Systems and methods for handling immediate data errors in flash memory

Abstract

A system that includes a multiplicity of flash memory cells; a reading apparatus; a writing apparatus for writing logical data from temporary memory into individual flash memory cells from among said multiplicity of flash memory cells, thereby to generate a physical representation of the logical data including a plurality of physical levels at least some of which represent, to said reading apparatus, at least one bit-worth of said logical data; and a special cell marking apparatus operative to store an earmark in at least an individual one of said multiplicity of flash memory cells for subsequent special treatment.

Description

FIELD OF THE INVENTION

The present invention relates generally to methods and systems for managing computer memory and more particularly to methods and systems for managing flash memory.

BACKGROUND OF THE INVENTION

Conventional flash memory technology is described in the following publications inter alia:

• [1] Paulo Cappelletti, Clara Golla, Piero Olivo, Enrico Zanoni, “Flash Memories”, Kluwer Academic Publishers, 1999
• [2] G. Campardo, R. Micheloni, D. Novosel, “CLSI-Design of Non-Volatile Memories”, Springer Berlin Heidelberg New York, 2005

U.S. Pat. Nos. 5,771,346; 7,203,874; and Published United States Patent Application Nos. 2003231532; 2004243909; and 2007101184.

The disclosures of all publications and patent documents mentioned in the specification, and of the publications and patent documents cited therein directly or indirectly, are hereby incorporated by reference.

SUMMARY OF THE INVENTION

Today's Flash memory devices store information with high density on Flash cells with ever smaller dimensions. In addition, Multi-Level Cells (MLCs) store several bits per cell by differentially setting the amount of charge in the cell. The amount of charge is then measured by a detector, e.g. in the form of a threshold voltage of the transistor gate. Due to inaccuracies during the programming procedure and charge loss due to retention in memory and temperature, the measured levels during a Read operation suffer from detection errors. The small dimensions of the Flash cells result in cells that can store very small amounts of charge, enhancing the effects of inaccuracies due to randomness of programming, retention and previous erase/write cycles. Thus, new single level cells (SLC) and multi-level cell devices have significantly increased bit error rate (BER), decreasing the reliability of the device.

Flash devices are typically organized into physical pages. Each page contains a section allocated for data (typically 512 bytes-4 Kbytes) and a small number of bytes (typically 16-32 bytes for every 512 data bytes) containing redundancy and management information. The redundancy bytes are used to store error correcting information, for correcting errors which may have occurred during the page program or page read. Each Read and Program operation is typically performed on an entire page. A number of pages are grouped together to form an Erase Block (EB). A page typically cannot be erased unless the entire EB which contains it is erased.

An important factor of flash memory cost is the proportion of space allocated to “spare bits”, especially redundant information used to correct read errors e.g. due to retention. The ratio between the number of redundancy bits to the number of data bits is called the code rate.

The code rate is chosen according to the flash memory bit error rate or the number of error bits per page. The code rate is always less than the capacity bound that can be computed for each error probability. As shown in FIG. 2, the erasure channel capacity is always greater than the binary channel, so using erasure coding to correct the program errors is much more powerful than using conventional error correction code. Conventional error correction code, such as BCH or Reed-Solomon, corrects random errors during a read operation and lacks knowledge of the errors' locations.

Erasure coding use verifies procedure information to detect exactly the error bits' locations and to encode them. An example described below illustrates use of 15 bits of redundancy for 2 Kbyte page to correct up to 7 errors by using erasures whereas conventional error correction code allows correction of only a single error. The term “erasure” refers to a dummy logical value assigned to a symbol to indicate that it is unclear which logical value is best to assign, e.g. because the physical level read from the cell which the symbol represents is intermediate to adjacent logical values such as 110 and 111. The term “erasure coding” refers to the addition of redundancy (“erasure code”) to a codeword to enable the codeword to be properly decoded even though it includes at least one erasure.

Certain embodiments of the present invention seek to provide a flash memory system in which a page being programmed is read immediately after programming to detect immediate errors and construct parity bits according to error location. The term “immediate errors” is intended to include data errors which occur, hence can be identified and taken into account, as the data is being written from a still existing temporary memory, as opposed to errors which occur only after the temporary memory from which the data has been copied, no longer exists.

The following terms may be construed either in accordance with any definition thereof appearing in the prior art literature or in accordance with the specification, or as follows:

Bit error rate (BER)=a parameter that a flash memory device manufacturer commits to vis a vis its customers, expressing the maximum proportion of wrongly read bits (wrongly read bits/total number of bits) that users of the flash memory device may expect at any time during the stipulated lifetime of the flash memory device e.g. 10 years.Block=a set of flash memory device cells which must, due to physical limitations of the flash memory device, be erased together. Also termed erase sector, erase block.Cell: A component of flash memory that stores one bit of information (in single-level cell devices) or n bits of information (in a multi-level device having 2 exp n levels).Typically, each cell comprises a floating-gate transistor. n may or may not be an integer. “Multi-level” means that the physical levels in the cell are, to an acceptable level of certainty, statistically partitionable into multiple distinguishable regions, plus a region corresponding to zero, such that digital values each comprising multiple bits can be represented by the cell. In contrast, in single-level cells, the physical levels in the cell are assumed to be statistically partitionable into only two regions, one corresponding to zero and one other, non-zero region, such that only one bit can be represented by a single-level cell.Charge level: the measured voltage of a cell which reflects its electric charge.Cycling: Repeatedly writing new data into flash memory cells and repeatedly erasing the cells between each, two writing operations.Decision regions: Regions extending between adjacent decision levels, e.g. if decision levels are 0, 2 and 4 volts respectively, the decision regions are under 0 V, 0 V-2 V, 2V-4 V, and over 4 V.Demapping: basic cell-level reading function in which a digital n-tuple originally received from an outside application is derived from a physical value representing a physical state in the cell having a predetermined correspondence to the digital n-tuple.Digital value or “logical value”: n-tuple of bits represented by a cell in flash memory capable of generating 2 exp n distinguishable levels of a typically continuous physical value such as charge, where n may or may not be an integer.Erase cycle: The relatively slow process of erasing a block of cells (erase sector), each block typically comprising more than one page, or, in certain non-flash memory devices, of erasing a single cell or the duration of so doing. An advantage of erasing cells collectively in blocks as in flash memory, rather than individually, is enhanced programming speed: Many cells and typically even many pages of cells are erased in a single erase cycle.Erase-write cycle: The process of erasing a block of cells (erase sector), each block typically comprising a plurality of pages, and subsequently writing new data into at least some of them. The terms “program” and “write” are used herein generally interchangeably.Flash memory: Non-volatile computer memory including cells that are erased block by block, each block typically comprising more than one page, but are written into and read from, page by page. Includes NOR-type flash memory, NAND-type flash memory, and PRAM, e.g. Samsung PRAM, inter alia, and flash memory devices with any suitable number of levels per cell, such as but not limited to 2, 4, or 8.Mapping: basic cell-level writing function in which incoming digital n-tuple is mapped to a program level by inducing a program level in the cell, having a predetermined correspondence to the incoming logical value.Physical Page=A portion, typically 512 or 2048 or 4096 bytes in size, of a flash memory e.g. a NAND or NOR flash memory device. Writing and reading is typically performed physical page by physical page, as opposed to erasing which can be performed only erase sector by erase sector. A few bytes, typically 16-32 for every 512 data bytes are associated with each page (typically 16, 64 or 128 per page), for storage of error correction information. A typical block may include 32 512-byte pages or 64 2048-byte pages.Precise read, soft read: Cell threshold voltages are read at a precision (number of bits) greater than the number of Mapping levels (2^n). The terms precise read or soft read are interchangeable. In contrast, in “hard read”, cell threshold voltages are read at a precision (number of bits) smaller than the number of Mapping levels (2^n where n=number of bits per cell).Present level, Charge level: The amount of charge in the cell. The Amount of charge currently existing in a cell, at the present time, as opposed to “program level”, the amount of charge originally induced in the cell (i.e. at the end of programming).Program: same as “write”.Program level (programmed level, programming level): amount of charge originally induced in a cell to represent a given logical value, as opposed to “present level”.Reprogrammability (Np): An aspect of flash memory quality. This is typically operationalized by a reprogrammability parameter, also termed herein “Np”, denoting the number of times that a flash memory can be re-programmed (number of erase-write cycles that the device can withstand) before the level of errors is so high as to make an unacceptably high proportion of those errors irrecoverable given a predetermined amount of memory devoted to redundancy. Typically recoverability is investigated following a conventional aging simulation process which simulates or approximates the data degradation effect that a predetermined time period e.g. a 10 year period has on the flash memory device, in an attempt to accommodate for a period of up to 10 years between writing of data in flash memory and reading of the data therefrom.Resolution: Number of levels in each cell, which in turn determines the number of bits the cell can store; typically a cell with 2^n levels stores n bits. Low resolution (partitioning the window, W, of physical values a cell can assume into a small rather than large number of levels per cell) provides high reliability.Retention: of original physical levels induced in the flash memory cells despite time which has elapsed and despite previous erase/write cycles; retention is typically below 100% resulting in deterioration of original physical levels into present levels.Retention time: The amount of time that data has been stored in a flash device, typically without, or substantially without, voltage having been supplied to the flash device i.e. the time which elapses between programming of a page and reading of the same page.Symbol: Logical valueThreshold level: the voltage (e.g.) against which the charge level of a cell is measured. For example, a cell may be said to store a particular digital n-tuple D if the charge level or other physical level of the cell falls between two threshold values T.Dummy charge level: a charge level which does not represent an n-tuple of logical data

Retention noise: read errors generated by degradation of data due to length of retention in flash memory and/or previous write-erase cycles, as opposed to known errors.

Known errors: Immediate errors, such as but not limited to read errors generated by erratic over-programming also termed “erratic over-programming noise”, as opposed to retention noise.

Code rate: ratio of data bits to data and redundancy bits in flash memory.

Data cells: cells storing data provided by host as opposed to “non-data cells” which do not store host-provided data, and may, for example, store instead error correction information, management information, redundancy information, spare bits or parity bits.

Logical page: a set of bits defined as a page typically having a unique page address, by a host external to a flash memory device.

Spare bits: Redundancy information, or all non-data information including management information.

Reliability: Reliability of a flash memory device may be operationalized as the probability that a worst-case logical page written and stored in that device for a predetermined long time period such as 10 years will be successfully read i.e. that sufficiently few errors, if any, will be present in the physical page/s storing each logical page such that the error code appended to the logical page will suffice to overcome those few errors.

In this specification, the terms “decision levels” and “threshold levels” are used interchangeably. “Reliably storing” and “reliable” are used to indicate that certain information is stored with high reliability in the sense that the information can be expected to be read without error throughout the guaranteed lifetime of the flash memory device.

There is thus provided, in accordance with at least one embodiment of the present invention, a flash memory system comprising temporary memory, writing apparatus for writing first logical data from the temporary memory into flash memory cells having at least two levels, thereby to generate a physical representation of the first logical data including known errors, reading apparatus for reading the physical representation from the cells, thereby to generate, and store in the temporary memory, second logical data which, if read immediately, is identical to the first logical data other than the known errors; and controlling apparatus controlling the writing apparatus and the reading apparatus and including known error ID apparatus operative to identify the known errors by comparing the first logical data to second logical data read immediately after the physical representation is generated, to store information characterizing the known errors and to use the information, when the second logical data is next read, to correct the known errors.

Also in accordance with at least one embodiment of the present invention, the information enables addresses of the known errors to be reconstructed when the second logical data is next read and wherein the controlling apparatus is operative to reconstruct the addresses, using the information, when the second logical data is next read.

Further in accordance with at least one embodiment of the present invention, the information comprises addresses of the known errors.

Still further in accordance with at least one embodiment of the present invention, the information comprises an earmark on each cell containing at least one known error and correct logical data for each cell bearing an earmark.

Further in accordance with at least one embodiment of the present invention, the earmark comprises a dummy physical level assigned to the cell.

Still further in accordance with at least one embodiment of the present invention, the information comprises the total number of known errors identified by the known error ID apparatus and a serial number of a set comprising the addresses of the known errors, within a sequence, having a predetermined order, of all possible sets of the addresses of the known errors given the total number of known errors.

Further in accordance with at least one embodiment of the present invention, at least a portion of the controlling apparatus resides in a microcontroller within a flash memory device within which the cells reside.

Still further in accordance with at least one embodiment of the present invention, at least a portion of the controlling apparatus resides in a controller external to a flash memory device within which the cells reside.

Additionally in accordance with at least one embodiment of the present invention, the cells comprise NAND cells or NOR cells.

Further in accordance with at least one embodiment of the present invention, the addresses comprise bit addresses or symbol addresses.

Also provided, in accordance with at least one embodiment of the present invention, is a flash memory system comprising a multiplicity of flash memory cells; reading apparatus; writing apparatus for writing logical data from temporary memory into individual flash memory cells from among the multiplicity of flash memory cells, thereby to generate a physical representation of the logical data including a plurality of physical levels at least some of which represent, to the reading apparatus, at least one bit-worth of the logical data; and special cell marking apparatus operative to earmark at least an individual one of the multiplicity of flash memory cells for subsequent special treatment.

Further in accordance with at least one embodiment of the present invention, the special cell marking apparatus is operative to earmark the individual one of the multiplicity of cells by assigning a dummy physical level assigned to the cell wherein the dummy physical level is characterized in that it does not represent logical data to the reading apparatus.

Additionally provided, in accordance with at least one embodiment of the present invention, is a method for storing a set of at least one consecutive integers in memory, the method comprising computing and storing at least one serial number identifying at least one respective position of at least one consecutive integer in the set respectively in a predetermined sequence of all possible addresses; and computing the at least one consecutive integer from the at least one serial number.

Further in accordance with at least one embodiment of the present invention, the set of at least one consecutive integers comprises at least one address.

Still further in accordance with at least one embodiment of the present invention, the address comprises a flash memory cell address.

Also provided, in accordance with yet a further embodiment of the present invention, is a flash memory utilization method comprising writing first logical data from temporary memory into flash memory cells having at least two levels, thereby to generate a physical representation of the first logical data including known errors; reading the physical representation from the cells, thereby to generate, and store in the temporary memory, second logical data which, if read immediately, is identical to the first logical data other than the known errors; and controlling the writing apparatus and the reading apparatus including identifying the known errors by comparing the first logical data to second logical data read immediately after the physical representation is generated, storing information characterizing the known errors and using the information, when the second logical data is next read, to correct the known errors.

Additionally provided, in accordance with at least one embodiment of the present invention, is a flash memory utilization method comprising writing logical data from temporary memory into individual flash memory cells from among a multiplicity of flash memory cells, thereby to generate a physical representation of the logical data including a plurality of physical levels at least some of which represent, to reading apparatus, at least one bit-worth of the logical data; and special cell marking apparatus operative to earmark at least an individual one of the multiplicity of flash memory cells for subsequent special treatment.

According to one embodiment of the present invention, a program, verify and erasure coding method is provided in which some or all of the following steps are performed in any suitable order such as but not limited to the following: programming data only (page without parity bits), verifying including detecting the error bits and erratic over-programming, storing at least one error address in temporary memory such as SRAM, generating erasure data e.g. as described herein with reference to FIG. 5 or 6, encoding the data and erasure bits using error correction code and obtaining the parity bits, and programming of the erasure and parity bits. In contrast, conventionally, a page of data and parity bits is programmed, followed by verification.

According to one embodiment of the present invention, a method for erasure coding which utilizes an additional level is provided, in which some or all of the following steps are performed in any suitable order such as but not limited to the following: encoding the page, such that result=data+parity, programming the page, verifying that the cell level is between the lower and upper values, and if not (e.g. due to erratic over-programming), increase the cell voltage to an erasure level.

Any suitable processor, display and input means may be used to process, display, store and accept information, including computer programs, in accordance with some or all of the teachings of the present invention, such as but not limited to a conventional personal computer processor, workstation or other programmable device or computer or electronic computing device, either general-purpose or specifically constructed, for processing; a display screen and/or printer and/or speaker for displaying; machine-readable memory such as optical disks, CDROMs, magnetic-optical discs or other discs; RAMs, ROMs, EPROMs, EEPROMs, magnetic or optical or other cards, for storing, and keyboard or mouse for accepting. The term “process” as used above is intended to include any type of computation or manipulation or transformation of data represented as physical, e.g. electronic, phenomena which may occur or reside e.g. within registers and/or memories of a computer.

The above devices may communicate via any conventional wired or wireless digital communication means, e.g. via a wired or cellular telephone network or a computer network such as the Internet.

The apparatus of the present invention may include, according to certain embodiments of the invention, machine readable memory containing or otherwise storing a program of instructions which, when executed by the machine, implements some or all of the apparatus, methods, features and functionalities of the invention shown and described herein. Alternatively or in addition, the apparatus of the present invention may include, according to certain embodiments of the invention, a program as above which may be written in any conventional programming language, and optionally a machine for executing the program such as but not limited to a general purpose computer which may optionally be configured or activated in accordance with the teachings of the present invention.

Any trademark occurring in the text or drawings is the property of its owner and occurs herein merely to explain or illustrate one example of how an embodiment of the invention may be implemented.

Unless specifically stated otherwise, as apparent from the following discussions, it is appreciated that throughout the specification discussions, utilizing terms such as, “processing”, “computing”, “estimating”, “selecting”, “ranking”, “grading”, “calculating”, “determining”, “generating”, “reassessing”, “classifying”, “generating”, “producing”, “stereo-matching”, “registering”, “detecting”, “associating”, “superimposing”, “obtaining” or the like, refer to the action and/or processes of a computer or computing system, or processor or similar electronic computing device, that manipulate and/or transform data represented as physical, such as electronic, quantities within the computing system's registers and/or memories, into other data similarly represented as physical quantities within the computing system's memories, registers or other such information storage, transmission or display devices.

The embodiments referred to above, and other embodiments, are described in detail in the following sections.

BRIEF DESCRIPTION OF THE DRAWINGS

Certain embodiments of the present invention are illustrated in the following drawings:

FIG. 1A is a logarithmic-scale graph of distributions of voltage levels within flash memory cells suffering from erratic over-programming (EOP);

FIG. 1B is a simplified block diagram illustration of a flash memory system constructed and operative in accordance with a first embodiment of the present invention;

FIG. 1C is a simplified block diagram illustration of a flash memory system constructed and operative in accordance with a second embodiment of the present invention;

FIG. 1D is a simplified block diagram illustration of a flash memory system constructed and operative in accordance with a third embodiment of the present invention;

FIG. 2 is a code rate vs. bit flip error probability graph showing a rate of erasure in a top graph and a binary channel in a bottom graph;

FIG. 3 is a logarithmic-scale graph of distributions of voltage levels within theoretical flash memory cells which do not suffer from erratic overprogramming;

FIGS. 4A and 4B are prior art subsequence-symbol tables;

FIG. 5 is a simplified flowchart illustration of a recursive method for compact encoding of erratic over-programming error locations constructed and operative in accordance with certain embodiments of the present invention which is suitable for performing the corresponding encoding step of FIG. 7;

FIG. 6 is a simplified flowchart illustration of a recursive method, constructed and operative in accordance with certain embodiments of the present invention, for decoding erratic over-programming error locations encoded as per the method of FIG. 5, the method being suitable for performing the corresponding decoding step of FIG. 8;

FIG. 7 is a simplified flowchart illustration of a first method for erratic over-programming coding, constructed and operative in accordance with certain embodiments of the present invention, which uses a verify-read operation to generate known error characterizing information re cells which suffered from erratic over-programming;

FIG. 8 is a simplified flowchart illustration of a method, constructed and operative in accordance with certain embodiments of the present invention, for reading a page programmed as per the method of FIG. 7;

FIG. 9 is a simplified flowchart illustration of a second method for erratic over-programming coding, constructed and operative in accordance with certain embodiments of the present invention;

FIG. 10 is a simplified flowchart illustration of a decoding method, constructed and operative in accordance with certain embodiments of the present invention, which corresponds to the coding method of FIG. 9; and

FIG. 11 is a redundancy vs. bit error rate graph useful in implementing some of the embodiments shown and described herein.

DETAILED DESCRIPTION OF CERTAIN EMBODIMENTS OF THE PRESENT INVENTION

According to certain embodiments of the present invention, the code rate is selected in the flash design stage. Experiments are performed in the course of which the bit error rate may be measured and the code rate computed e.g. as shown in FIG. 11. FIG. 11 illustrates a redundancy allocation per any bit error rate for a given page size. Conventional programming may include several steps e.g. as shown and described below including incremental injection of charge into the flash. The charge monotonically increases until the cell voltage reaches the pre-defined target value.

In technologies in which the charge can only increase, some cell voltages may overshoot their intended targets due to a random process known as erratic over-programming (EOP). It is appreciated however that certain embodiments of the present invention are described below in terms of erratic over-programming merely for simplicity, their applicability now being limited to applications in which erratic over-programming is actually occurring.

Erratic over-programming causes errors in the stored data. These errors are an example, but not the only example, of errors which, fortunately, may be detected immediately after the programming procedure ends in accordance with certain embodiments of the present invention. In FIG. 1A, erratic over-programming manifests itself as a long tail, indicated in dashed lines, on the right of the cell voltage distribution. FIG. 3, in contrast, is a theoretical illustration of how the distribution might appear in the absence of erratic over-programming. FIG. 1A too is not necessarily accurate in its parameters and is merely intended to illustrate the concept of erratic over-programming.

The errors during program operation can be detected immediately if a verify-read operation 230 is instituted following the page program operation 220, as shown in FIG. 7. The verify-read operation 230 is typically executed between successive repetitions of program steps 220 in order to learn the exact voltage value of the cell during the programming procedure. During the programming operation a cell voltage typically cannot be restored to a lower value, however, the verify-read information may be employed to construct code that corrects program errors.

Certain embodiments of the present invention employ program/verify and error correction to improve the flash programming quality. During normal programming operation some cells experience erratic over-programming. Both erratic over-programming noise and retention noise degrade the flash quality and generate read errors. Conventional error correction does not distinguish between the erratic over-programming and retention noise which are treated as a single read noise source. The flash suffers from aging as a result of program/erase cycles and retention time. The aging process results in loss of window size and increase in noise variance of each program level e.g. each of the four programming levels V1, . . . , V4 in FIG. 1A. The consequence may be loss in the signal to noise ratio and increase in number of error bits.

In order to encode information and to protect it against errors, redundancy information is typically appended to the original data. A bit (or symbol) sequence representing data (typically a pageful of data) and redundancy is termed herein a “codeword”. A “code rate” of a codeword may be the ratio between the number of bits (or symbols) in the codeword which serve to store data, and the total number of bits (or symbols) in the codeword which may for example be 1024 Bytes to 4096 Bytes. A bit may flip to the wrong value with probability p.

The bottom curve in FIG. 2 shows the maximum code rate achievable assuming there is no prior information on which bit flips and how many such bits there are. The top curve in FIG. 2 shows the maximum rate achievable if it is known which bits are suspicious and if such bits are marked as erasures so as to indicate that they may be either 0 or 1, with equal probability. As is apparent from FIG. 2, more density can be obtained from the flash if locations of erratic over-programming errors are recorded and erratic over-programming noise removed, using coding in accordance with any embodiment of the present invention. Advantages of these embodiments may include one or both of the following:

a. Narrowing of the program symbol regions (voltage distributions), e.g. removal of the erratic over-programming tail. (A “symbol” is an n-tuple of bits in a logical page, represented by a discrete charge level on a physical page. For example: ‘00’=V0, ‘01’=V1, ‘10’=V2 and ‘11’=V3 are 4 symbol/charge level relationships); and

b. Use of erasure coding to encode erratic over-programming cells.

According to one embodiment of the present invention, e.g. as shown in FIG. 1A, erratic over-programming is detected following a programming procedure and a sequence of bits (or symbols) may be allocated which represents the locations where erratic over-programming occurred. The sequence is then typically appended or stored separately (e.g. in redundancy symbols).

A second embodiment, as shown in FIG. 3, is to allocate an additional program level which will be denoted as an erasure level at each program symbol. The erasure symbols may be denoted by the top program level. The locations of erratic over-programming are then marked by doing a second programming procedure which raises the program levels of the erratic over-programming locations to the top level. FIG. 3 is an example of a case of a multi-level cell with 4 program levels and one erasure level marked as V5. More generally, a region between any two program levels may be deemed an erasure region. The program window may be divided into multiple erasure regions interspersed with multiple symbol regions figures shown in FIG. 3. In FIG. 3, by way of example, there are four erasure regions marked E1, E2, E3 and E4. The levels are tuned according to the erasure coding capability. If a specific cell's programmed level lies in the erasure region above it, or in any of the regions above that, the cell may be marked as erasure.

In the verify operation the erratic over-programming may be detected. By using the lower and upper verify level for each symbol, a cell which has moved beyond the lower or upper limits can be detected. If so the program erasure may be moved in the next step. If an erratic over-programming bit is detected, its physical value may be increased to the dummy value (V5 in the illustrated embodiment) which indicates that the cell suffers from erratic over-programming error.

Once marked by either erasures or in a separate sequence as described in detail below, a second code may be applied to both parts of the data (i.e. the data part and the erasure part), thereby protecting the information against additional errors due to retention. As a result, the programming errors are eliminated and more errors may be corrected compared with conventional error correction methods.

FIG. 1B is a simplified functional block diagram of a flash memory system constructed and operative, in accordance with a first embodiment of the present invention, to identify and rectify data errors which occur while the temporary memory from which the data was read, still exists. As shown, the system of FIG. 1C includes a host 100 interfacing with a flash memory device 105 including a microcontroller 110 (some or all of whose functions may alternatively be performed by an external microcontroller connected between the flash memory and the host), and one or more erase sectors 120 each having one or more physical pages 130 each of which comprises a plurality of data cells 140 as well as non-data cells 121. Also included is erasing circuitry 150, writing circuitry 160 and reading circuitry 170. The microcontroller 110 finds known errors by reading back data from cells 140 while original host-supplied data is still available for comparison. The non-data cells 121 are operative to store management info, redundancy info and information re known errors. It is appreciated that some or all of the functionality of the microcontroller 110 can be provided in fact by an external controller instead.

FIG. 1C is a simplified functional block diagram of a flash memory system constructed and operative, in accordance with a second embodiment of the present invention, to identify and rectify data errors which occur while the temporary memory from which the data was read, still exists. In the embodiment of FIG. 1D, the microcontroller 110, or an external controller, finds known errors by reading back data from cells 140 while original host-supplied data is still available for comparison. The controller also typically re-writes data, appending addresses of known errors thereto; and, during reading, flips bits at these addresses, all as described in detail below with reference to FIGS. 7-8. In this embodiment, non-data cells 121 typically store management information, redundancy information and known error bit addresses.

FIG. 1D is a simplified functional block diagram of a flash memory system constructed and operative, in accordance with a third embodiment of the present invention, to identify and rectify data errors which occur while the temporary memory, from which the data was read, still exists. In the embodiment of FIG. 1D, the microcontroller 110, or an external controller, finds known errors by reading back data from cells 140 while original host-supplied data is still available for comparison, re-writes data replacing known errors with dummy values and appending correct values, and, during reading, replaces dummy values with appended correct values. Non-data cells 121 typically store management info, redundancy info and content for cells found to be in dummy state, all as described in detail below with reference to FIGS. 9-10. In this embodiment, the data cells 140 have n data states plus one additional dummy state earmarking cell as suffering from known error.

A first embodiment of erratic over-programming coding, as illustrated in FIG. 7, uses a verify-read operation 230 to generate known error characterizing information re cells which suffered from erratic over-programming. Locations of these cells may be encoded, preferably as compactly as possible, and stored in the redundancy area of the page along with additional typically conventional error correction information. The error correction information may be generated from the erroneous page and the encoded erratic over-programming cell locations. A second programming procedure 270, may be then performed to program the redundancy cells. In this embodiment, no erasure regions are provided between programming levels.

The method of FIG. 7 typically includes some or all of the following steps in a suitable order e.g. as shown:

Step 210: Receive original data bits from host, store in temporary memory, and map the original data bits into levels. The mapping process converts n bits into 2^n levels, e.g. 2 bits per cell are converted to 4 levels to be program. This process may be done by applying Grey coding e.g. as shown in FIG. 4A for the case of 8 levels.

Step 220: Program the levels into cells reserved for data in a flash memory cell array

Step 230: while the original data still exists in temporary memory, read back a pageful of cell values from the array and decode them e.g. by mapping them back into bits.

Step 240: Compare the read result with the corresponding pageful of original data still residing in temporary memory. Record the locations of the erroneous bits in temporary memory, optionally in a compact form. It may be possible to store the locations, or to store the first locations followed by the intervals between each two adjacent locations, or to use any other suitable method for compactly storing the location information such as the method of FIG. 5.

Step 250: generate non-data bits for correcting retention errors using an error correction code to decode the data read from the device (which may include erratic over-programming errors)

Step 255: generate non-data bits for correcting known errors using an error correction code to encode the info re known error locations recorded in step 240

Step 260: Map the non-data bits generated in steps 250, 255 into levels

Step 270: Program the levels mapped in step 260, into non-data cells

Typically, according to the method of FIG. 7, the page is programmed in two sections (steps 220 and 270), first the data without parity then the erasure index and parity. If additional level coding is used, programming may occur in a single step (data and parity), since the erasure index may be programmed with the additional level.

A suitable method for reading a page programmed as per the method of FIG. 7 is illustrated in FIG. 8. As shown, the method of FIG. 8 may include some or all of the following steps, suitably ordered e.g. as shown:

Step 810: Read a physical page-full of cell values (data+non-data bits) into temporary memory and de-map them into bits.

Step 820: correct retention errors by error correction-decoding of the non-data cells storing the info encoded in step 250 (typically also correcting thereby, errors that occurred due to erratic over-programming in the programming of the redundancy. Since parity may be programmed in the second step it might be corrupted with erratic over-programming. So in the decoding step the entire page is typically corrected including the erratic over-programming errors in the parity bits.

Step 830: Access error location info encoded in step 255 & decode (e.g. using the method of FIG. 6 if locations were encoded using the method of FIG. 6) correct known errors by flipping the values of the data bits corresponding to the decoded error locations.

Reference is now made to FIG. 5 which illustrates a recursive method, including a recursive step 625, for compact encoding of erratic over-programming error locations suitable for performing step 240 of FIG. 7. FIG. 6 illustrates a recursive method, including a recursive step 685, for decoding erratic over-programming error locations encoded as per the method of FIG. 5 and is suitable for performing step 830 of FIG. 8.

These methods achieve near optimum encoding. Let k denote the number of locations and let n be the number of bits (or symbols) in the original data sequence. There are exactly

$\left(\begin{array}{c}n\\ k\end{array}\right)=\frac{n!}{k!\left(n-k\right)!}$ possible sequences of k out of n error locations. Therefore, at least

$\lceil {\log }_2\left(\begin{array}{c}n\\ k\end{array}\right)\rceil$ bits are employed to encode a sequence. First, k bits are encoded. If k<K, ┌log₂ K┐ bits may be reserved for this, where K may be any integer greater than k. Next, encode the sequence of k out of n locations, typically in a compact form employing

$\lceil {\log }_2\left(\begin{array}{c}n\\ k\end{array}\right)\rceil$

bits.

In order to encode the sequence of k out of n locations, a serial number may be assigned to each ordered set of k possible locations between 0 and

$\left(\begin{array}{c}n\\ k\end{array}\right)-1.$ This serial number may be then presented as a binary number; since the correspondence between serial number and ordered set of locations is known, the ordered set of locations can be retrieved. This may be done in a recursive manner. Assume the location of the first error is 1. There are then

$\hspace{1em}\left(\begin{array}{c}n-1\\ k-1\end{array}\right)$ ways to define all possible k−1 locations of the remaining possible n−1 locations. Therefore, to encode a sequence of k out of n locations in which the first location is 1, these sequences may be numbered between 0 and

$\left(\begin{array}{c}n-1\\ k-1\end{array}\right)-1.$ If the first location was not 1 but 2, there are

$\hspace{1em}\left(\begin{array}{c}n-2\\ k-1\end{array}\right)$ ways to define all possible k−1 locations of the possible (left) n−2 locations. Therefore, to encode a sequence of k out of n locations in which the first location is 2, these sequences are numbered between

$\hspace{1em}\left(\begin{array}{c}n-1\\ k-1\end{array}\right)$ and

$\hspace{1em}\left(\begin{array}{c}n-1\\ k-1\end{array}\right)+\hspace{1em}\left(\begin{array}{c}n-2\\ k-1\end{array}\right)-1.\hspace{1em}\left(\begin{array}{c}n-1\\ k-1\end{array}\right)$ may be added to the numbers to distinguish these cases from the case in which the first error was found in the first location. This procedure may be repeated iteratively until the first location is found and recursively to give the precise number of k−1 numbers out of n−v numbers where v is the location of the first error.

In summary, a compact and perhaps the most compact way to store a subset of cell locations, from among an original data sequence stored in n cell locations, which are special in some sense (e.g. in the sense that the cell locations in the subset suffer from known errors) comprises the following procedure as shown in FIG. 5: storing the number (k) of such cell locations in the redundancy bits, converting each possible set of cell locations into a cell location sequence having a predetermined order, typically increasing order of address, and arranging all possible cell location sequences in a known order, thereby define a sequence of all possible selections of k cell locations from among the total number, n, of cell locations. If this is done, it may be sufficient to store the serial number of the particular set of known error locations within the sequence; from this and from the known number k of cell locations, the known error locations can be derived e.g. as per the method of FIG. 6.

For example, there may be k=5 cells with known errors in a flash memory physical page containing a total of n=1024 cells. The addresses of these cells may be 1, 6, 100, 457 and 900. There are 1024!/5! (1024−5)!=9291,185,992,704 different ordered sets of 5 addresses in total which may be selected from 1024 cells, of which (1, 6, 100, 457 and 900) is but one example. These 1024!/5! (1024−5)! ordered sets of addresses may be arranged in the following known order: (1, 2, 3, 4, 5); (1, 2, 3, 4, 6); . . . (1, 2, 3, 4, 1024); (1, 2, 3, 5, 6); (1, 2, 3, 5, 7); . . . (1, 2, 3, 5, 1024); . . . (1, 2, 3, 1022, 1023); (1, 2, 3, 1022, 1024); (1, 2, 3, 1023, 1024); (1, 2, 4, 5, 6) . . . , . . . , (1, 2, 4, 1023, 1024); . . . (1, 2, 1022, 1023, 1024); (1, 3, 4, 5, 6) . . . (1, 3, 1022, 1023, 1024); . . . ; . . . ; (1, 1021, 1022, 1023, 1024); (2, 3, 4, 5, 6) . . . (2, 3, 4, 5, 1024); . . . ; . . . ; (2, 3, 1022; 1023, 1024); . . . (2, 1021; 1022; 1023; 1024); . . . (1020; 1021; 1022; 1023; 1024), thereby to form a sequence of all possible selections of 5 ordered cell addresses from among 1024 addresses total. Using the method of FIG. 5, it may be determined that the serial number (“number”) of (1, 6, 100, 457 and 900) in the above sequence of selected sets of 5 addresses, is 575,218,469. To retrieve (1, 6, 100, 457 and 900), plug n=1024, k=5, number=575,218,469 into the method of FIG. 6.

The erratic over-programming encoding method of FIG. 7 may be modified by encoding only the symbols in which erratic over-programming errors occurred instead of the bits in which they occurred. Thus, only k out of n′ symbol locations may be encoded, where n′ is defined by n/log 2L and where L is the number of levels programmed per cell. Thus, fewer bits may be employed to encode the error locations.

In the erratic over-programming correction process it can typically be assumed that errors occur only in one direction. That is, typically, one may mistakenly program a higher level than is appropriate (e.g. V4 instead of V3) whereas one never programs a lower level than the appropriate level (e.g. V3 instead of V4), since a too-low level is raised one level higher. Thus, once it is known that a certain location contains an error, the output read level may be decreased by 1 with respect to the level actually read.

The following example explains how the method of FIG. 6 enhances compactness of flash memory. Consider an example where 16384 bits of data are programmed on an multi-level cell flash containing 3 bits per cell (i.e. 8 levels per cell). Correct n1=50 erratic over-programming errors+n2=5 errors which occur due to retention. Using the method of FIG. 7, encode at least the 16384th bit over 5462 cells. To encode n1=50 locations out of 5462 possible locations using, e.g., the method of FIG. 6,

$\lceil {\log }_{2}50\rceil +\lceil {\log }_2\left(\begin{array}{c}5462\\ 50\end{array}\right)\rceil =413\mathrm{bits}\mathrm{are}\mathrm{employed}.$

A binary BCH code, say, may be used to protect against the retention errors. This code encodes both the data read from the device (with the erratic over-programming errors) and the 413 bits encoding up to 50 erratic over-programming error locations. Such a BCH code would employ 16×5=80 redundancy bits. Therefore, a total of 493 bits may be used. This outcome may be compared with a conventional code that does not distinguish between erratic over-programming errors and retention errors hence may be operative to correct 55 errors. If BCH code is used, this would employ 55*16=880 bits of redundancy. This is almost twice the redundancy provided in the above example of usage of the method of FIG. 7.

A second method for erratic over-programming coding is now described with reference to FIG. 9. The corresponding decoding method is shown in FIG. 10. In FIG. 9, instead of encoding the erratic over-programming error locations, the cells that suffered from erratic over-programming are marked within the cells themselves e.g. by programming the cells to the highest programming level which may be especially reserved for this purpose and is referred to as the erasure level. For example, FIG. 3 illustrates 5 bell curve distributions of 5 charge levels respectively, in a 2-bit-per-cell flash memory device. The fifth level may be reserved for erasure.

In step 910, the original data is programmed with redundancy which contains parity bits. The parity bits are generated by an error correction encoder which is designed to address erasures. An example of such an encoder is a Low Density Parity Check (LDPC) encoder which is known in the art (e.g. in Modern Coding Theory, T. Richardson and R. Urbanke, Cambridge University Press, Chapter 3, page 77) as especially suitable for erasure. Thus low redundancy may be provided to facilitate erasure correction, as shown in FIG. 2. The encoder may also be used to correct a small number of errors which are not marked as erasures and which are due to retention.

Step 940 identifies which of the cells were over-programmed. Step 950 marks the over-programmed cells by raising their programming level to the highest one (e.g. V5 in FIG. 3). It is appreciated that once a level is over-programmed it cannot be lowered to the correct value. Lowering levels can only be effected in the course of an erase operation and only on multiple pages simultaneously.

In summary, the encoding process of FIG. 9 typically comprises some or all of the following steps, suitably ordered e.g. as shown:

Step 910: Get original data bits from a host and append redundancy bits using an error correction code capable of coping with erasure coding e.g. LDPC codes

Step 920: Map the data and redundancy bits into levels (e.g. using the table of FIG. 4A or the table of FIG. 4B). Program the levels into the data cells+redundancy cells, respectively, in flash memory

Step 930: while the original data bits are still available (e.g. in temporary memory), read the symbols from the flash memory and compare to the original data bits to identify known error locations.

Step 940: for each known error location identified in step 930, store its contents, e.g. store error bits as part of the redundancy data (non-data) in the temporary memory

Step 950: Program the page again, raising the program levels of those cells found in step 930 to suffer from known errors, to erasure level and programming the additional error bits as part of the redundancy data stored in the temporary memory.

The decoding process of FIG. 10 typically comprises some or all of the following steps, suitably ordered e.g. as shown:

Step 1010: Read a pageful of cells (data+redundancy) from flash memory into SRAM and de-map into bits.

Step 1020: for each Bit mapped to a cell programmed to the erasure level, store bit's addresses in another SRAM

Step 1030: Decode the data bits+erasure addresses stored in step 1020+correct contents stored in FIG. 9 using the error correction code.

Step 1040: Output correct codeword and finish, including putting correct contents sequentially into addresses decoded in step 1030

It is appreciated that software components of the present invention including programs and data may, if desired, be implemented in ROM (read only memory) form including CD-ROMs, EPROMs and EEPROMs, or may be stored in any other suitable computer-readable medium such as but not limited to disks of various kinds, cards of various kinds and RAMs. Components described herein as software may, alternatively, be implemented wholly or partly in hardware, if desired, using conventional techniques.

Included in the scope of the present invention, inter alia, are electromagnetic signals carrying computer-readable instructions for performing any or all of the steps of any of the methods shown and described herein, in any suitable order; machine-readable instructions for performing any or all of the steps of any of the methods shown and described herein, in any suitable order; program storage devices readable by machine, tangibly embodying a program of instructions executable by the machine to perform any or all of the steps of any of the methods shown and described herein, in any suitable order; a computer program product comprising a computer useable medium having computer readable program code having embodied therein, and/or including computer readable program code for performing, any or all of the steps of any of the methods shown and described herein, in any suitable order; any technical effects brought about by any or all of the steps of any of the methods shown and described herein, when performed in any suitable order; any suitable apparatus or device or combination of such, programmed to perform, alone or in combination, any or all of the steps of any of the methods shown and described herein, in any suitable order; information storage devices or physical records, such as disks or hard drives, causing a computer or other device to be configured so as to carry out any or all of the steps of any of the methods shown and described herein, in any suitable order; a program pre-stored e.g. in memory or on an information network such as the Internet, before or after being downloaded, which embodies any or all of the steps of any of the methods shown and described herein, in any suitable order, and the method of uploading or downloading such, and a system including server/s and/or client/s for using such; and hardware which performs any or all of the steps of any of the methods shown and described herein, in any suitable order, either alone or in conjunction with software.

Certain operations are described herein as occurring in the microcontroller internal to a flash memory device. Such description is intended to include operations which may be performed by hardware which may be associated with the microcontroller such as peripheral hardware on a chip on which the microcontroller may reside. It is also appreciated that some or all of these operations, in any embodiment, may alternatively be performed by the external, host-flash memory device interface controller including operations which may be performed by hardware which may be associated with the interface controller such as peripheral hardware on a chip on which the interface controller may reside. Finally it is appreciated that the internal and external controllers may each physically reside on a single hardware device, or alternatively on several operatively associated hardware devices.

Any data described as being stored at a specific location in memory may alternatively be stored elsewhere, in conjunction with an indication of the location in memory with which the data is associated. For example, instead of storing page- or erase-sector-specific information within a specific page or erase sector, the same may be stored within the flash memory device's internal microcontroller or within a microcontroller interfacing between the flash memory device and the host, and an indication may be stored of the specific page or erase sector associated with the cells.

It is appreciated that the teachings of the present invention can, for example, be implemented by suitably modifying, or interfacing externally with, flash controlling apparatus. The flash controlling apparatus controls a flash memory array and may comprise either a controller external to the flash array or a microcontroller on-board the flash array or otherwise incorporated therewithin. Examples of flash memory arrays include Samsung's K9XXG08UXM series, Hynix' HY27UK08BGFM Series, Micron's MT29F64G08TAAWP or other arrays such as but not limited to NOR or phase change memory. Examples of controllers which are external to the flash array they control include STMicroelectrocincs's ST7265x microcontroller family, STMicroelectrocincs's ST72681 microcontroller, and SMSC's USB97C242, Traspan Technologies' TS-4811, Chipsbank CBM2090/CBM1190. Example of commercial IP software for Flash file systems are: Denali's Spectra™ NAND Flash File System, Aarsan's NAND Flash Controller IP Core and Arasan's NAND Flash File System. It is appreciated that the flash controller apparatus need not be NAND-type and can alternatively, for example, be NOR-type or phase change memory-type.

Flash controlling apparatus, whether external or internal to the controlled flash array, typically includes the following components: a Memory Management/File system, a NAND interface (or other flash memory array interface), a Host Interface (USB, SD or other), error correction circuitry (ECC) typically comprising an Encoder and matching decoder, and a control system managing all of the above.

The present invention may for example interface with or modify, as per any of the embodiments described herein, one, some or all of the above components and particularly the error correction code and NAND interface components.

Features of the present invention which are described in the context of separate embodiments may also be provided in combination in a single embodiment. Conversely, features of the invention, including method steps, which are described for brevity in the context of a single embodiment or in a certain order may be provided separately or in any suitable subcombination or in a different order.

Claims

1. A system comprising: a multiplicity of flash memory cells;a reading apparatus;a writing apparatus for writing logical data from temporary memory into individual flash memory cells from among said multiplicity of flash memory cells, thereby to generate a physical representation of the logical data including a plurality of physical levels at least some of which represent, to said reading apparatus, at least one bit-worth of said logical data; anda special cell marking apparatus operative to store an earmark in a certain flash memory cell of said multiplicity of flash memory cells for subsequent special-treatment by programming the certain flash memory cell to store a dummy physical level, said dummy physical level differs from any physical level used for representing one or more logical data bits in the certain flash memory cell.

2. The system according to claim 1 wherein each one of the multiplicity of flash memory is programmable to a plurality (2 by the power of n) of physical levels that represent logical values of n logical data bits and to the dummy physical level, n being a positive integer.

3. The system according to claim 1 wherein the dummy physical level is an erasure physical value.

4. The system according to claim 1 wherein the subsequent special treatment comprises error correction.

5. The system according to claim 1 comprising a reading circuitry that is arranged to read a content of the certain flash memory cell to provide a dummy value; and a microcontroller that is arranged to detect the dummy value, apply an error correction process to provide a correct value and to replace the dummy value with the correct value.

6. The system according to claim 1 wherein the special cell marking apparatus is operative to store an earmark in each one of a plurality of flash memory cells of said multiplicity of flash memory cells for subsequent special-treatment by programming each one of the plurality of flash memory cell to store the dummy physical level.

7. A flash memory utilization method comprising: writing logical data from temporary memory into individual flash memory cells from among a multiplicity of flash memory cells, thereby to generate a physical representation of the logical data including a plurality of physical levels at least some of which represent, to reading apparatus, at least one bit-worth of said logical data; andearmarking, by a special cell marking apparatus, a certain flash memory cell of said multiplicity of flash memory cells for subsequent special treatment by programming the certain flash memory cells to store a dummy physical, said dummy physical level differs from any physical level used for representing one or more logical data bits in the certain flash memory cell.

8. The method according to claim 7 wherein each one of the multiplicity of flash memory is programmable to a plurality (2 by the power of n) of physical levels that represent logical values of n logical data bits and to the dummy physical level, n being a positive integer.

9. The method according to claim 7 wherein the dummy physical level is an erasure physical value.

10. The method according to claim 7 wherein the subsequent special treatment comprises error correction.

11. The method according to claim 7 comprising reading a flash memory cell that is programmed to store the dummy physical level to provide a dummy value; detecting the dummy value, applying an error correction process to provide a correct value and replacing the dummy value with the correct value.

12. The method according to claim 7 comprising storing an earmark in each one of a plurality of flash memory cells of said multiplicity of flash memory cells for subsequent special-treatment by programming each one of the plurality of flash memory cell to store the dummy physical level.

13. A flash memory utilization method comprising: writing first logical data from temporary memory into flash memory cells having at least two levels, thereby to generate a physical representation of the first logical data including known errors;reading said physical representation from the cells, thereby to generate, and store in said temporary memory, second logical data which if read immediately is identical to said first logical data other than said known errors; andcontrolling, by a controlling apparatus, said writing apparatus and said reading apparatus, wherein the controlling comprises: identifying said known errors by comparing said first logical data to second logical data read immediately after said physical representation is generated, storing information characterizing said known errors;wherein said information enables addresses of said known errors to be reconstructed when said second logical data is next read;wherein said information comprises a total number of known errors to be identified by the controlling apparatus and a serial number of a set comprising the addresses of the known errors, within a sequence out of multiple sequences, the sequence having a predetermined order of all possible sets of the addresses of the known errors given the total number of known errors; wherein different sequences of the multiple sequences are associated with different numbers of known addresses; andusing said information, when said second logical data is next read, to correct said known errors.

14. A non-transitory machine readable memory that stores instructions for: writing logical data from temporary memory into individual flash memory cells from among a multiplicity of flash memory cells, thereby to generate a physical representation of the logical data including a plurality of physical levels at least some of which represent, to reading apparatus, at least one bit-worth of said logical data; andearmarking a certain flash memory cell of said multiplicity of flash memory cells for subsequent treatment by programming the certain flash memory cells to store a dummy physical level, said dummy physical level differs from any physical level used for representing one or more logical data bits in the certain flash memory cells.

15. The non-transitory machine readable memory according to claim 14 wherein each one of the multiplicity of flash memory is programmable to a plurality (2 by the power of n) of physical levels that represent logical values of n logical data bits and to the dummy physical level, n being a positive integer.

16. The non-transitory machine readable memory according to claim 14 wherein the dummy physical level is an erasure physical value.

17. The non-transitory machine readable memory according to claim 14 wherein the subsequent special treatment comprises error correction.

18. The non-transitory machine readable memory according to claim 14 that stores instructions for reading a flash memory cell that is programmed to store the dummy physical level to provide a dummy value; detecting the dummy value, applying an error correction process to provide a correct value and replacing the dummy value with the correct value.

19. The non-transitory machine readable memory according to claim 14 that stores instructions for storing an earmark in each one of a plurality of flash memory cells of said multiplicity of flash memory cells for subsequent special-treatment by programming each one of the plurality of flash memory cell to store the dummy physical level.

20. A non-transitory machine readable memory that stores instructions for: writing first logical data from temporary memory into flash memory cells having at least two levels, thereby to generate a physical representation of the first logical data including known errors;reading said physical representation from the cells, thereby to generate, and store in said temporary memory, second logical data which if read immediately is identical to said first logical data other than said known errors; andcontrolling said writing apparatus and said reading apparatus, wherein the controlling comprises: identifying said known errors by comparing said first logical data to second logical data read immediately after said physical representation is generated, storing information characterizing said known errors; wherein said information enables addresses of said known errors to be reconstructed when said second logical data is next read; wherein said information comprises a total number of known errors to be identified by a controlling apparatus and a serial number of a set comprising the addresses of the known errors, within a sequence out of multiple sequences, the sequence having a predetermined order of all possible sets of the addresses of the known errors given the total number of known errors; wherein different sequences of the multiple sequences are associated with different numbers of known addresses; andusing said information, when said second logical data is next read, to correct said known errors.