packing lower bound and the Shannon limit. For block sizes ranging from 56 information bits to 11970 information bits, the IVA can perform to within about 1 dB of the Shannon sphere-packing lower bound at a block error rate of 10/sup -4/. We show that the IVA has a very low complexity and can be applied to many current standard systems, for example, the Qualcomm code-division multiple-access (CDMA) system and the NASA concatenated system, with very little modification or, for some cases, without any modification.

In this paper an optimal importance sampling (IS) method is derived for a transient Markov system. Several propositions are presented. It is shown that the optimal IS method is unique, and it must converge to the standard Monte Carlo (MC) simulation method when the sample path length approaches infinity. Therefore, 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. Numerical results are presented to support the argument.

A novel channel coding scheme is proposed for the multicarrier modulation system. With the parity-concatenated trellis coded modulation, the significant performance improvement (over 2 dB net gain) can be achieved in a multi-carrier system using the iterative Viterbi decoding algorithm. Due to its low complexity and compatibility with the standard Viterbi algorithm, this channel coding scheme may have the potential for practical applications, e.g., ADSL.

We construct parity-concatenated trellis codes in which a trellis code is used as the inner code and a simple parity-check code is used as the outer code. From the Tanner-Wiberg-Loeliger (1981, 1996) graph representation, several iterative decoding algorithms can be derived. However, since the graph of the parity-concatenated code contains many short cycles, the conventional min-sum and sum-product algorithms cannot achieve near-optimal decoding. After some simple modifications, we obtain near-optimal iterative decoders. The modifications include either (a) introducing a normalization operation in the min-sum and sum-product algorithms or (b) cutting the short cycles which arise in the iterative Viterbi algorithm (IVA). After modification, all three algorithms can achieve near-optimal performance, but the IVA has the least average complexity. We also show that asymptotically maximum-likelihood (ML) decoding and a posteriori probability (APP) decoding can be achieved using iterative decoders with only two iterations. Unfortunately, this asymptotic behavior is only exhibited when the bit-energy-to-noise ratio is above the cutoff rate. Simulation results show that with trellis shaping, iterative decoding can perform within 1.2 dB of the Shannon limit at a bit error rate (BER) of 4/spl times/10/sup -5/ for a block size of 20000 symbols. For a block size of 200 symbols, iterative decoding can perform within 2.1 dB of the Shannon limit.

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.

In this paper, we study importance sampling (IS) methods to construct long convolutional codes with fast recovery capability. For codes with long memory length (m/spl ges/12), the simulation method based on IS can avoid the excessive amount of computation required by other methods like analytical computation and standard Monte Carlo simulation. We establish a suboptimal IS method to search for good fast recovery convolutional codes with long memory lengths. The speed-up factors of two to six orders of magnitude over standard Monte Carlo simulation are obtained. Finally, we outline the code search procedures, present the code search results and give some applications of the codes.

We study the decoding problem in an uncertain noise environment. If the receiver knows the noise probability density function (PDF) at each time slot or its a priori probability, the standard Viterbi (1967) algorithm (VA) or the a posteriori probability (APP) algorithm can achieve optimal performance. However, if the actual noise distribution differs from the noise model used to design the receiver, there can be significant performance degradation due to the model mismatch. The minimax concept is used to minimize the worst possible error performance over a family of possible channel noise PDFs. We show that the optimal robust scheme is difficult to derive; therefore, alternative, practically feasible, robust decoding schemes are presented and implemented on a VA decoder and two-way APP decoder. The performance analysis and numerical results show our robust decoders have a performance advantage over standard decoders in uncertain noise channels, with no or little computational overhead. Our robust decoding approach can also explain why for turbo decoding overestimating the noise variance gives better results than underestimating it.

We derive an upper bound on the bit-error probability (BEP) in limited-search detection over a finite interference channel. A unified channel model is presented; this includes finite-length intersymbol interference channels and multiuser CDMA channels as two special cases. We show that the BEP of the M-algorithm (MA) is bounded from above by the sum of three terms: an upper bound on the error probability of the Viterbi (1967) algorithm (VA) detection given by Forney Jr. (1972), and upper bounds on the error probabilities of two types of erroneous decision caused by the correct path loss event. We prove that error propagation (in terms of the mean recovery step number) is finite for all finite interference channels. The convergence and asymptotic behavior of the upper bounds are studied. The results show that, if a channel satisfies certain mild conditions, all series in the bounds are convergent. One of the key results is that, for any finite interference channel satisfying certain mild conditions. the asymptotic BEP of the MA is bounded by the same upper and lower bounds (which have the same asymptotical behavior) as those for the VA if the correct path loss probability is smaller than that of the VA. Furthermore, we extend the above results to near optimally decode long convolutional codes in a short packet format (about 200-300 bits). We present a nonsorting combined M/T algorithm and showed that the M/T algorithm with M>2(/sup d/free//sup n/) and T>(d/sub free/E/sub b/)/n can near-optimally decode the code. We also propose a hierarchical decoding algorithm (HDA) to further cut down the average decoding complexity. Numerical results show that the bounds are reasonably tight. The HDA can achieve a performance within about 0.8 dB of the sphere-packing lower bound for a packet error rate of 10/sup -4/ and a packet length below 200 bits, which is the best reported decoding performance so far for block sizes from 100 to 200 bits.

We study and develop several robust decoding algorithms based on the minimax rule. The algorithms robust to estimation errors and channel variations. The decoding problem is studied when using a matched and mismatched decoder. Examples using robust the Viterbi algorithm (1967) and MAP algorithm are also presented.

A bootstrap iterative Viterbi algorithm (BIVA) is proposed based on a bootstrap structure. Two different modifications are then considered for both very short size blocks (say 100-250 bits) and the medium size blocks (1000-3000 bits). It shows that the iterative decoding can be achieved by using the conventional Viterbi algorithm, which does not require the noise variance estimation. The numerical results show the significant performance improvement over the standard Viterbi algorithm is possible. For a block length of 1500 bits and with a 32 state VA, the 2D BIVA can achieve a bit error rate of 2/spl times/10/sup -5/ at an E/sub b//E/sub 0/ of 2.3 dB away from the Shannon limit. For both information block lengths of 1944 and 11970 bits, in term of its performance respect to the Shannon limit and the Shannon sphere packing bound, the 2D-BIVA is about 0.2-0.3 dB worse than the best known rate 1/2 JPL turbo codes of similar information block sizes. With some simple modifications, most of current systems (where the Viterbi algorithms used) can benefit significantly from this iterative decoding procedure.

In this letter we estimate the bit error probability (BEP) of optimum multiuser detection for synchronous and asynchronous code division multiple access (CDMA) systems on Gaussian and fading channels. We first compute an upper bound and a lower bound on the bit error probability for a given spreading code, then average the bounds over a few thousand sets of spreading codes. These bounds are obtained from a partial distance spectrum. On Gaussian channels, the upper bound converges to the lower bound at moderate to large signal-to-noise ratios. However, on fading channels the upper bound does not converge, hence we present our results for the lower bound only. The numerical results show that: 1) the BEP of a 31-user CDMA system with binary random spreading codes of length 31 is only two to four times higher than the BEP of the single user system; 2) the number of users that can be accommodated in an asynchronous CDMA system is larger than the processing gain; and 3) optimum multiuser detection outperforms linear detection (e.g., the decorrelating detector) by about 2.8 to 5.7 dB.

Simple reduced tree-search detection schemes of the breadth-first type are applied to suboptimal joint multiuser detection in bit-synchronous code-division multiple access (CDMA) systems over both Gaussian and two-path Rayleigh-fading channels. It is pointed out that in contrast to the case of the optimal multiuser detector, the choice of the receiver filter severely influences the performance of suboptimal multiuser detectors. Simulation results supported by analysis show that breadth-first tree-search algorithms using a decorrelating noise whitening receiver filter perform better than similar receivers, which solely use a matched filter (MF) for virtually all nonsingular spreading code sets studied. Most of the code sets are randomly generated. The M- and T-algorithm detectors based on decorrelating noise whitening filter (WF) outputs can achieve near optimum performance at a very low complexity compared to the optimal detector, although the proposed detectors are more complex than some known suboptimum detectors. Furthermore, the use of combining techniques is considered for a two-path Rayleigh-fading channel, and a semi-synchronous CDMA structure is proposed. It is shown that if maximum ratio combining (MRC) is employed, the decorrelating noise WF still exists. The corresponding suboptimal combining detector with a decorrelating noise WF outperforms a similar noncombining detector.

In this correspondence, we first correct a mistake in Best et al. (1995) and then present a method to compute the exact probability of information bit error as a function of truncation length K for a rate 1/2, 2 state code, Finally, we generalize the method to compute the exact bit-error probability of the above convolutional code when the information bits are transmitted in blocks. The simulation results are compared with the analytical results and good agreement is observed.

In this paper, we evaluate the performance of optimum multiuser detection by union bounding techniques for a large number of users. It is a difficult task to analytically compute the average bit error probability of multiuser DS-CDMA systems. In this paper we aim to use bounds to accurately evaluate the optimal performance of a multiuser DS-CDMA system, both synchronous and asynchronous. We present a general algorithm to compute the partial distance spectrum of the multiuser system. Numerical results for both systems with binary random signature waveforms of length 31 are used to illustrate the method. It has been found that the optimal bounds for the asynchronous system have a lower bit error probability (BEP) than synchronous systems. Focus is given to two areas namely 1) computing bit error probability (BEP) given a particular correlation matrix, 2) applying optimal conditional importance sampling and computing bit error probability for randomly generated correlation matrices.

We study commonalities of new bandwidth efficient and power efficient quadrature-quadrature phase shift keying (Q/sup 2/PSK), constant envelope Q/sup 2/PSK (CEQ/sup 2/PSK), rotative QPSK (RQPSK), frequency and phase shift keying (FPSK), expurgated FPSK (E-FPSK), and the well-known orthogonal frequency division multiplexing (OFDM) (or multicarrier modulation) and L-orthogonal (LO) signaling on AWGN channels. "Identical" systems are defined as systems that have the same bit error rate (BER) versus the bit energy to noise ratio function and the same power spectral density. The results show that: (a) Q/sup 2/PSK, FPSK, and OFDM are "identical", and (b) CEQ/sup 2/PSK, E/sub 4/-FPSK and LO are "identical". Also, a mistake in an article by Fleisher and Qu (see IEEE J. Select. Areas Commun., vol.10, no.8, p.1243-1253, 1992) is corrected.

A near ideal noise whitening filter for a time-varying code-division multiple-access (CDMA) system is examined. First, the structure of the ideal noise whitening filter is determined. The ideal noise whitening filter for a time-varying CDMA system is dependent on unknown future system parameters and is, therefore, impractical. A near ideal, realizable whitening filter is introduced as a solution. The convergence of the factorization method for a time-varying CDMA system is considered. The truncation of the number of taps of the ideal noise whitening filter is studied and a metric function based on the near ideal noise whitening filter for a tree search detection algorithm is formulated. Simulation results are obtained for five and ten-user time-varying CDMA systems with binary random signature sequences of length 10 and a rectangular chip waveform. The results show that the near ideal noise whitening filter can accurately approximate the ideal noise whitening filter at a low complexity level. The performance degradation of a suboptimal tree search detector for a time-varying, asynchronous CDMA system using a typical near ideal noise whitening filter is minimal compared to an identical system using the ideal noise whitening filter.

In this paper we estimate the average bit-error probability of a direct-sequence spread-spectrum multiple-access (DS-SSMA) system using MPSK and a linear coherent detector on the satellite mobile channel (SMC). The formulas derived in this paper are suitable for various types of signature sequences and chip waveforms. The numerical results are presented for DS-SSMA using BPSK and QPSK with random signature sequences and three different chip waveforms: the rectangular, the cosine, and the root Nyquist filter (RNF) with rolloff rate, /spl beta/=0.4. The results show that the performance of a DS-SSMA system with complex random signature sequences is superior to a system using binary random signature sequences on Gaussian and Rician (K=10) channels, while on flat fading Rayleigh channels the performance for both systems is similar. In DS-SSMA, the RNF has the highest bandwidth efficiency of the three chip waveforms. The performance of DS-SSMA is also analyzed on the SMC using the Gaussian approximation (GA) method. Compared to the estimated results, GA gives a pessimistic approximation for binary random signature sequences on Gaussian and Rician channels.>

The performance of multi-user orthogonal frequency division multiplexing (OFDM) with raised cosine time domain pulse shaping is studied on the satellite mobile channel (SMC) and the two-path Rayleigh fading channel. A multi-user time and carrier frequency synchronization scheme is discussed. The relationship between the synchronization requirement and the roll-off rate (/spl beta/) of the pulse shaping is explored. In Gaussian and typical Rician (K=10) channels, multi-user OFDM with /spl beta/=0.2 requires timing and carrier frequency synchronization accuracies of 4% and 2%, respectively, in order to avoid severe degradation due to multi-user adjacent channel interference, while on the two-path Rayleigh channel these values must be better than 2% for error floors less than 10/sup -3/. Timing and carrier frequency accuracies are normalized to T and 1/T respectively, where T is the symbol duration. Multi-user OFDM is less affected by the multipath time delay and slightly more severely affected by the Doppler frequency shift than traditional FDM with root Nyquist filtering (FDM/RNF) for the same value of /spl beta/.>