Browsing by Subject "Decoding"

Now showing 1 - 20 of 31

Open Access
Adaptive routing framework for network on chip architectures
(ACM, 2016-01) Mustafa, Naveed Ul; Öztürk, Özcan; Niar, S.
In this paper we suggest and demonstrate the idea of applying multiple routing algorithms during the execution of a real application mapped on a Network-on-Chip (NoC). Traffic pattern of a real application may change during its execution. As performance of an algorithm depends on the traffic pattern, using the same routing algorithm for the entire span of execution may be inefficient. We study the feasibility of this idea for applications such as SPARSE and MPEG-4 decoder, by applying different routing algorithms. By applying more than one routing algorithms, throughput improves up to 17.37% and 6.74% in the case of SPARSE and MPEG-4 decoder applications, respectively, as compared to the application of single routing algorithm. © 2016 ACM.
Open Access
Binary signaling under subjective priors and costs as a game
(Institute of Electrical and Electronics Engineers Inc., 2019) Sarıtaş, S.; Gezici, Sinan; Yüksel, S.; Teel, A. R.; Egerstedt, M.
Many decentralized and networked control problems involve decision makers which have either misaligned criteria or subjective priors. In the context of such a setup, in this paper we consider binary signaling problems in which the decision makers (the transmitter and the receiver) have subjective priors and/or misaligned objective functions. Depending on the commitment nature of the transmitter to his policies, we formulate the binary signaling problem as a Bayesian game under either Nash or Stackelberg equilibrium concepts and establish equilibrium solutions and their properties. In addition, the effects of subjective priors and costs on Nash and Stackelberg equilibria are analyzed. It is shown that there can be informative or non-informative equilibria in the binary signaling game under the Stackelberg assumption, but there always exists an equilibrium. However, apart from the informative and non-informative equilibria cases, under certain conditions, there does not exist a Nash equilibrium when the receiver is restricted to use deterministic policies. For the corresponding team setup, however, an equilibrium typically always exists and is always informative. Furthermore, we investigate the effects of small perturbations in priors and costs on equilibrium values around the team setup (with identical costs and priors), and show that the Stackelberg equilibrium behavior is not robust to small perturbations whereas the Nash equilibrium is.
Open Access
Channel polarization: a method for constructing capacity-achieving codes for symmetric binary-input memoryless channels
(IEEE, 2009) Arikan, E.
A method is proposed, called channel polarization, to construct code sequences that achieve the symmetric capacity I(W) of any given binary-input discrete memoryless channel (B-DMC) W. The symmetric capacity is the highest rate achievable subject to using the input letters of the channel with equal probability. Channel polarization refers to the fact that it is possible to synthesize, out of N independent copies of a given B-DMC W, a second set of N binary-input channels {WN (i): 1 ≤ i ≤ N} becomes large, the fraction of indices i for which I(WN (i) is near 1 approaches I(W) and the fraction for which I(WN (i) is near 0 approaches 1 - I(W). The polarized channels WN (i) are well-conditioned for channel coding: one need only send data at rate 1 through those with capacity near 1 and at rate 0 through the remaining. Codes constructed on the basis of this idea are called polar codes. The paper proves that, given any B-DMC W with I(W) and any target rate R < I(W), there exists a sequence of polar codes {Cn;n ≥ 1 such that Cn has block-length N = 2n, rate ≥ R, and probability of block error under successive cancellation decoding bounded as Pe (N, R) ≤ O(N-1/4 independently of the code rate. This performance is achievable by encoders and decoders with complexity O(N\log N) for each.
Open Access
Decoding strategies at the relay with physical-layer network coding
(Institute of Electrical and Electronics Engineers, 2012) Bhat, U.; Duman, T. M.
A two-way relay channel is considered where two users exchange information via a common relay in two transmission phases using physical-layer network coding (PNC). We consider an optimal decoding strategy at the relay to decode the network coded sequence during the first transmission phase, which is approximately implemented using a list decoding (LD) algorithm. The algorithm jointly decodes the codewords transmitted by the two users and sorts the L most likely pair of sequences in the order of decreasing a-posteriori probabilities, based on which, estimates of the most likely network coded sequences and the decoding results are obtained. Using several examples, it is observed that a lower complexity alternative, that jointly decodes the two transmitted codewords, has a performance similar to the LD based decoding and offers a near-optimal performance in terms of the error rates corresponding to the XOR of the two decoded sequences. To analyze the error rate at the relay, an analytical approximation of the word-error rate using the joint decoding (JD) scheme is evaluated over an AWGN channel using an approach that remains valid for the general case of two users adopting different codebooks and using different power levels. We further extend our study to frequency selective channels where two decoding approaches at the relay are investigated, namely; a trellis based joint channel detector/physical-layer network coded sequence decoder (JCD/PNCD) which is shown to offer a near-optimal performance, and a reduced complexity channel detection based on a linear receiver with minimum mean squared error (MMSE) criterion which is particularly useful where the number of channel taps is large.
Open Access
The design of finite-state machines for quantization using simulated annealing
(IEEE, 1993) Kuruoğlu, Ercan Engin; Ayanoğlu, E.
In this paper, the combinatorial optimization algorithm known as simulated annealing is used for the optimization of the trellis structure or the next-state map of the decoder finite-state machine in trellis waveform coding. The generalized Lloyd algorithm which finds the optimum codebook is incorporated into simulated annealing. Comparison of simulation results with previous work in the literature shows that this combined method yields coding systems with good performance.
Open Access
Design of LDPC codes for two-way relay systems with physical-layer network coding
(IEEE, 2013) Tanc, A. K.; Duman, T. M.; Tepedelenlioglu, C.
This letter presents low-density parity-check (LDPC) code design for two-way relay (TWR) systems employing physical-layer network coding (PLNC). We focus on relay decoding, and propose an empirical density evolution method for estimating the decoding threshold of the LDPC code ensemble. We utilize the proposed method in conjunction with a random walk optimization procedure to obtain good LDPC code degree distributions. Numerical results demonstrate that the specifically designed LDPC codes can attain improvements of about 0.3 dB over off-the-shelf LDPC codes (designed for point-to-point additive white Gaussian noise channels), i.e., it is new code designs are essential to optimize the performance of TWR systems.
Open Access
Design of trellis waveform coders with near-optimum structure
(IET, 1992) Kuruoglu, E.E.; Ayanoglu, E.
In this Letter the combinatorial optimisation algorithm known as simulated annealing is used for the optimisation of the trellis structure of the next-state map of the decoder finite-state machine in trellis waveform coding. The generalised Lloyd algorithm which finds the optimum codebook is incorporated into simulated annealing so that near-optimum coding systems are designed. Comparison of simulation results with previous work in the literature shows that this method yields better coding systems than those published in the literature.
Open Access
An efficient computation model for coarse grained reconfigurable architectures and its applications to a reconfigurable computer
(IEEE, 2010-07) Atak, Oğuzhan; Atalar, Abdullah
The mapping of high level applications onto the coarse grained reconfigurable architectures (CGRA) are usually performed manually by using graphical tools or when automatic compilation is used, some restrictions are imposed to the high level code. Since high level applications do not contain parallelism explicitly, mapping the application directly to CGRA is very difficult. In this paper, we present a middle level Language for Reconfigurable Computing (LRC). LRC is similar to assembly languages of microprocessors, with the difference that parallelism can be coded in LRC. LRC is an efficient language for describing control data flow graphs. Several applications such as FIR, multirate, multichannel filtering, FFT, 2D-IDCT, Viterbi decoding, UMTS and CCSDC turbo decoding, Wimax LDPC decoding are coded in LRC and mapped to the Bilkent Reconfigurable Computer with a performance (in terms of cycle count) close to that of ASIC implementations. The applicability of the computation model to a CGRA having low cost interconnection network has been validated by using placement and routing algorithms. © 2010 IEEE.
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Exact expression and tight bound on pairwise error probability for performance analysis of turbo codes over Nakagami-m fading channels
(IEEE, 2007) Ali, S. A.; Kambo, N. S.; İnce, E. A.
This letter presents derivation for an exact and efficient expression on pairwise error probability over fully interleaved Nakagami-m fading channels under ideal channel state information at the decoder. As an outcome, this derivation also leads to a tight upper bound on pairwise error probability which is close to the exact expression. Pairwise error probability plots for different values of Nakagami parameter m along with an already existing numerically computable expression are provided. As an application of pairwise error probability, average union upper bounds for turbo codes having (1, 7/5, 7/5) and (1, 5/7, 5/7) generator polynomials employing transfer function approach are presented to illustrate the usefulness of the new efficient results. © 2007 IEEE.
Open Access
Fibre products of superelliptic curves and codes therefrom
(IEEE, 1997) Stepanov, Serguei A.; Özbudak, Ferruh
A method of constructing long geometric Goppa codes coming from fiber products of superelliptic curves is presented. A family of smooth projective curves with a lot of Fq-rational points are needed to produce a family of asymptotically good geometric Goppa codes. The genus in every such family is considerably less than the number of rational points, so the corresponding geometric Goppa codes have rather good parameters. Examples of such families are provided by modular curves, by Drinfeld modular curves, and by Artin-Schreier coverings of the projective line.
Open Access
An FPGA implementation architecture for decoding of polar codes
(IEEE, 2011) Pamuk, Alptekin
Polar codes are a class of codes versatile enough to achieve the Shannon bound in a large array of source and channel coding problems. For that reason it is important to have efficient implementation architectures for polar codes in hardware. Motivated by this fact we propose a belief propagation (BP) decoder architecture for an increasingly popular hardware platform; Field Programmable Gate Array (FPGA). The proposed architecture supports any code rate and is quite flexible in terms of hardware complexity and throughput. The architecture can also be extended to support multiple block lengths without increasing the hardware complexity a lot. Moreover various schedulers can be adapted into the proposed architecture so that list decoding techniques can be used with a single block. Finally the proposed architecture is compared with a convolutional turbo code (CTC) decoder for WiMAX taken from a Xilinx Product Specification and seen that polar codes are superior to CTC codes both in hardware complexity and throughput. © 2011 IEEE.
Open Access
Fractional fourier transform in time series prediction
(IEEE, 2022-12-09) Koç, Emirhan; Koç, Aykut
Several signal processing tools are integrated into machine learning models for performance and computational cost improvements. Fourier transform (FT) and its variants, which are powerful tools for spectral analysis, are employed in the prediction of univariate time series by converting them to sequences in the spectral domain to be processed further by recurrent neural networks (RNNs). This approach increases the prediction performance and reduces training time compared to conventional methods. In this letter, we introduce fractional Fourier transform (FrFT) to time series prediction by RNNs. As a parametric transformation, FrFT allows us to seek and select better-performing transformation domains by providing access to a continuum of domains between time and frequency. This flexibility yields significant improvements in the prediction power of the underlying models without sacrificing computational efficiency. We evaluated our FrFT-based time series prediction approach on synthetic and real-world datasets. Our results show that FrFT gives rise to performance improvements over ordinary FT.
Open Access
Generalized approximate message-passing decoder for universal sparse superposition codes
(IEEE, 2017-06) Bıyık, Erdem; Barbier, J.; Dia, M.
Sparse superposition (SS) codes were originally proposed as a capacity-achieving communication scheme over the additive white Gaussian noise channel (AWGNC) [1]. Very recently, it was discovered that these codes are universal, in the sense that they achieve capacity over any memoryless channel under generalized approximate message-passing (GAMP) decoding [2], although this decoder has never been stated for SS codes. In this contribution we introduce the GAMP decoder for SS codes, we confirm empirically the universality of this communication scheme through its study on various channels and we provide the main analysis tools: state evolution and the potential. We also compare the performance of GAMP with the Bayes-optimal MMSE decoder. We empirically illustrate that despite the presence of a phase transition preventing GAMP to reach the optimal performance, spatial coupling allows to boost the performance that eventually tends to capacity in a proper limit. We also prove that, in contrast with the AWGNC case, SS codes for binary input channels have a vanishing error floor in the limit of large codewords. Moreover, the performance of Hadamard-based encoders is assessed for practical implementations. © 2017 IEEE.
Open Access
Guessing with lies
(IEEE, 2002-06-07) Arıkan, Erdal; Boztaş, S.
A practical algorithm was obtained for directly generating an optimal guessing sequence for guessing under lies. An optimal guessing strategy was defined as one which minimizes the number of average number of guesses in determining the correct value of a random variable. The information-theoretic bounds on the average number of guesses for optimal strategies were also derived.
Open Access
Implementing the Han-Kobayashi scheme using low density parity check codes over Gaussian interference channels
(Institute of Electrical and Electronics Engineers Inc., 2015) Sharifi S.; Tanc, A. K.; Duman, T. M.
We focus on Gaussian interference channels (GICs) and study the Han-Kobayashi coding strategy for the two-user case with the objective of designing implementable (explicit) channel codes. Specifically, low-density parity-check codes are adopted for use over the channel, their benefits are studied, and suitable codes are designed. Iterative joint decoding is used at the receivers, where independent and identically distributed channel adapters are used to prove that log-likelihood-ratios exchanged among the nodes of the Tanner graph enjoy symmetry when BPSK or QPSK with Gray coding is employed. This property is exploited in the proposed code optimization algorithm adopting a random perturbation technique. Code optimization and convergence threshold computations are carried out for different GICs employing finite constellations by tracking the average mutual information. Furthermore, stability conditions for the admissible degree distributions under strong and weak interference levels are determined. Via examples, it is observed that the optimized codes using BPSK or QPSK with Gray coding operate close to the capacity boundary for strong interference. For the case of weak interference, it is shown that nontrivial rate pairs are achievable via the newly designed codes, which are not possible by single user codes with time sharing. Performance of the designed codes is also studied for finite block lengths through simulations of specific codes picked with the optimized degree distributions with random constructions, where, for one instance, the results are compared with those of some structured designs. © 1972-2012 IEEE.
Open Access
An inequality on guessing and its application to sequential decoding
(Institute of Electrical and Electronics Engineers, 1996-01) Arikan, E.
Let (X,Y) be a pair of discrete random variables with X taking one of M possible values, Suppose the value of X is to be determined, given the value of Y, by asking questions of the form "Is X equal to x?" until the answer is "Yes". Let G(x|y) denote the number of guesses in any such guessing scheme when X=x, Y=y. We prove that E[G(X|Y)/sup /spl rho//]/spl ges/(1+lnM)/sup -/spl rho///spl Sigma//sub y/[/spl Sigma//sub x/P/sub X,Y/(x,y)/sup 1/1+/spl rho//]/sup 1+/spl rho// for any /spl rho//spl ges/0. This provides an operational characterization of Renyi's entropy. Next we apply this inequality to the estimation of the computational complexity of sequential decoding. For this, we regard X as the input, Y as the output of a communication channel. Given Y, the sequential decoding algorithm works essentially by guessing X, one value at a time, until the guess is correct. Thus the computational complexity of sequential decoding, which is a random variable, is given by a guessing function G(X|Y) that is defined by the order in which nodes in the tree code are hypothesized by the decoder. This observation, combined with the above lower bound on moments of G(X|Y), yields lower bounds on moments of computation in sequential decoding. The present approach enables the determination of the (previously known) cutoff rate of sequential decoding in a simple manner; it also yields the (previously unknown) cutoff rate region of sequential decoding for multiaccess channels. These results hold for memoryless channels with finite input alphabets.
Open Access
An inequality on guessing and its application to sequential decoding
(IEEE, 1995) Arıkan, Erdal
Let (X,Y) be a pair of discrete random variables with X taking values from a finite set. Suppose the value of X is to be determined, given the value of Y, by asking questions of the form 'is X equal to x?' until the answer is 'yes'. Let G(x|y) denote the number of guesses in any such guessing scheme when X=x, Y=y. The main result is a tight lower bound on nonnegative moments of G(X|Y). As an application, lower bounds are given on the moments of computation in sequential decoding. In particular, a simple derivation of the cutoff rate bound for a single-user channels is obtained, and the previously unknown cutoff rate region of multi-access channels is determined.
Open Access
Joint detection and decoding in the presence of prior information with uncertainty
(Institute of Electrical and Electronics Engineers Inc., 2016) Bayram, S.; Dulek, B.; Gezici, Sinan
An optimal decision framework is proposed for joint detection and decoding when the prior information is available with some uncertainty. The proposed framework provides tradeoffs between the average inclusive error probability (computed using estimated prior probabilities) and the worst case inclusive error probability according to the amount of uncertainty while satisfying constraints on the probability of false alarm and the maximum probability of miss-detection. Theoretical results that characterize the structure of the optimal decision rule according to the proposed criterion are obtained. The proposed decision rule reduces to some well-known detectors in the case of perfect prior information or when the constraints on the probabilities of miss-detection and false alarm are relaxed. Numerical examples are provided to illustrate the theoretical results. © 2016 IEEE.
Open Access
Joint source-channel coding and guessing with application to sequential decoding
(Institute of Electrical and Electronics Engineers, 1998-09) Arikan, E.; Merhav, N.
We extend our earlier work on guessing subject to distortion to the joint source-channel coding context. We consider a system in which there is a source connected to a destination via a channel and the goal is to reconstruct the source output at the destination within a prescribed distortion level with respect to (w.r.t.) some distortion measure. The decoder is a guessing decoder in the sense that it is allowed to generate successive estimates of the source output until the distortion criterion is met. The problem is to design the encoder and the decoder so as to minimize the average number of estimates until successful reconstruction. We derive estimates on nonnegative moments of the number of guesses, which are asymptotically tight as the length of the source block goes to infinity. Using the close relationship between guessing and sequential decoding, we give a tight lower bound to the complexity of sequential decoding in joint source-channel coding systems, complementing earlier works by Koshelev and Hellman. Another topic explored here is the probability of error for list decoders with exponential list sizes for joint source-channel coding systems, for which we obtain tight bounds as well. It is noteworthy that optimal performance w.r.t. the performance measures considered here can be achieved in a manner that separates source coding and channel coding.
Open Access
Large deviations of probability rank
(IEEE, 2000) Arıkan, Erdal
Consider a pair of random variables (X,Y) with distribution P. The probability rank function is defined so that G(x|y) = 1 for the most probable outcome x conditional on Y = y, G(x|y) = 2 for the second most probable outcome, and so on, resolving ties between elements with equal probabilities arbitrarily. The function G was considered in [1] in the context of finding the unknown outcome of a random experience by asking question of the form 'Is the outcome equal to x?' sequentially until the actual outcome is determined. The primary focus in [1], and the subsequent works [2], [3], was to find tight bounds on the moments E[G(X|Y)θ]. The present work is closely related to these works but focuses more directly on the large deviations properties of the probability rank function.