Maximum-likelihood (AIL) estimation of long chaotic sequences is generally statistically inefficient. Therefore, as the length of the sequences increase we do not obtain the usual Nil. behavior of consistency and norm...
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Maximum-likelihood (AIL) estimation of long chaotic sequences is generally statistically inefficient. Therefore, as the length of the sequences increase we do not obtain the usual Nil. behavior of consistency and normality. We discuss here a specific class of chaotic sequences for which consistency is preserved. The itineraries of the chaotic sequences in this class are derived from a set of binary code words. As a result, we are able to guarantee a minimal Hamming distance between them which increases linearly with the sequences length. In other words, pairs of sequences from this class have a non vanishing normalized Hamming distance between their itineraries as their length goes to infinity. We derive expressions related to the associated Euclidean distance between these chaotic sequences. Using these expressions we show that the condition for consistent estimation of a sequence from the class is satisfied with probability 1. Throughout the paper, we use the discrete-time symmetric tent chaotic sequences as an example and the expressions are derived for this specific case. We argue, however, that our results apply for a wider class of chaotic sequences. We mention the applicability of the work to the field of error-correcting codes for analog signals. However, it may be of interest for readers working on other aspects of chaotic maps as well.
In Long-Term Evolution (LTE) downlink control channel, a large number of blind decoding attempts are made, while the number of valid codewords is limited. The blind decoding results are then verified using a 16-bit cy...
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In Long-Term Evolution (LTE) downlink control channel, a large number of blind decoding attempts are made, while the number of valid codewords is limited. The blind decoding results are then verified using a 16-bit cyclic redundancy check (CRC). However, even with the 16-bit CRC, the false alarm (FA) rate of such blind decoding is inevitably high. This paper investigates the problem of pruning of blind decoding results for reduction of the FA rate. To the best of our knowledge, the approach using a soft correlation metric (SCM) shows the best FA reduction performance among existing schemes. However, following the Bayes principle, we propose novel likelihood-based pruning that provides systematic balancing between the FA rate and the miss (MS) rate. Moreover, the simulation results show that the signal-to-noise ratio (SNR) gain of our proposed scheme is unbounded, with respect to the SCM-based scheme, in the independent and identically distributed (i.i.d.) Rayleigh fading channel. Moreover, the proposed scheme is shown to be less complex than the existing scheme. Finally, it is proved that, as SNR increases, the proposed approach has the decision error probability that approaches the minimum value yielding near-optimal contraction of Voronoi regions for pruning of blind decoding results.
Low-Density Parity-Check (LDPC) codes are very powerful channel coding schemes with a broad range of applications. The existence of low complexity (i.e., linear time) iterative message passing decoders with close to o...
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Low-Density Parity-Check (LDPC) codes are very powerful channel coding schemes with a broad range of applications. The existence of low complexity (i.e., linear time) iterative message passing decoders with close to optimum errorcorrection performance is one of the main strengths of LDPC codes. It has been shown that the performance of these decoders can be further enhanced if the LDPC codes are extended to higher order Galois fields, yielding so called non-binary LDPC codes. However, this performance gain comes at the cost of rapidly increasing decoding complexity. To deal with this increased complexity, we present an efficient implementation of a signed-log domain FFT decoder for non-binary irregular LDPC codes which exploits the inherent massive parallelization capabilities of message passing decoders. We employ Nvidia's Compute Unified Device Architecture (CUDA) to incorporate the available processing power of state-of-the-art Graphics Processing Units (GPUs). Furthermore, we present a CUDA implementation of the signed-log domain FFT decoder using the so-called layered update rule, in which check nodes are updated one after another. This sequential updating of nodes has been shown to converge about twice as fast as the traditional flooding scheme. To achieve a high speedup of the layered CUDA implementation, we employ quasi-cyclic non-binary LDPC codes since they allow to update multiple neighboring check nodes in parallel without any performance loss.
An embedded transmission (ET) scheme is proposed to easily apply error-correcting codes into optical code-division multiple-access (CDMA) systems for immunity from multiple-access interference (MAI). The ET scheme:off...
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An embedded transmission (ET) scheme is proposed to easily apply error-correcting codes into optical code-division multiple-access (CDMA) systems for immunity from multiple-access interference (MAI). The ET scheme:offers high transmission capability over the traditional scheme using pulse position modulation (PPM) signaling, because a 2(J)-ary symbol of each user is embedded in the signature sequence with 2(J) weighted positions. Furthermore, the ET scheme with 2(J)-ary PPM signaling makes the optical CDMA system J parallel transmission systems, because J bits consisting of 2(J)-ary symbol are separately decided. Since such a separate decision is a comparison decision, the effect of MAI added in the optical channel is converted to symmetric errors in the individual parallel transmission systems. Using the symmetric error-correcting (SEC) code immunizes the individual parallel transmission systems against MAI more easily than the embedded-modulation scheme described in [1] because the ET scheme avoids using the asymmetric error correcting code, which is difficult to implement. We analyze the bit error rate under Poisson Photon counting channel and show that the ET scheme has an advantage of good energy efficiency over the traditional scheme in applying SEC codes.
Arbitrarily tight upper and lower bounds on the pairwise error probability (PEP) of a trellis-coded or convolutional-coded direct-sequence spread-spectrum multiple-access (DS/SSMA) communication system over a Rayleigh...
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Arbitrarily tight upper and lower bounds on the pairwise error probability (PEP) of a trellis-coded or convolutional-coded direct-sequence spread-spectrum multiple-access (DS/SSMA) communication system over a Rayleigh fading channel are derived. A new set of probability density functions (pdf's) and cumulative distribution functions (cdf's) of the multiple-access interference (MAI) statistic is derived, and a modified bounding technique is proposed to obtain the bounds. The upper bounds and lower bounds together specify the accuracy of the resulting estimation of the PEP, and give an indication of the system error performance. Several suboptimum decoding schemes are proposed and their performances are compared to that of the optimum decoding scheme by the average pairwise error probability (APEP) values. The approach can be used to accurately study the multiple-access capability of the coded DS/SSMA system without numerical integrations.
We investigate how forward errorcorrection (FEC) can be combined with automatic repeat request (ARQ) to achieve scalable reliable multicast transmission. We consider the two scenarios where FEC is introduced as a tra...
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We investigate how forward errorcorrection (FEC) can be combined with automatic repeat request (ARQ) to achieve scalable reliable multicast transmission. We consider the two scenarios where FEC is introduced as a transparent layer underneath a reliable multicast layer that uses ARQ, and where FEC and ARQ are both integrated into a single layer that uses the retransmission of parity data to recover from the loss of original data packets. To evaluate the performance improvements due to FEC, we consider different loss rates and different types of loss behaviors (spatially or temporally correlated loss, homogeneous or heterogeneous loss) for up to 10(6) receivers, Our results show that introducing FEC as a transparent layer below ARQ can improve multicast transmission efficiency and scalability. However, there are substantial additional improvements when FEC and ARQ are integrated.
In this paper, we develop efficient decoders for non-binary low-density parity-check codes using the alternating direction method of multipliers (ADMM). We apply ADMM to two decoding problems. The first problem is lin...
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In this paper, we develop efficient decoders for non-binary low-density parity-check codes using the alternating direction method of multipliers (ADMM). We apply ADMM to two decoding problems. The first problem is linear programming (LP) decoding. In order to develop an efficient algorithm, we focus on non-binary codes in fields of characteristic two. This allows us to transform each constraint in F-2m to a set of constraints in F-2 that has a factor graph representation. Applying ADMM to the LP decoding problem results in two types of non-trivial sub-routines. The first type requires us to solve an unconstrained quadratic program. We solve this problem efficiently by leveraging new results obtained from studying the above factor graphs. The second type requires Euclidean projections onto polytopes that are studied in the literature. Such projections can be solved efficiently using off-the-shelf techniques, which scale linearly in the dimension of the vector to project. ADMM LP decoding scales linearly with block length, linearly with check degree, and quadratically with field size. The second problem we consider is a penalized LP decoding problem. This problem is obtained by incorporating a penalty term into the LP decoding objective. The purpose of the penalty term is to make non-integer solutions (pseudocodewords) more expensive and hence to improve decoding performance. The ADMM algorithm for the penalized LP problem requires Euclidean projection onto a polytope formed by embedding the constraints specified by the non-binary single parity-check code, which can be solved by applying the ADMM technique to the resulting quadratic program. Empirically, this decoder achieves a much reduced error rate than LP decoding at low signal-to-noise ratios.
In this paper, a method to design regular (2, d(c))-LDPC codes over GF(q) with both good waterfall and error floor properties is presented, based on the algebraic properties of their binary image. First, the algebraic...
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In this paper, a method to design regular (2, d(c))-LDPC codes over GF(q) with both good waterfall and error floor properties is presented, based on the algebraic properties of their binary image. First, the algebraic properties of rows of the parity check matrix H associated with a code are characterized and optimized to improve the waterfall. Then the algebraic properties of cycles and stopping sets associated with the underlying Tanner graph are studied and linked to the global binary minimum distance of the code. Finally, simulations are presented to illustrate the excellent performance of the designed codes.
In this paper the impact of the approximation error on the decisions taken by LDPC decoders is studied. In particular, we analyze the mechanism, by means of which approximation error alters the decisions of a finite-w...
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In this paper the impact of the approximation error on the decisions taken by LDPC decoders is studied. In particular, we analyze the mechanism, by means of which approximation error alters the decisions of a finite-word-length implementation of the decoding algorithm, with respect to the decisions taken by the infinite precision case, approximated here by double-precision floating-point. We focus on four popular algorithms for LDPC decoding, namely Log Sum-Product, Min-Sum, normalized Min-Sum and offset Min-Sum. A corresponding theoretical model is developed which derives an expression for the probability of altering the decision due to approximation. The model is applied to the above algorithms for the case of the first iteration as well as for higher numbers of iterations. Finally, experimental results prove the validity of the proposed model.
We introduce a class of finite systems models of gene regulatory networks exhibiting behavior of the cell cycle. The network is an extension of a Boolean network model. The system spontaneously cycles through a finite...
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We introduce a class of finite systems models of gene regulatory networks exhibiting behavior of the cell cycle. The network is an extension of a Boolean network model. The system spontaneously cycles through a finite set of internal states, tracking the increase of an external factor such as cell mass, and also exhibits checkpoints in which errors in gene expression levels due to cellular noise are automatically corrected. We present a 7-gene network based on Projective Geometry codes, which can correct, at every given time, one gene expression error. The topology of a network is highly symmetric and requires using only simple Boolean functions that can be synthesized using genes of various organisms. The attractor structure of the Boolean network contains a single cycle attractor. It is the smallest nontrivial network with such high robustness. The methodology allows construction of artificial gene regulatory networks with the number of phases larger than in natural cell cycle.
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