Power Spectra of Constrained Codes With Level-Based Signaling: Overcoming Finite-Length Challenges

Centers, Jessica; Tan, Xinyu; Hareedy, Ahmed; Calderbank, Robert

doi:10.1109/tcomm.2021.3073179

Cited by 8 publications

(4 citation statements)

References 30 publications

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“…Moreover, we devised a general method to design LOCO codes for any finite set of patterns to forbid [22], which will be useful in this paper. We studied the power spectra of binary LOCO codes in [23]. LOCO codes are capacity-achieving, simple, and easily reconfigurable [19], [22].…”

Section: Introductionmentioning

confidence: 99%

Efficient Constrained Codes That Enable Page Separation in Modern Flash Memories

Hareedy¹,

Zheng²,

Siegel³

et al. 2023

Preprint

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The pivotal storage density win achieved by solid-state devices over magnetic devices in 2015 is a result of multiple innovations in physics, architecture, and signal processing. One of the most important innovations in that regard is enabling the storage of more than one bit per cell in the Flash device, i.e., having more than two charge levels per cell. Constrained coding is used in Flash devices to increase reliability via mitigating inter-cell interference that stems from charge propagation among cells. Recently, capacity-achieving constrained codes were introduced to serve that purpose in modern Flash devices, which have more than two levels per cell. While these codes result in minimal redundancy via exploiting the underlying physics, they result in non-negligible complexity increase and access speed limitation since pages cannot be read separately. In this paper, we suggest new constrained coding schemes that have low-complexity and preserve the desirable high access speed in modern Flash devices. The idea is to eliminate error-prone patterns by coding data either only on the left-most page (binary coding) or only on the two left-most pages (4-ary coding) while leaving data on all the remaining pages uncoded. Our coding schemes work for any number of levels q ≥ 4 per cell, offer systematic encoding and decoding, and are capacity-approaching. Since the proposed schemes enable the separation of pages, except the two left-most pages in the case of 4-ary coding, we refer to them as read-and-run (RR) constrained coding schemes as opposed to schemes adopting read-and-wait for other pages. The 4-ary RR coding scheme is introduced in order to limit the rate loss incurred by the binary RR coding schemes, and we show that our 4-ary RR coding scheme is also competitive when it comes to complexity and error propagation. We analyze the new RR coding schemes and discuss their impact on the probability of

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Section: Introductionmentioning

confidence: 99%

Efficient Constrained Codes That Enable Page Separation in Modern Flash Memories

Hareedy¹,

Zheng²,

Siegel³

et al. 2023

Preprint

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show abstract

“…In this work, a unified framework to quantify periodic and aperiodic power spectral components of electroand magneto-encephalograms is developed based on a Markov chain description. The power spectral density is estimated in terms of time-sequences according to a statistical approach originally pioneered in the communication and information theory context [18][19][20][21][22][23][24]. Line spectral components are generated by Markov matrices corresponding to closed loop sequences of firing neurons characterized by a set of heterogeneous states.…”

Section: Introductionmentioning

confidence: 99%

Periodic and non-periodic brainwaves emerging via random syncronization of closed loops of firing neurons

Mazzetti¹,

Carbone²

2022

Preprint

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Periodic and nonperiodic components of electrophysiological signals are modelled in terms of syncronized sequences of closed loops of firing neurons correlated in Markov chains. Single closed loops of firing neurons reproduce fundamental and harmonic components, appearing as lines in the power spectra at frequencies ranging about from 0.5Hz to 100Hz. Further interesting features of the brainwave signals emerge by considering multiple syncronized sequences of closed loops. In particular, we show that the fluctuations of the number of syncronized loops leads to the onset of broadband power spectral components. By effect of the fluctuations of the number of synchronized loops and the emergence of the related broadband component, highly distorted waveform and nonstationarity of the signal are observed, consistently with empirical EEG and MEG signals. The analytical relationships of the periodic and aperiodic components are evaluated by using typical firing neuron pulse amplitudes and durations.

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“…Periodic components of brain signals and their frequency bands (delta (1-3 Hz), theta (4-8 Hz), alpha (9-12 Hz), beta (12)(13)(14)(15)(16)(17)(18)(19)(20)(21)(22)(23)(24)(25)(26)(27)(28)(29)(30), gamma (>30 Hz)) are central to neuroscience basic research and clinical protocols [1][2][3]. Aperiodic components, initially disregarded in comparison to periodic ones as considered to be just background noise, represent a significant part of signals.…”

Section: Introductionmentioning

confidence: 99%

“…In this work, a unified framework to quantify periodic and aperiodic power spectral components of electro-and magneto-encephalograms is developed based on a Markov-chain description. The power spectral density is estimated in terms of time sequences according to a statistical approach originally pioneered in the communication and information-theory context [18][19][20][21][22][23][24]. Line spectral components are generated by Markov matrices corresponding to closed-loop sequences of firing neurons characterized by a set of heterogeneous states.…”

Section: Introductionmentioning

confidence: 99%

Periodic and Non-Periodic Brainwaves Emerging via Stochastic Syncronization of Closed Loops of Firing Neurons

Mazzetti

Carbone

2022

Algorithms

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Periodic and non-periodic components of electrophysiological signals are modelled in terms of syncronized sequences of closed loops of firing neurons correlated according to a Markov chain. Single closed loops of firing neurons reproduce fundamental and harmonic components, appearing as lines in the power spectra at frequencies ranging from 0.5 Hz to 100 Hz. Further interesting features of the brainwave signals emerge by considering multiple syncronized sequences of closed loops. In particular, we show that fluctuations in the number of syncronized loops lead to the onset of a broadband power spectral component. By the effects of these fluctuations and the emergence of a broadband component, a highly distorted waveform and nonstationarity of the signal are observed, consistent with empirical EEG and MEG signals. The amplitudes of the periodic and aperiodic components are evaluated by using typical firing neuron pulse amplitudes and durations.

show abstract

Power Spectra of Constrained Codes With Level-Based Signaling: Overcoming Finite-Length Challenges

Cited by 8 publications

References 30 publications

Efficient Constrained Codes That Enable Page Separation in Modern Flash Memories

Efficient Constrained Codes That Enable Page Separation in Modern Flash Memories

Periodic and non-periodic brainwaves emerging via random syncronization of closed loops of firing neurons

Periodic and Non-Periodic Brainwaves Emerging via Stochastic Syncronization of Closed Loops of Firing Neurons

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