Browsing UA Faculty Publications by Authors
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2D LDPC Codes and Joint Detection and Decoding for TwoDimensional Magnetic RecordingMatcha, Chaitanya Kumar; Roy, Shounak; Bahrami, Mohsen; Vasic, Bane; Srinivasa, Shayan Garani; Univ Arizona, Dept Elect & Comp Engn (IEEEINST ELECTRICAL ELECTRONICS ENGINEERS INC, 201802)Twodimensional magnetic recording (TDMR) is a promising technology for boosting areal densities (ADs) using sophisticated signal processing algorithms within a systems framework. The read/write channel architectures have to effectively tackle 2D intersymbol interference (ISI), 2D synchronization errors, media and electronic noise sources, as well as thermal asperities resulting in burst erasures. The 1D lowdensity parity check (LDPC) codes are well studied to correct large 1D burst errors/erasures. However, such 1D LDPC codes are not suitable for correcting 2D burst errors/erasures due to the 2D span of errors. In this paper, we propose construction of a native 2D LDPC code to effectively correct 2D burst erasures. We also propose a joint detection and decoding engine based on the generalized belief propagation algorithm to simultaneously handle 2D ISI, as well as correct bit/burst errors for TDMR channels. This paper is novel in two aspects: 1) we propose the construction of native 2D LDPC codes to correct large 2D burst erasures and 2) we develop a 2D joint signal detectiondecoder engine that incorporates 2D ISI constraints, and modulation code constrains along with LDPC decoding. The native 2D LDPC code can correct >20% more burst erasures compared with the 1D LDPC code over a 128 x 256 2D page of detected bits. Also, the proposed algorithm is observed to achieve a signaltonoise ratio gain of >0.5 dB in bit error rate performance (translating to 10% increase in ADs around the 1.8 Tb/in(2) regime with grain sizes of 9 nm) as compared with a decoupled detectordecoder system configuration over a small 2D LDPC code of size 16 x 16. The efficacy of our proposed algorithm and system architecture is evaluated by assessing AD gains via simulations for a TDMR configuration comprising of a 2D generalized partial response over the Voronoi media model assuming perfect 2D synchronization.

Analysis and Implementation of Resource Efficient Probabilistic Gallager B LDPC DecoderUnal, Burak; Ghaffari, Fakhreddine; Akoglu, Ali; Declercq, David; Vasic, Bane; Univ Arizona, Dept Elect & Comp Engn (IEEE, 201708)LowDensityParityCheck (LDPC) codes have gained popularity in communication systems and standards due to their capacityapproaching errorcorrection performance. In this paper, we first expose the tradeoff between decoding performance and hardware performance across three LDPC harddecision decoding algorithms: Gallager B (GaB), Gradient Descent Bit Flipping (GDBF), and Probabilistic Gradient Descent Bit Flipping (PGDBF). We show that GaB architecture delivers the best throughput while using fewest Field Programmable Gate Array (FPGA) resources, however performs the worst in terms of decoding performance. We then modify the GaB architecture, introduce a new Probabilistic stimulation function (PGaB), and achieve dramatic decoding performance improvement over the GaB, exceeding the performance of GDBF, without sacrificing its superior maximum operating frequency.

Applicability of single and twohiddenlayer neural networks in decoding linear block codesBrkic, Srdan; Ivanis, Predrag; Vasic, Bane; University of Arizona, Department of Electrical and Computer Engineering (IEEE, 20211123)In this paper, we analyze applicability of single and twohiddenlayer feedforward artificial neural networks, SLFNs and TLFNs, respectively, in decoding linear block codes. Based on the provable capability of SLFNs and TLFNs to approximate discrete functions, we discuss sizes of the network capable to perform maximum likelihood decoding. Furthermore, we propose a decoding scheme, which use artificial neural networks (ANNs) to lower the errorfloors of lowdensity paritycheck (LDPC) codes. By learning a small number of error patterns, uncorrectable with typical decoders of LDPC codes, ANN can lower the errorfloor by an order of magnitude, with only marginal average complexity incense.

Asymptotic Error Probability of the Gallager B Decoder Under Timing ErrorsDupraz, Elsa; Declercq, David; Vasic, Bane; Univ Arizona, Dept Elect & Comp Engn (IEEE, 20170104)In a circuit, timing errors occur when a logic gate output does not switch before the clock rising edge. In this letter, we consider Gallager B decoders under timing errors, following the error model derived by Amaricai et al. from SPICE measurements. For this model, we provide a theoretical analysis of the performance of LDPC decoders. This letter is based on the analysis of the computation trees of the decoder free of logic gate errors and of the decoder with timing errors. As a main result, we show that as the number of iterations goes to infinity, the error probability of the decoder with timing errors converges to the error probability of the logic gate errorfree decoder. Monte Carlo simulations confirm this result even for moderate code lengths, which is in accordance with the experimental observations.

Checkhybrid GLDPC codes: Systematic elimination of trapping sets and guaranteed error correction capabilityRavanmehr, Vida; Khatami, Mehrdad; Declercq, David; Vasic, Bane; Univ Arizona, Dept Elect & Comp Engn (WILEYBLACKWELL, 20161012)In this paper, we propose a new approach to construct a class of checkhybrid generalized lowdensity paritycheck (CHGLDPC) codes, which are free of small trapping sets. The approach is based on converting some selected check nodes involving a trapping set into super checks corresponding to a 2errorcorrecting component code. Specifically, we follow 2 main purposes to construct the checkhybrid codes; first, on the basis of the knowledge of trapping sets of an LDPC code, single parity checks are replaced by super checks to disable the trapping sets. We show that by converting specified single check nodes, denoted as critical checks, to super checks in a trapping set, the parallel bit flipping decoder corrects the errors on a trapping set. The second purpose is to minimize the rate loss through finding the minimum number of such critical checks. We also present an algorithm to find critical checks in a trapping set of a columnweight 3 LDPC code of girth 8 and then provide upper bounds on the minimum number of such critical checks such that the decoder corrects all error patterns on elementary trapping sets. Guaranteed error correction capability of the CHGLDPC codes is also studied. We show that a CHGLDPC code in which each variable node is connected to 2 super checks corresponding to a 2errorcorrecting component code corrects up to 5 errors. The results are also extended to columnweight 4 LDPC codes of girth 6. Finally, we investigate eliminating of trapping sets of a columnweight 3 LDPC code of girth 8 using the Gallager B decoding algorithm.

Combinatorial Constructions of LowDensity ParityCheck Codes for Iterative DecodingVasic, Bane; Milenkovic, O.; Univ Arizona, Dept Elect & Comp Engn (IEEE, 20040601)This paper introduces several new combinatorial constructions of lowdensity paritycheck (LDPC) codes, in contrast to the prevalent practice of using long, randomlike codes. The proposed codes are well structured, and unlike random codes can lend themselves to a very lowcomplexity implementation. Constructions of regular Gallager codes based on cyclic difference families, cycleinvariant difference sets, and affine 1configurations are introduced. Several constructions of difference families used for code design are presented, as well as bounds on the minimal distance of the codes based on the concept of a generalized Pasch configuration.

A Deliberate Bit Flipping Coding Scheme for DataDependent TwoDimensional ChannelsBahrami, Mohsen; Vasic, Bane; Univ Arizona, Dept Elect & Comp Engn (Institute of Electrical and Electronics Engineers (IEEE), 202002)In this paper, we present a deliberate bit flipping (DBF) coding scheme for binary twodimensional (2D) channels, where specific patterns in channel inputs are the significant cause of errors. The idea is to eliminate a constrained encoder and, instead, embed a constraint into an error correction codeword that is arranged into a 2D array by deliberately flipping the bits that violate the constraint. The DBF method relies on the error correction capability of the code being used so that it should be able to correct both deliberate errors and channel errors. Therefore, it is crucial to flip minimum number of bits in order not to overburden the error correction decoder. We devise a constrained combinatorial formulation for minimizing the number of flipped bits for a given set of harmful patterns. The generalized belief propagation algorithm is used to find an approximate solution for the problem. We evaluate the performance gain of our proposed approach on a datadependent 2D channel, where 2D isolatedbits patterns are the harmful patterns for the channel. Furthermore, the performance of the DBF method is compared with classical 2D constrained coding schemes for the 2D no isolatedbits constraint on a memoryless binary symmetric channel.

Designing Finite Alphabet Iterative Decoders of LDPC Codes Via Recurrent Quantized Neural NetworksXiao, Xin; Vasic, Bane; Tandon, Ravi; Lin, Shu; Univ Arizona, Dept Elect & Comp Engn (IEEE, 20200406)In this paper, we propose a new approach to design finite alphabet iterative decoders (FAIDs) for LowDensity Parity Check (LDPC) codes over binary symmetric channel (BSC) via recurrent quantized neural networks (RQNN). We focus on the linear FAID class and use RQNNs to optimize the message update lookup tables by jointly training their message levels and RQNN parameters. Existing neural networks for channel coding work well over Additive White Gaussian Noise Channel (AWGNC) but are inefficient over BSC due to the finite channel values of BSC fed into neural networks. We propose the bit error rate (BER) as the loss function to train the RQNNs over BSC. The low precision activations in the RQNN and quantization in the BER cause a critical issue that their gradients vanish almost everywhere, making it difficult to use classical backward propagation. We leverage straightthrough estimators as surrogate gradients to tackle this issue and provide a joint training scheme. We show that the framework is flexible for various code lengths and column weights. Specifically, in high column weight case, it automatically designs low precision linear FAIDs with superior performance, lower complexity, and faster convergence than the floatingpoint belief propagation algorithms in waterfall region.

Diagnosis of Weaknesses in Modern Error Correction Codes: A Physics ApproachStepanov, M. G.; Chernyak, V.; Chertkov, M.; Vasic, Bane; Univ Arizona, Dept Elect & Comp Engn (AMER PHYSICAL SOC, 20051122)One of the main obstacles to the wider use of the modern errorcorrection codes is that, due to the complex behavior of their decoding algorithms, no systematic method which would allow characterization of the biterrorrate (BER) is known. This is especially true at the weak noise where many systems operate and where coding performance is difficult to estimate because of the diminishingly small number of errors. We show how the instanton method of physics allows one to solve the problem of BER analysis in the weak noise range by recasting it as a computationally tractable minimization problem.

An Efficient Instanton Search Algorithm for LP Decoding of LDPC Codes Over the BSCChilappagari, Shashi Kiran; Chertkov, Michael; Vasic, Bane; Univ Arizona, Dept Elect & Comp Engn (IEEE, 20110620)We consider linear programming (LP) decoding of a fixed lowdensity paritycheck (LDPC) code over the binary symmetric channel (BSC). The LP decoder fails when it outputs a pseudocodeword which is not equal to the transmitted codeword. We design an efficient algorithm termed the Instanton Search Algorithm (ISA) which generates an error vector called the BSCinstanton. We prove that: (a) the LP decoder fails for any error pattern with support that is a superset of the support of an instanton; (b) for any input, the ISA outputs an instanton in the number of steps upperbounded by twice the number of errors in the input error vector. We then find the number of unique instantons of different sizes for a given LDPC code by running the ISA sufficient number of times.

Eliminating trapping sets in lowdensity paritycheck codes by using Tanner graph coversIvkovic, Milos; Chilappagari, Shashi Kiran; Vasic, Bane; Univ Arizona, Dept Elect & Comp Engn (IEEE, 20080801)We discuss error floor asympotics and present a method for improving the performance of lowdensity paritycheck (LDPC) codes in the high SNR (error floor) region. The method is based on Tanner graph covers that do not have trapping sets from the original code. The advantages of the method are that it is universal, as it can be applied to any LDPC code/channel/decoding algorithm and it improves performance at the expense of increasing the code length, without losing the code regularity, without changing the decoding algorithm, and, under certain conditions, without lowering the code rate. The proposed method can be modified to construct convolutional LDPC codes also. The method is illustrated by modifying Tanner, MacKay and Margulis codes to improve performance on the binary symmetric channel (BSC) under the Gallager B decoding algorithm. Decoding results on AWGN channel are also presented to illustrate that optimizing codes for one channel/decoding algorithm can lead to performance improvement on other channels.

Error Correction Capability of ColumnWeightThree LDPC Codes Under the Gallager A Algorithm—Part IIChilappagari, Shashi Kiran; Nguyen, Dung Viet; Vasic, Bane; Marcellin, Michael W.; Univ Arizona, Dept Elect & Comp Engn (IEEE, 20100518)The relation between the girth and the error correction capability of columnweightthree LDPC codes under the Gallager A algorithm is investigated. It is shown that a columnweightthree LDPC code with Tanner graph of girth g ¿ 10 can correct all error patterns with up to (g /21) errors in at most g /2 iterations of the Gallager A algorithm. For codes with Tanner graphs of girth g ¿ 8, it is shown that girth alone cannot guarantee correction of all error patterns with up to (g /21) errors under the Gallager A algorithm. Sufficient conditions to correct (g /21) errors are then established by studying trapping sets.

Error Correction on a Tree: An Instanton ApproachChernyak, V.; Chertkov, M.; Stepanov, M. G.; Vasic, Bane; Univ Arizona, Dept Elect & Comp Engn (AMER PHYSICAL SOC, 20041105)We introduce a method that allows analytical or semianalytical estimating of the posterror correction bit error rate (BER) when a forwarderror correction is utilized for transmitting information through a noisy channel. The generic method that applies to a variety of errorcorrection schemes in the regimes where the BER is low is illustrated using the example of a finitesize code approximated by a treelike structure. Exploring the statistical physics formulation of the problem we find that the BER decreases with the signaltonoise ratio nonuniformly, i.e., crossing over through a sequence of phases. The higher the signaltonoise ratio the lower the symmetry of the phase dominating BER.

Error Errore Eicitur: A Stochastic Resonance Paradigm for Reliable Storage of Information on Unreliable MediaIvanis, Predrag; Vasic, Bane; Univ Arizona, Dept Elect & Comp Engn (IEEEINST ELECTRICAL ELECTRONICS ENGINEERS INC, 201609)We give an architecture of a storage system consisting of a storage medium made of unreliable memory elements and an error correction circuit made of a combination of noisy and noiseless logic gates that is capable of retaining the stored information with the lower probability of error than a storage system with a correction circuit made completely of noiseless logic gates. Our correction circuit is based on the iterative decoding of lowdensity parity check codes, and uses the positive effect of errors in logic gates to correct errors in memory elements. In the spirit of Marcus Tullius Cicero's Clavus clavo eicitur (one nail drives out another), the proposed storage system operates on the principle: error errore eiciturone error drives out another. The randomness that is present in the logic gates makes these classes of decoders superior to their noiseless counterparts. Moreover, random perturbations do not require any additional computational resources as they are inherent to unreliable hardware itself. To utilize the benefits of logic gate failures, our correction circuit relies on two key novelties: a mixture of reliable and unreliable gates and decoder rewinding. We present a method based on absorbing Markov chains for the probability of error analysis, and explain how the randomness in the variable and check node update function helps a decoder to escape to local minima associated with trapping sets.

ErrorCorrection Capability of ColumnWeightThree LDPC CodesChilappagari, Shashi Kiran; Vasic, Bane; Univ Arizona, Dept Elect & Comp Engn (IEEE, 20090421)In this paper, the errorcorrection capability of columnweightthree lowdensity paritycheck (LDPC) codes when decoded using the Gallager A algorithm is investigated. It is proved that a necessary condition for a code to correct all error patterns with up to k ges 5 errors is to avoid cycles of length up to 2k in its Tanner graph. As a consequence of this result, it is shown that given any alpha > 0, exist N such that forall n > N, no code in the ensemble of columnweightthree codes can correct all alphan or fewer errors. The results are extended to the bit flipping algorithms.

FAID Diversity via Neural NetworksXiao, Xin; Raveendran, Nithin; Vasic, Bane; Lin, Shu; Tandon, Ravi; University Of Arizona (IEEE, 20210830)Decoder diversity is a powerful error correction framework in which a collection of decoders collaboratively correct a set of error patterns otherwise uncorrectable by any individual decoder. In this paper, we propose a new approach to design the decoder diversity of finite alphabet iterative decoders (FAIDs) for LowDensity Parity Check (LDPC) codes over the binary symmetric channel (BSC), for the purpose of lowering the error floor while guaranteeing the waterfall performance. The proposed decoder diversity is achieved by training a recurrent quantized neural network (RQNN) to learn/design FAIDs. We demonstrated for the first time that a machinelearned decoder can surpass in performance a manmade decoder of the same complexity. As RQNNs can model a broad class of FAIDs, they are capable of learning an arbitrary FAID. To provide sufficient knowledge of the error floor to the RQNN, the training sets are constructed by sampling from the set of most problematic error patterns  trapping sets. In contrast to the existing methods that use the crossentropy function as the loss function, we introduce a frameerrorrate (FER) based loss function to train the RQNN with the objective of correcting specific error patterns rather than reducing the bit error rate (BER). The examples and simulation results show that the RQNNaided decoder diversity increases the error correction capability of LDPC codes and lowers the error floor.

FaultTolerant Probabilistic GradientDescent Bit Flipping DecoderRasheed, Omran Al; Ivanis, Predrag; Vasic, Bane; Univ Arizona, Dept Elect & Comp Engn (IEEE, 20140730)We propose a gradient descent type bit flipping algorithm for decoding low density parity check codes on the binary symmetric channel. Randomness introduced in the bit flipping rule makes this class of decoders not only superior to other decoding algorithms of this type, but also robust to logicgate failures. We report a surprising discovery that for a broad range of gate failure probability our decoders actually benefit from faults in logic gates which serve as an inherent source of randomness and help the decoding algorithm to escape from local minima associated with trapping sets.

Finite alphabet iterative decoders for LDPC codes surpassing floatingpoint iterative decodersPlanjery, S.K.; Declercq, D.; Danjean, L.; Vasic, Bane; Univ Arizona, Dept Elect & Comp Engn (Institution of Engineering and Technology (IET), 2011)Introduced is a new type of messagepassing (MP) decoders for lowdensity paritycheck (LDPC) codes over the binary symmetric channel. Unlike traditional belief propagation (BP) based MP algorithms which propagate probabilities or loglikelihoods, the new MP decoders propagate messages requiring only a finite number of bits for their representation in such a way that good performance in the error floor region is ensured. Additionally, these messages are not quantised probabilities or loglikelihoods. As examples, MP decoders are provided that require only three bits for message representation, but surpass the floatingpoint BP (which requires a large number of bits for representation) in the errorfloor region.

Finite Alphabet Iterative Decoders for LDPC Codes: Optimization, Architecture and AnalysisCai, Fang; Zhang, Xinmiao; Declercq, David; Planjery, Shiva Kumar; Vasic, Bane; Univ Arizona, Dept Elect & Comp Engn (IEEE, 20140320)Lowdensity paritycheck (LDPC) codes are adopted in many applications due to their Shannonlimit approaching errorcorrecting performance. Nevertheless, beliefpropagation (BP) based decoding of these codes suffers from the errorfloor problem, i.e., an abrupt change in the slope of the errorrate curve that occurs at very low error rates. Recently, a new type of decoders termed finite alphabet iterative decoders (FAIDs) were introduced. The FAIDs use simple Boolean maps for variable node processing, and can surpass the BPbased decoders in the error floor region with very short word length. We restrict the scope of this paper to regular d v =3 LDPC codes on the BSC channel. This paper develops a lowcomplexity implementation architecture for the FAIDs by making use of their properties. Particularly, an innovative bitserial check node unit is designed for the FAIDs, and a smallarea variable node unit is proposed by exploiting the symmetry in the Boolean maps. Moreover, an optimized data scheduling scheme is proposed to increase the hardware utilization efficiency. From synthesis results, the proposed FAID implementation needs only 52% area to reach the same throughput as one of the most efficient standard MinSum decoders for an example (7807, 7177) LDPC code, while achieving better errorcorrecting performance in the errorfloor region. Compared to an offset MinSum decoder with longer word length, the proposed design can achieve higher throughput with 45% area, and still leads to possible performance improvement in the errorfloor region.

Finite Alphabet Iterative Decoders—Part I: Decoding Beyond Belief Propagation on the Binary Symmetric ChannelPlanjery, Shiva Kumar; Declercq, David; Danjean, Ludovic; Vasic, Bane; Univ Arizona, Dept Elect & Comp Engn (IEEE, 20130916)We introduce a new paradigm for finite precision iterative decoding on lowdensity paritycheck codes over the binary symmetric channel. The messages take values from a finite alphabet, and unlike traditional quantized decoders which are quantized versions of the belief propagation (BP) decoder, the proposed finite alphabet iterative decoders (FAIDs) do not propagate quantized probabilities or loglikelihoods and the variable node update functions do not mimic the BP decoder. Rather, the update functions are maps designed using the knowledge of potentially harmful subgraphs that could be present in a given code, thereby rendering these decoders capable of outperforming the BP in the error floor region. On certain columnweightthree codes of practical interest, we show that there exist {FAIDs that surpass the floatingpoint BP decoder in the error floor region while requiring only three bits of precision for the representation of the messages}. Hence, FAIDs are able to achieve a superior performance at much lower complexity. We also provide a methodology for the selection of FAIDs that is not codespecific, but gives a set of candidate FAIDs containing potentially good decoders in the error floor region for any columnweightthree code. We validate the code generality of our methodology by providing particularly good threebit precision FAIDs for a variety of codes with different rates and lengths.