The present invention relates generally to systems and methods of retrieving data from a Flash memory, and in particular, to systems and methods of retrieving damaged data from a Flash memory.
A storage device such as a flash memory module stores encoded data. The encoded data is expected to be decoded by a memory controller. The memory controller is expected to successfully decode the encoded data during the lifespan of the flash memory module. A failure of the memory controller to decode encoded data, for example, when the amount of errors in a memory are beyond the ability of the controller to correct, renders the encoded data invalid, and the controller responds to a retrieval request with an error message. Such a failure may occur, for example, when the flash memory is exposed to high temperatures, or for other reasons.
Memory controllers are expected to be relatively cheap and are required to read and decode encoded information in real time. Accordingly, these requirements may impose a low sampling rate of the encoded data and a use of a decoding scheme that has limited error correction capabilities. Typically, memory controllers use “hard” decoding techniques, i.e., provide a definite determination of the data stored on each cell. However, such techniques may be insufficient to retrieve damaged data.
According to embodiments of the invention, a system and method are provided for restoring damaged data programmed on a memory. A system may include a memory controller associated with a memory, the memory controller adapted to perform a first decoding algorithm having a first error correction capability on a portion of encoded data stored on the memory, wherein in the event of a failure of the first decoding algorithm to decode the portion of encoded data, the memory controller is adapted to send a failure notification. The system may further include a recovery module associated with a processor, said recovery module being adapted to receive the failure notification, send a request for soft sampling of the portion of encoded data stored on the memory. The memory controller may be further adapted to receive the request for soft sampling of the portion of encoded data stored on the memory, perform the soft sampling of the portion of encoded data accordingly, and send the results of the soft sampling to the recovery module. The recovery module may be adapted to receive the results of the soft sampling and perform thereon a second decoding algorithm having a second error correction capability, wherein the second error correction capability exceeds the first error correction capability.
A method for restoring damaged data programmed on a memory according to embodiments of the invention may include receiving an indication from a memory controller associated with a memory that a first decoding algorithm having a first error correction capability has failed to decode a portion of encoded data stored on the memory, sending a request for soft sampling of the portion of encoded data stored on the memory, receiving the results of the soft sampling from the memory controller, and performing on the results of the soft sampling a second decoding algorithm having a second error correction capability, wherein the second error correction capability exceeds the first error correction capability.
The subject matter regarded as the invention is particularly pointed out and distinctly claimed in the concluding portion of the specification. The invention, however, both as to organization and method of operation, together with objects, features, and advantages thereof, may best be understood by reference to the following detailed description when read with the accompanying drawings in which:
It will be appreciated that for simplicity and clarity of illustration, elements shown in the figures have not necessarily been drawn to scale. For example, the dimensions of some of the elements may be exaggerated relative to other elements for clarity. Further, where considered appropriate, reference numerals may be repeated among the figures to indicate corresponding or analogous elements.
In the following detailed description, numerous specific details are set forth in order to provide a thorough understanding of the invention. However, it will be understood by those skilled in the art that the present invention may be practiced without these specific details. In other instances, well-known methods, procedures, and components have not been described in detail so as not to obscure the present invention.
The subject matter regarded as the invention is particularly pointed out and distinctly claimed in the concluding portion of the specification. The invention, however, both as to organization and method of operation, together with objects, features, and advantages thereof, may best be understood by reference to the following detailed description when read with the accompanying drawings.
It will be appreciated that for simplicity and clarity of illustration, elements shown in the figures have not necessarily been drawn to scale. For example, the dimensions of some of the elements may be exaggerated relative to other elements for clarity. Further, where considered appropriate, reference numerals may be repeated among the figures to indicate corresponding or analogous elements.
Embodiments of the invention may be applicable to various types of memory, including, for example, Secure Digital (SD) cards, solid-state drive (SSD) devices, as well as to other storage devices as hard-drives, optical media, magnetic tapes, etc.
System 100 includes a storage device 110 (such as but not limited to an SD card) that includes a memory controller 111 and memory 112 and a computer 120. Memory 112 can be a flash memory module or other non-volatile memory module, and may include multiple memory blocks, each including multiple memory pages. Different memory pages may share physical memory rows.
Computer 120 may be connected to storage device 20 (and more specifically, to memory controller 111) through a wired or wireless link, over a network, or any other communication link. Computer 120 can be a remote server, a desktop computer, a laptop computer, a personal digital assistant (PDA), a tablet computer, and the like.
Although in the illustrated embodiment, computer 120 is depicted as being connected to the memory controller 111 via a wired link 130, it will be understood that computer 120 can be connected to memory controller 111 via one or more wireless links, or a combination of wired and wireless links. Computer 120 can be communicatively connected to memory controller 111 directly, or via a network, etc.
In some embodiments of the invention, memory controller 111 may be a small and inexpensive processor, and may have limited computing power, and therefore, limited decoding abilities. According to a mode of operation of embodiments of the invention, memory controller 111 may attempt to retrieve encoded data stored on memory 112, for example, a codeword, a portion of a codeword, or more than a single codeword. Memory controller 111 may first apply a first decoding algorithm that has a certain error correction capability, for example, a hard decoding algorithm. If memory controller 111 fails to successfully decode data stored on memory 112, it may determine that the data is damaged and enter a damaged data restoration mode.
In some embodiments of the invention, a data decoding failure event may be detected by the memory controller 111. For example, memory controller 111 may determines that it failed to successfully decode the encoded data if, for example, it detects that a number of errors in the encoded data exceeds the number of errors that can be amended by the memory controller 111. It will be understood that in some embodiments, the failure to decode encoded data may be detected by an application or a process that uses the decoded data, for example, an application or process executed by or on computer 120. For example, a decoding failure event may be detected by the application or process if the content of the decoded data differs from an expected content.
An indication of failure to successfully decode data encoded and stored on memory 112 may be generated, for example, by memory controller 111. A failure event indication may be sent to computer 120 which may respond by initiating a data restoration or recovery process.
Computer 120 may include interface 122, and a recovery module 121. It will be recognized that according to embodiments of the invention, the recovery module differs from the memory controller, for example, it may be part of a computer having more processing power than the memory controller. The recovery module 121 may include hardware, software and a combination thereof. Recovery module 121 may instruct memory controller 111 to operate in a data restoration mode. In this mode, the memory controller 111 may sample or retrieve the raw or (“hard”) encoded data (e.g., voltage levels, etc.), and provide a representation of the encoded data in soft format to computer 120.
In some embodiments of the invention, the memory controller 111 may first provide certain physical memory information to controller 120. For example, the physical memory information may include one or all of: an identity of a page storing the encoded data, an identity of the memory block storing the encoded data, an identity of a die storing the encoded data, a cycle count of the memory block storing the encoded data, an indication about an existence of an old version of the encoded data on storage device 112, one or more coding parameters of the encoded data, scrambling information of the encoded data, and the like.
Computer 120 may instruct the memory controller 111 to sample and retrieve the encoded data stored in storage device 112. The sampling may involve obtaining the encoded data at a fine resolution using, for example, majority sampling. Thus, for a given voltage threshold value, the memory controller 111 can sample the encoded data multiple (k) times to provide multiple sets of k samples and then process each set of k samples to provide a soft sample. For example, the memory controller 111 can process each set of k samples by selecting a median value of the set. In some embodiments of the invention, computer 120 may determine the sampling resolution to be used and communicate the sampling parameters to memory controller 111. This determination may be responsive to the encoded data physical information provided by memory controller 111.
Upon obtaining and/or processing the soft samples, memory controller 111 may send the soft samples to computer 120, for example, by way of interface 122. Computer 120 may decode the soft samples of the encoded data, for example, by applying a second decoding algorithm having a higher or better error correction capability than the error correction capability of the first decoding algorithm applied by the memory controller 111. In some embodiments of the invention, the second decoding algorithm may be a soft decoding algorithm. For example, the soft decoding algorithm applied as the second decoding algorithm may be a soft version of the first decoding algorithm, or it may be another soft decoding algorithm. In some embodiments of the invention, the second decoding algorithm may be a hard decoding algorithm having better error correction capability than the first decoding algorithm.
According to some embodiments of the invention, the determination of the parameters of the second decoding algorithm may be responsive to one or more of the following: (i) threshold values shift along a memory block that stores the encoded data; (ii) decoded bits stored in another memory page of the storage device, wherein the other memory page and the memory page that stores the encoded data share memory rows; this can include decoded bits that belong to another logical layer such as most significant bit, least significant bit and CSB; (iii) soft samples obtained while supplying different bias voltage to the memory page that stores the encoded data; and (iv) an old version of the encoded data that may be stored in another memory page.
According to some embodiments, second decoding algorithm may be very involved or time-consuming Accordingly, computer 120 may apply the second decoding algorithm over long periods of time (in comparison to the decoding period of the memory controller 111) and by using stronger computational resources. Increased decoding time and/or computational resources may increase the probability of successful decoding using the second decoding algorithm by computer 120. According to some embodiments of the invention, by applying the second decoding algorithm, the reliability of the storage device may increase by an order of magnitude. For example, the raw Bit Error Rate can be increased by tenfold (i.e., the SNR gain may be 1-3 dB). See, e.g., R. Kotter and A. Vardy, “Algebraic soft decision decoding of Reed-Solomon codes”, IEEE Trans. Inform. Theory, vol 49, No. 11, pp. 2809-2825, November 2003 (demonstrating performance differences between hard and soft decoding using Kotter-Vardy algorithm).
At stage 210, storage device may attempt to decode encoded data stored in a memory, for example, by operating a memory controller employing a first decode algorithm, for example, a “hard” decoding algorithm. At stage 220, a failure of the first decoding algorithm may be detected, for example, by the memory controller, or by an application operating on a computer requesting data from the storage device.
At stage 230, a failure indication may be sent, for example, to a recovery module on a computer.
In some embodiments of the invention, after stage 230, the method may proceed to stage 240 or bypass stages 240-260 and proceed directly to stage 270. At stage 240, the storage device may receive a request, for example, from the recovery module, requesting certain physical information pertaining to the encoded data that could not be recovered. The encoded data physical information may include one or more of: (i) a cycle count of a memory block that stores the encoded data, (ii) coding parameters of the memory block that stores the encoded data, (iii) scrambling information of the encoded data, (iv) an identifier of the memory block that stores the encoded data, and (v) an existence of a older version of the encoded data in the storage device. At stage 250, the memory controller may obtain the requested physical information, and at stage 260, it may send the requested information to the recovery module.
At stage 270, the memory controller may receive parameters for performing soft sampling of the encoded data. If stages 240-260 were bypassed, the recovery module may determine the soft sampling parameters based on preset values. In other instances, the recovery module may use the physical information to determine the soft sampling parameters to be used by memory controller in performing the soft sampling.
The soft sampling parameters or instructions may include any of a variety of different parameters or instructions. For example, in some embodiments, the memory controller may be instructed to sample each bit of the encoded data multiple times to provide a set of samples and to process the set of samples to provide the soft samples of the encoded data. In some embodiments, the memory controller may be instructed to sample each bit of the encoded data multiple times to provide a set of samples and to return as a soft sample of the bit of the encoded data a median value of the set of samples. In some embodiments, the memory controller may be instructed to generate soft samples of the encoded data and to generate soft samples of at least one additional encoded data stored at the storage device. In some embodiments, the memory controller may be instructed to generate a first set of soft samples of the encoded data that is generated by performing a read process that involves providing a first bias voltage and to generate a second set of soft samples of the encoded data that is generated by performing a read process that involves providing a second bias voltage that differs from the first bias voltage.
At stage 280, the memory controller may perform soft sampling of the encoded data. If stages 230-270 were bypassed, the memory controller may use preset parameters to perform the soft sampling. In other embodiments, the memory controller may use the soft sampling parameters communicated to it by the recovery module at stage 270.
The soft sampling may be performed in any of a variety of different methods. In some embodiments of the invention, each bit of the encoded data may be sampled multiple times to provide a set of samples and to process the set of samples to provide the soft samples of the encoded data. In some embodiments, each bit of the encoded data may be sampled multiple times to provide a set of samples and to return as a soft sample of the bit of the encoded data a median value of the set of samples. Some embodiments of the invention may include generating soft samples of the encoded data and generating soft samples of at least one additional encoded data stored at the storage device. Some embodiments of the invention may include generating a first set of soft samples of the encoded data that is generated by performing a read process that involves providing a first bias voltage and generating a second set of soft samples of the encoded data that is generated by performing a read process that involves providing a second bias voltage that differs from the first bias voltage. The generating is not limited to two sets of soft samples that are generated by providing two different bias voltages and more that a pair of sets can be generated by providing more than a pair of bias voltages.
At stage 290, the soft samples may be sent to the recovery module for decoding using a second decoding algorithm. According to embodiments of the invention, and as described in connection with the method performed by the recovery module, if a second decoding algorithm performed by the recovery module was unsuccessful, the memory controller may be provided with additional or different soft sampling parameters or instructions, and accordingly, may repeat at least one of stages 270-290.
At stage 310, the recovery module may receive an indication of failure of a first decoding algorithm (e.g., sent at stage 230). In some embodiments of the invention, the method may bypass stages 320-330 or 320-340 and proceed to stage 350 (described below). At stage 320, the recovery module may request certain physical information pertaining to the encoded data to be recovered. At stage 330, the requested information may be received. At stage 340, the recovery module may determine, for example, based on information obtained at stage 330, or based on preset defaults, the soft sampling recovery scheme to be performed, and the parameters required for the memory controller to perform the required sampling.
At stage 350, the recovery module may instruct the memory controller to perform soft sampling of the encoded data to provide soft samples of the encoded data. If stage 340 was performed, the instruction may include parameters obtained at stage 340.
At stage 360, the requested soft sampling data may be obtained from the memory controller.
At stage 370 the recovery module may apply a second (“soft”) decoding algorithm on the soft samples of the encoded data provided, in order to provide restored data. The second decoding algorithm may have an error correction capability that exceeds an error correction capability of the first decoding algorithm. The second decoding algorithm can be a soft version of the first decoding algorithm. Soft sampling of data can reduce the error probability of a given code that uses the soft sampled data. Moreover, substantially all commonly used codes (e.g., RS/BCH codes, LDPC codes, Turbo codes, etc.) have feasible soft-decoding algorithms that use soft data sampling to reduce the error probability, as illustrated by: (i) R. Kotter and A. Vardy, “Algebraic soft decision decoding of Reed-Solomon codes,” IEEE Trans. Inform. Theory, vol 49, No. 11, pp. 2809-2825, November 2003; (ii) M. Fossorier, M Mihaljevi'c, and H. Imai, “Reduced Complexity Iterative Decoding of Low-Density Parity Check Codes Based on Belief Propagation,” IEEE Trans. Comm., vol. 47, No. 5, pp. 673-680, May 1999; and (iii) C. Berrou, and A. Glavieux, “Near optimum error correcting coding and decoding: turbo codes,” IEEE Trans. Comm vol. 44, No. 10, pp. 1261-1271, October 1996.
It will be understood that in some embodiments of the invention, the second decoding algorithm performed on the soft sampled data may be based on the encoded data physical information. For example, based on the additional physical information provided on a codeword that could not be “hard” decoded, the restoration algorithm can employ different strategies during its operation, e.g., (a) the amount of cycles the physical page experienced can suggest which programming parameters were used to program this page, what is the expected mean and STD (standard deviation) of each cell and other statistical parameters which are correlated to the cycling count of the block; (b) the coding parameters are needed when the correct decoding scheme is activated (some controllers can change the encoder's parameters based on bit type value, cycle count and other physical parameters); (c) the scrambling parameters are needed to produce the correct data. Usually, the data is scrambled just before the encoding phase. In order to produce the original data de-scrambling is done just after the decoding phase therefore the restoration process might need the scrambling parameters; and (d) the exact location of the pages within the block can suggest what were the drifts (shifts) in threshold values along the block were, which in turn can improve the estimation of the optimal thresholds needed to read the page. Moreover, using decoupling techniques one can read adjacent rows and use that information to reduce the coupling effect imposed on the erroneous page/s.
The second decoding algorithm may be applied based on the provided information. For example, reading and decoding other page data in the same physical row (e.g., different bit layers of the row) can help to identify programming errors (e.g., errors occurred when the upper bit layer is read erroneously as part of the programming process). In another example, older versions of the information can help to identify error bits.
At stage 380, the recovery module determines whether the second decoding algorithm successfully decoded the sampled data. If so, the method may proceed to stage 390. If not, the recovery module may determine that another attempt may be more successful, and may repeat some previous stages. For example, the recovery module may optionally repeat stage 340, determining a different soft sampling recovery scheme to be performed, and the parameters required for the memory controller to perform the required sampling. These may be requested and received at repeated stages 350 and 360, and another decoding process performed at stage 370. A number of repetitions of stages 340-370 or 350-370 may be repeated until success is achieved, or until a stop condition is reached, e.g., maximum number of tries, etc.
Finally, at stage 390, the data recovered by the second decoding algorithm may be used. For example, the data may be displayed, stored, transmitted, etc.
In some instances, after recovery of damaged data, use of the card may continue. For example, the memory controller may declare that the block where the first decoding algorithm failed is a bad block, and continue working with the card while refraining from using that block. In another instance, the recovery process may result in a recommendation to stop using the storage device altogether, for example, due to its excessively high bit-error-rate.
While certain features of the invention have been illustrated and described herein, many modifications, substitutions, changes, and equivalents will now occur to those of ordinary skill in the art. It is, therefore, to be understood that the appended claims are intended to cover all such modifications and changes as fall within the true spirit of the invention.
This application claims the benefit of U.S. Provisional Patent Application Ser. No. 61/321,310, filed on Apr. 6, 2010, which is incorporated in its entirety by reference herein.
Number | Name | Date | Kind |
---|---|---|---|
4463375 | Macovski | Jul 1984 | A |
4584686 | Fritze | Apr 1986 | A |
4589084 | Fling et al. | May 1986 | A |
4866716 | Weng | Sep 1989 | A |
5077737 | Leger et al. | Dec 1991 | A |
5297153 | Baggen et al. | Mar 1994 | A |
5657332 | Auclair et al. | Aug 1997 | A |
5729490 | Calligaro et al. | Mar 1998 | A |
5793774 | Usui et al. | Aug 1998 | A |
5926409 | Engh et al. | Jul 1999 | A |
5956268 | Lee | Sep 1999 | A |
5982659 | Irrinki et al. | Nov 1999 | A |
6038634 | Ji et al. | Mar 2000 | A |
6094465 | Stein et al. | Jul 2000 | A |
6119245 | Hiratsuka | Sep 2000 | A |
6182261 | Haller et al. | Jan 2001 | B1 |
6192497 | Yang et al. | Feb 2001 | B1 |
6195287 | Hirano | Feb 2001 | B1 |
6199188 | Shen et al. | Mar 2001 | B1 |
6209114 | Wolf et al. | Mar 2001 | B1 |
6259627 | Wong | Jul 2001 | B1 |
6278633 | Wong et al. | Aug 2001 | B1 |
6279133 | Vafai et al. | Aug 2001 | B1 |
6301151 | Engh et al. | Oct 2001 | B1 |
6370061 | Yachareni et al. | Apr 2002 | B1 |
6374383 | Weng | Apr 2002 | B1 |
6504891 | Chevallier | Jan 2003 | B1 |
6532169 | Mann et al. | Mar 2003 | B1 |
6532556 | Wong et al. | Mar 2003 | B1 |
6553533 | Demura et al. | Apr 2003 | B2 |
6560747 | Weng | May 2003 | B1 |
6637002 | Weng et al. | Oct 2003 | B1 |
6639865 | Kwon | Oct 2003 | B2 |
6674665 | Mann et al. | Jan 2004 | B1 |
6704902 | Shinbashi et al. | Mar 2004 | B1 |
6751766 | Guterman et al. | Jun 2004 | B2 |
6772274 | Estakhri | Aug 2004 | B1 |
6781910 | Smith | Aug 2004 | B2 |
6792569 | Cox et al. | Sep 2004 | B2 |
6873543 | Smith et al. | Mar 2005 | B2 |
6891768 | Smith et al. | May 2005 | B2 |
6914809 | Hilton et al. | Jul 2005 | B2 |
6915477 | Gollamudi et al. | Jul 2005 | B2 |
6952365 | Gonzalez et al. | Oct 2005 | B2 |
6961890 | Smith | Nov 2005 | B2 |
6990012 | Smith et al. | Jan 2006 | B2 |
6996004 | Fastow et al. | Feb 2006 | B1 |
6999854 | Roth | Feb 2006 | B2 |
7010739 | Feng et al. | Mar 2006 | B1 |
7012835 | Gonzalez et al. | Mar 2006 | B2 |
7038950 | Hamilton et al. | May 2006 | B1 |
7068539 | Guterman et al. | Jun 2006 | B2 |
7079436 | Perner et al. | Jul 2006 | B2 |
7149950 | Spencer et al. | Dec 2006 | B2 |
7177977 | Chen et al. | Feb 2007 | B2 |
7191379 | Adelmann et al. | Mar 2007 | B2 |
7196946 | Chen et al. | Mar 2007 | B2 |
7203874 | Roohparvar | Apr 2007 | B2 |
7290203 | Emma et al. | Oct 2007 | B2 |
7292365 | Knox | Nov 2007 | B2 |
7301928 | Nakabayashi et al. | Nov 2007 | B2 |
7441067 | Gorobets et al. | Oct 2008 | B2 |
7466575 | Shalvi et al. | Dec 2008 | B2 |
7533328 | Alrod et al. | May 2009 | B2 |
7558109 | Brandman et al. | Jul 2009 | B2 |
7593263 | Sokolov et al. | Sep 2009 | B2 |
7697326 | Sommer et al. | Apr 2010 | B2 |
7706182 | Shalvi et al. | Apr 2010 | B2 |
7804718 | Kim | Sep 2010 | B2 |
7805663 | Brandman et al. | Sep 2010 | B2 |
7805664 | Yang et al. | Sep 2010 | B1 |
7844877 | Litsyn et al. | Nov 2010 | B2 |
7961797 | Yang et al. | Jun 2011 | B1 |
8020073 | Emma et al. | Sep 2011 | B2 |
8099652 | Alrod et al. | Jan 2012 | B1 |
8122328 | Liu et al. | Feb 2012 | B2 |
20020063774 | Hillis et al. | May 2002 | A1 |
20020085419 | Kwon et al. | Jul 2002 | A1 |
20020154769 | Petersen et al. | Oct 2002 | A1 |
20030065876 | Lasser | Apr 2003 | A1 |
20030101404 | Zhao et al. | May 2003 | A1 |
20030105620 | Bowen | Jun 2003 | A1 |
20030192007 | Miller et al. | Oct 2003 | A1 |
20040015771 | Lasser et al. | Jan 2004 | A1 |
20040030971 | Tanaka et al. | Feb 2004 | A1 |
20040153722 | Lee | Aug 2004 | A1 |
20040153817 | Norman et al. | Aug 2004 | A1 |
20040181735 | Xin | Sep 2004 | A1 |
20050013165 | Ban | Jan 2005 | A1 |
20050018482 | Cemea et al. | Jan 2005 | A1 |
20050083735 | Chen et al. | Apr 2005 | A1 |
20050117401 | Chen et al. | Jun 2005 | A1 |
20050120265 | Pline et al. | Jun 2005 | A1 |
20050128811 | Kato et al. | Jun 2005 | A1 |
20050138533 | Le-Bars et al. | Jun 2005 | A1 |
20050144213 | Simkins et al. | Jun 2005 | A1 |
20050144368 | Chung et al. | Jun 2005 | A1 |
20050169057 | Shibata et al. | Aug 2005 | A1 |
20050172179 | Brandenberger et al. | Aug 2005 | A1 |
20050213393 | Lasser | Sep 2005 | A1 |
20060059406 | Micheloni et al. | Mar 2006 | A1 |
20060059409 | Lee | Mar 2006 | A1 |
20060064537 | Oshima et al. | Mar 2006 | A1 |
20060101193 | Murin | May 2006 | A1 |
20060203587 | Li et al. | Sep 2006 | A1 |
20060221692 | Chen | Oct 2006 | A1 |
20060248434 | Radke et al. | Nov 2006 | A1 |
20060268608 | Noguchi et al. | Nov 2006 | A1 |
20060294312 | Walmsley | Dec 2006 | A1 |
20070025157 | Wan et al. | Feb 2007 | A1 |
20070063180 | Asano et al. | Mar 2007 | A1 |
20070103992 | Sakui et al. | May 2007 | A1 |
20070104004 | So et al. | May 2007 | A1 |
20070109858 | Conley et al. | May 2007 | A1 |
20070124652 | Litsyn et al. | May 2007 | A1 |
20070143561 | Gorobets | Jun 2007 | A1 |
20070150694 | Chang et al. | Jun 2007 | A1 |
20070168625 | Cornwell et al. | Jul 2007 | A1 |
20070171714 | Wu et al. | Jul 2007 | A1 |
20070171730 | Ramamoorthy et al. | Jul 2007 | A1 |
20070180346 | Murin | Aug 2007 | A1 |
20070223277 | Tanaka et al. | Sep 2007 | A1 |
20070226582 | Tang et al. | Sep 2007 | A1 |
20070226592 | Radke | Sep 2007 | A1 |
20070228449 | Takano et al. | Oct 2007 | A1 |
20070253249 | Kang et al. | Nov 2007 | A1 |
20070253250 | Shibata et al. | Nov 2007 | A1 |
20070263439 | Cornwell et al. | Nov 2007 | A1 |
20070266291 | Toda et al. | Nov 2007 | A1 |
20070271494 | Gorobets | Nov 2007 | A1 |
20080010581 | Alrod et al. | Jan 2008 | A1 |
20080028014 | Hilt et al. | Jan 2008 | A1 |
20080055989 | Lee et al. | Mar 2008 | A1 |
20080082897 | Brandman et al. | Apr 2008 | A1 |
20080092026 | Brandman et al. | Apr 2008 | A1 |
20080104309 | Cheon et al. | May 2008 | A1 |
20080109703 | Brandman | May 2008 | A1 |
20080116509 | Harari et al. | May 2008 | A1 |
20080126686 | Sokolov et al. | May 2008 | A1 |
20080127104 | Li et al. | May 2008 | A1 |
20080128790 | Jung | Jun 2008 | A1 |
20080130341 | Shalvi et al. | Jun 2008 | A1 |
20080137413 | Kong et al. | Jun 2008 | A1 |
20080148115 | Sokolov et al. | Jun 2008 | A1 |
20080158958 | Shalvi et al. | Jul 2008 | A1 |
20080159059 | Moyer | Jul 2008 | A1 |
20080162079 | Astigarraga et al. | Jul 2008 | A1 |
20080168216 | Lee | Jul 2008 | A1 |
20080168320 | Cassuto et al. | Jul 2008 | A1 |
20080181001 | Shalvi | Jul 2008 | A1 |
20080198650 | Shalvi et al. | Aug 2008 | A1 |
20080198652 | Shalvi et al. | Aug 2008 | A1 |
20080219050 | Shalvi et al. | Sep 2008 | A1 |
20080225599 | Chae | Sep 2008 | A1 |
20080263262 | Sokolov et al. | Oct 2008 | A1 |
20080282106 | Shalvi et al. | Nov 2008 | A1 |
20080285351 | Shlick et al. | Nov 2008 | A1 |
20080301532 | Uchikawa et al. | Dec 2008 | A1 |
20090024905 | Shalvi et al. | Jan 2009 | A1 |
20090043951 | Shalvi et al. | Feb 2009 | A1 |
20090072303 | Prall et al. | Mar 2009 | A9 |
20090091979 | Shalvi | Apr 2009 | A1 |
20090103358 | Sommer et al. | Apr 2009 | A1 |
20090106485 | Anholt | Apr 2009 | A1 |
20090113275 | Chen et al. | Apr 2009 | A1 |
20090125671 | Flynn et al. | May 2009 | A1 |
20090144600 | Perlmutter et al. | Jun 2009 | A1 |
20090150748 | Egner et al. | Jun 2009 | A1 |
20090157964 | Kasorla et al. | Jun 2009 | A1 |
20090158126 | Perlmutter et al. | Jun 2009 | A1 |
20090168524 | Golov et al. | Jul 2009 | A1 |
20090187803 | Anholt et al. | Jul 2009 | A1 |
20090199074 | Sommer | Aug 2009 | A1 |
20090213653 | Perlmutter et al. | Aug 2009 | A1 |
20090213654 | Perlmutter et al. | Aug 2009 | A1 |
20090228761 | Perlmutter et al. | Sep 2009 | A1 |
20090240872 | Perlmutter et al. | Sep 2009 | A1 |
20090319859 | Alrod et al. | Dec 2009 | A1 |
20100005270 | Jiang | Jan 2010 | A1 |
20100058146 | Weingarten et al. | Mar 2010 | A1 |
20100064096 | Weingarten et al. | Mar 2010 | A1 |
20100088557 | Weingarten et al. | Apr 2010 | A1 |
20100091535 | Sommer et al. | Apr 2010 | A1 |
20100095186 | Weingarten | Apr 2010 | A1 |
20100110787 | Shalvi et al. | May 2010 | A1 |
20100115376 | Shalvi et al. | May 2010 | A1 |
20100122113 | Weingarten et al. | May 2010 | A1 |
20100124088 | Shalvi et al. | May 2010 | A1 |
20100131580 | Kanter et al. | May 2010 | A1 |
20100131697 | Alrod et al. | May 2010 | A1 |
20100131806 | Weingarten et al. | May 2010 | A1 |
20100131809 | Katz | May 2010 | A1 |
20100131826 | Shalvi et al. | May 2010 | A1 |
20100131827 | Sokolov et al. | May 2010 | A1 |
20100131831 | Weingarten et al. | May 2010 | A1 |
20100146191 | Katz | Jun 2010 | A1 |
20100146192 | Weingarten et al. | Jun 2010 | A1 |
20100149881 | Lee et al. | Jun 2010 | A1 |
20100180073 | Weingarten et al. | Jul 2010 | A1 |
20100199149 | Weingarten et al. | Aug 2010 | A1 |
20100211724 | Weingarten | Aug 2010 | A1 |
20100211833 | Weingarten | Aug 2010 | A1 |
20100211856 | Weingarten | Aug 2010 | A1 |
20100251066 | Radke | Sep 2010 | A1 |
20100253555 | Weingarten et al. | Oct 2010 | A1 |
20100257309 | Barsky et al. | Oct 2010 | A1 |
20100293321 | Weingarten | Nov 2010 | A1 |
20110051521 | Levy et al. | Mar 2011 | A1 |
20110055461 | Steiner et al. | Mar 2011 | A1 |
20110096612 | Steiner et al. | Apr 2011 | A1 |
20110119562 | Steiner et al. | May 2011 | A1 |
20110153919 | Sabbag | Jun 2011 | A1 |
20110161775 | Weingarten | Jun 2011 | A1 |
20110214029 | Steiner et al. | Sep 2011 | A1 |
20110214039 | Steiner et al. | Sep 2011 | A1 |
20110246792 | Weingarten | Oct 2011 | A1 |
20110246852 | Sabbag | Oct 2011 | A1 |
20110252187 | Segal et al. | Oct 2011 | A1 |
20110252188 | Weingarten | Oct 2011 | A1 |
20110271043 | Segal et al. | Nov 2011 | A1 |
20110274981 | Yamada et al. | Nov 2011 | A1 |
20110302428 | Weingarten | Dec 2011 | A1 |
20120001778 | Steiner et al. | Jan 2012 | A1 |
20120005554 | Steiner et al. | Jan 2012 | A1 |
20120005558 | Steiner et al. | Jan 2012 | A1 |
20120005560 | Steiner et al. | Jan 2012 | A1 |
20120008401 | Katz et al. | Jan 2012 | A1 |
20120008414 | Katz et al. | Jan 2012 | A1 |
20120051144 | Weingarten et al. | Mar 2012 | A1 |
20120063227 | Weingarten et al. | Mar 2012 | A1 |
20120066441 | Weingarten | Mar 2012 | A1 |
20120110250 | Sabbag et al. | May 2012 | A1 |
Entry |
---|
Search Report of PCT Patent Application WO 2009/118720 A3. |
Search Report of PCT Patent Application WO 2009/095902 A3. |
Search Report of PCT Patent Application WO 2009/078006 A3. |
Search Report of PCT Patent Application WO 2009/074979 A3. |
Search Report of PCT Patent Application WO 2009/074978 A3. |
Search Report of PCT Patent Application WO 2009/072105 A3. |
Search Report of PCT Patent Application WO 2009/072104 A3. |
Search Report of PCT Patent Application WO 2009/072103 A3. |
Search Report of PCT Patent Application WO 2009/072102 A3. |
Search Report of PCT Patent Application WO 2009/072101 A3. |
Search Report of PCT Patent Application WO 2009/072100 A3. |
Search Report of PCT Patent Application WO 2009/053963 A3. |
Search Report of PCT Patent Application WO 2009/053962 A3. |
Search Report of PCT Patent Application WO 2009/053961 A3. |
Search Report of PCT Patent Application WO 2009/037697 A3. |
Yani Chen, Kcshab K. Parhi, “Small Area Parallel Chien Search Architectures for Long BCH Codes”, Ieee Transactions on Very Large Scale Integration(VLSI) Systems, vol. 12, No. 5, May 2004. |
Yuejian Wu, “Low Power Decoding of BCH Codes”, Nortel Networks, Ottawa, Ont., Canada, in Circuits and systems, 2004. ISCAS '04. Proceeding of the 2004 International Symposium on Circuits and Systems, published May 23-26, 2004, vol. 2, pp. II-369-II-372 vol. 2. |
Michael Purser, “Introduction to Error Correcting Codes”, Artech House Inc., 1995. |
Ron M. Roth, “Introduction to Coding Theory”, Cambridge University Press, 2006. |
Akash Kumar, Sergei Sawitzki, “High-Throughput and Low Power Architectures for Reed Solomon Decoder”, (a.kumar at tue.nl, Eindhoven University of Technology and sergei.sawitzki at philips.com). |
Todd K.Moon, “Error Correction Coding Mathematical Methods and Algorithms”, A John Wiley & Sons, Inc., 2005. |
Richard E. Blahut, “Algebraic Codes for Data Transmission”, Cambridge University Press, 2003. |
David Esseni, Bruno Ricco, “Trading-Off Programming Speed and Current Absorption in Flash Memories with the Ramped-Gate Programming Technique”, Ieee Transactions on Electron Devices, vol. 47, No. 4, Apr. 2000. |
Giovanni Campardo, Rino Micheloni, David Novosel, “VLSI-Design of Non-Volatile Memories”, Springer Berlin Heidelberg New York, 2005. |
John G. Proakis, “Digital Communications”, 3rd ed., New York: McGraw-Hill, 1995. |
J.M. Portal, H. Aziza, D. Nee, “EEPROM Memory: Threshold Voltage Built in Self Diagnosis”, ITC International Test Conference, Paper 2.1. |
J.M. Portal, H. Aziza, D. Nee, “EEPROM Diagnosis Based on Threshold Voltage Embedded Measurement”, Journal of Electronic Testing: Theory and Applications 21, 33-42, 2005. |
G. Tao, A. Scarpa, J. Dijkstra, W. Stidl, F. Kuper, “Data retention prediction for modern floating gate non-volatile memories”, Microelectronics Reliability 40 (2000), 1561-1566. |
T. Hirncno, N. Matsukawa, H. Hazama, K. Sakui, M. Oshikiri, K. Masuda, K. Kanda, Y. Itoh, J. Miyamoto, “A New Technique for Measuring Threshold Voltage Distribution in Flash EEPROM Devices”, Proc. IEEE 1995 Int. Conference on Microelectronics Test Structures, vol. 8, Mar. 1995. |
Boaz Eitan, Guy Cohen, Assaf Shappir, Eli Lusky, Amichai Givant, Meir Janai, Ilan Bloom, Yan Polansky, Oleg Dadashev, Avi Lavan, Ran Sahar, Eduardo Maayan, “4-bit per Cell NROM Reliability”, Appears on the website of Saifun.com |
Paulo Cappelletti, Clara Golla, Piero Olivo, Enrico Zanoni, “Flash Memories”, Kluwer Academic Publishers, 1999. |
JEDEC Standard, “Stress-Test-Driven Qualification of Integrated Circuits”, JEDEC Solid State Technology Association. JEDEC Standard No. 47F pp. 1-26. |
Dempster, et al., “Maximum Likelihood from Incomplete Data via the EM Algorithm”, Journal of the Royal Statistical Society. Series B (Methodological), vol. 39, No. 1 (1997), pp. 1-38. |
Mielke, et al., “ Flash EEPROM Threshold Instabilities due to Charge Trapping During Program/Erase Cycling”, IEEE Transactions on Device and Materials Reliability, vol. 4, No. 3, Sep. 2004, pp. 335-344. |
Daneshbeh, “Bit Serial Systolic Architectures for Multiplicative Inversion and Division over GF (2)”, A thesis presented to the University of Waterloo, Ontario, Canada, 2005, pp. 1-118. |
Chen, Formulas for the solutions of Quadratic Equations over GF (2), IEEE Trans. Inform. Theory, vol. IT-28, No. 5, Sep. 1982, pp. 792-794. |
Berlekamp et al., “On the Solution of Algebraic Equations over Finite Fields”, Inform. Cont. 10, Oct. 1967, pp. 553-564. |
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20110246852 A1 | Oct 2011 | US |
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61321310 | Apr 2010 | US |