Time-Space Constrained Codes for Phase-Change Memories

Phase-change memory (PCM) is a promising non-volatile solid-state memory technology. A PCM cell stores data by using its amorphous and crystalline states. The cell changes between these two states using high temperature. However, since the cells are sensitive to high temperature, it is important, when programming cells, to balance the heat both in time and space. In this paper, we study the time-space constraint for PCM, which was originally proposed by Jiang et al. A code is called an \emph{$(\alpha,\beta,p)$-constrained code} if for any $\alpha$ consecutive rewrites and for any segment of $\beta$ contiguous cells, the total rewrite cost of the $\beta$ cells over those $\alpha$ rewrites is at most $p$. Here, the cells are binary and the rewrite cost is defined to be the Hamming distance between the current and next memory states. First, we show a general upper bound on the achievable rate of these codes which extends the results of Jiang et al. Then, we generalize their construction for $(\alpha\geq 1, \beta=1,p=1)$-constrained codes and show another construction for $(\alpha = 1, \beta\geq 1,p\geq1)$-constrained codes. Finally, we show that these two constructions can be used to construct codes for all values of $\alpha$, $\beta$, and $p$

Systematic Error-Correcting Codes for Rank Modulation

The rank-modulation scheme has been recently proposed for efficiently storing data in nonvolatile memories. Error-correcting codes are essential for rank modulation, however, existing results have been limited. In this work we explore a new approach, \emph{systematic error-correcting codes for rank modulation}. Systematic codes have the benefits of enabling efficient information retrieval and potentially supporting more efficient encoding and decoding procedures. We study systematic codes for rank modulation under Kendall's $\tau$-metric as well as under the $\ell_\infty$-metric. In Kendall's $\tau$-metric we present $[k+2,k,3]$-systematic codes for correcting one error, which have optimal rates, unless systematic perfect codes exist. We also study the design of multi-error-correcting codes, and provide two explicit constructions, one resulting in $[n+1,k+1,2t+2]$ systematic codes with redundancy at most $2t+1$. We use non-constructive arguments to show the existence of $[n,k,n-k]$-systematic codes for general parameters. Furthermore, we prove that for rank modulation, systematic codes achieve the same capacity as general error-correcting codes. Finally, in the $\ell_\infty$-metric we construct two $[n,k,d]$ systematic multi-error-correcting codes, the first for the case of $d=O(1)$, and the second for $d=\Theta(n)$. In the latter case, the codes have the same asymptotic rate as the best codes currently known in this metric

Quantum noise, entanglement and chaos in the quantum field theory of mind/brain states

We review the dissipative quantum model of brain and present recent developments related with the r\^ole of entanglement, quantum noise and chaos in the model.Comment: 15 page

Scalable Recollections for Continual Lifelong Learning

Given the recent success of Deep Learning applied to a variety of single tasks, it is natural to consider more human-realistic settings. Perhaps the most difficult of these settings is that of continual lifelong learning, where the model must learn online over a continuous stream of non-stationary data. A successful continual lifelong learning system must have three key capabilities: it must learn and adapt over time, it must not forget what it has learned, and it must be efficient in both training time and memory. Recent techniques have focused their efforts primarily on the first two capabilities while questions of efficiency remain largely unexplored. In this paper, we consider the problem of efficient and effective storage of experiences over very large time-frames. In particular we consider the case where typical experiences are O(n) bits and memories are limited to O(k) bits for k << n. We present a novel scalable architecture and training algorithm in this challenging domain and provide an extensive evaluation of its performance. Our results show that we can achieve considerable gains on top of state-of-the-art methods such as GEM.Comment: AAAI 201

Quantum noise induced entanglement and chaos in the dissipative quantum model of brain

We discuss some features of the dissipative quantum model of brain in the frame of the formalism of quantum dissipation. Such a formalism is based on the doubling of the system degrees of freedom. We show that the doubled modes account for the quantum noise in the fluctuating random force in the system-environment coupling. Remarkably, such a noise manifests itself through the coherent structure of the system ground state. The entanglement of the system modes with the doubled modes is shown to be permanent in the infinite volume limit. In such a limit the trajectories in the memory space are classical chaotic trajectories.Comment: 14 page

A coding approach for detection of tampering in write-once optical disks

We present coding methods for protecting against tampering of write-once optical disks, which turns them into a secure digital medium for applications where critical information must be stored in a way that prevents or allows detection of an attempt at falsification. Our method involves adding a small amount of redundancy to a modulated sector of data. This extra redundancy is not used for normal operation, but can be used for determining, say, as a testimony in court, that a disk has not been tampered with