In one embodiment, a tape drive includes a magnetic head having a plurality of read sensors, each read sensor being configured to read data simultaneously. The tape drive also includes a controller and logic integrated with and/or executable by the controller. The logic is configured to receive encoded data read from a plurality of tracks of a magnetic tape medium simultaneously. The logic is also configured to perform priority-based decoding on the encoded data based on erasure coefficients associated with at least one codeword of the encoded data. In another embodiment, a controller-implemented method includes receiving encoded data read from a plurality of tracks of a magnetic tape medium simultaneously and performing priority-based decoding on the encoded data based on erasure coefficients associated with at least one codeword of the encoded data.

BACKGROUND

The present invention relates to tape storage systems, and more specifically, to error-and-erasure decoding based on priority.

Currently-used linear tape drives apply product codes for error-correction coding (ECC). These product codes contain two Reed-Solomon component codes consisting of a C1 row code and a C2 column code. Failure to decode a product codeword, which requires successful decoding of all C1 rows and all C2 columns within a product code, leads to a temporary and/or permanent error. These temporary or permanent errors are a significant problem when attempting to store data to tape.

Typically, current tape drives implement ECC with two modes of operation: 1) Error-only decoding (decoding in which no information about uncorrectable C1 codewords is passed to the C2 decoder); and 2) Erasure-decoding (decoding in which information about C1 uncorrectable codewords are passed from the C1 decoder to the C2 decoder).

The second mode, erasure-decoding, is beneficial in the case where C1 uncorrectable codewords having a large number of byte errors are used as erasure pointers for C2 decoding. Conversely, the second mode likely leads to performance degradation in the case where C1 uncorrectables with only a small number of errors (only slightly beyond the error correction capability of the C1 decoder) are used as erasure pointers for C2 decoding. Therefore, it is not always beneficial to utilize erasure-decoding when implementing ECC in tape drives.

SUMMARY

In one embodiment, a tape drive includes a magnetic head having a plurality of read sensors, each read sensor being configured to read data simultaneously. The tape drive also includes a controller and logic integrated with and/or executable by the controller. The logic is configured to receive encoded data read from a plurality of tracks of a magnetic tape medium simultaneously. The logic is also configured to perform priority-based decoding on the encoded data based on erasure coefficients associated with at least one codeword of the encoded data.

In another embodiment, a controller-implemented method includes receiving encoded data read from a plurality of tracks of a magnetic tape medium simultaneously and performing priority-based decoding on the encoded data based on erasure coefficients associated with at least one codeword of the encoded data.

In yet another embodiment, a computer program product includes a computer readable storage medium having program instructions embodied therewith. The embodied program instructions are executable by a controller to cause the controller to receive, by the controller, encoded data read from a plurality of tracks of a magnetic tape medium simultaneously. The embodied program instructions are also executable by the controller to cause the controller to perform, by the controller, priority-based decoding on the encoded data based on erasure coefficients associated with at least one codeword of the encoded data.

DETAILED DESCRIPTION

It must also be noted that, as used in the specification and the appended claims, the singular forms “a,” “an” and “the” include plural referents unless otherwise specified. It will be further understood that the terms “comprises” and/or “comprising,” when used in this specification, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof. The term “about” as used herein indicates the value preceded by the term “about,” along with any values reasonably close to the value preceded by the term “about,” as would be understood by one of skill in the art. When not indicated otherwise, the term “about” denotes the value preceded by the term “about”±10% of the value. For example, “about 10” indicates all values from and including 9.0 to 11.0.

The following description discloses several preferred embodiments of systems, methods, and computer program products for a priority-based decoding scheme that utilizes track-dependent erasure coefficients for erasure pointers in C2 decoding. The coefficients represent a likelihood that the corresponding C1 bytes are treated as erasures in C2 decoding.

The erasure coefficients in a C1 codeword are independent of one another, and therefore may all be different. For example, in the case of a time-varying signal-to-noise ratio (SNR) over the course of a C1 codeword, the erasure coefficients may be determined from the SNR which may significantly vary over the C1 codeword as written on tracks of the magnetic tape. The erasure coefficient for a particular byte may also be determined from a single run-length limited (RLL) decoding failure. Again, in this case, e.g., in response to a rate 16/17 RLL code being used, a RLL decoding failure indicates that one or two bytes at the RLL decoder are in error. This results in a high erasure coefficient for these two bytes at the output of the RLL decoder.

These erasure pointers and track-dependent erasure coefficients, in one embodiment, are used by a priority-based C2 decoder to perform error-and-erasure decoding that depends on all the erasure pointers in a C2 codeword. This scheme adapts to the channel as observed by the C2 decoder, in order to improve decoding performance. The C2 decoding algorithm is adapted to the number and type of erasure pointers in a C2 codeword and thereby provides improved error rate performance in the presence of both random errors and temporary/permanent burst errors on tape tracks at the expense of a moderate increase in implementation complexity.

In one general embodiment, a tape drive includes a magnetic head having a plurality of read sensors, each read sensor being configured to read data simultaneously. The tape drive also includes a controller and logic integrated with and/or executable by the controller. The logic is configured to receive encoded data read from a plurality of tracks of a magnetic tape medium simultaneously. The logic is also configured to perform priority-based decoding on the encoded data based on erasure coefficients associated with at least one codeword of the encoded data.

In another general embodiment, a controller-implemented method includes receiving encoded data read from a plurality of tracks of a magnetic tape medium simultaneously and performing priority-based decoding on the encoded data based on erasure coefficients associated with at least one codeword of the encoded data.

In yet another general embodiment, a computer program product includes a computer readable storage medium having program instructions embodied therewith. The embodied program instructions are executable by a controller to cause the controller to receive, by the controller, encoded data read from a plurality of tracks of a magnetic tape medium simultaneously. The embodied program instructions are also executable by the controller to cause the controller to perform, by the controller, priority-based decoding on the encoded data based on erasure coefficients associated with at least one codeword of the encoded data.

Referring now toFIG. 1, a schematic of a network storage system10is shown according to one embodiment. This network storage system10is only one example of a suitable storage system and is not intended to suggest any limitation as to the scope of use or functionality of embodiments of the invention described herein. Regardless, network storage system10is capable of being implemented and/or performing any of the functionality set forth hereinabove.

FIG. 2Aillustrates a simplified tape drive100of a tape-based data storage system, which may be employed in the context of the present invention. While one specific implementation of a tape drive is shown inFIG. 2A, it should be noted that the embodiments described herein may be implemented in the context of any type of tape drive system.

As shown, a tape supply cartridge120and a take-up reel121are provided to support a tape122. One or more of the reels may form part of a removable cartridge and are not necessarily part of the tape drive100. The tape drive, such as that illustrated inFIG. 2A, may further include drive motor(s) to drive the tape supply cartridge120and the take-up reel121to move the tape122over a tape head126of any type. Such head may include an array of readers, writers, or both.

Guides125guide the tape122across the tape head126. Such tape head126is in turn coupled to a controller128via a cable130. The controller128, may be or include a processor and/or any logic for controlling any subsystem of the tape drive100. For example, the controller128typically controls head functions such as servo following, data writing, data reading, etc. The controller128may include at least one servo channel and at least one data channel, each of which include data flow processing logic configured to process and/or store information to be written to and/or read from the tape122. The controller128may operate under logic known in the art, as well as any logic disclosed herein, and thus may be considered as a processor for any of the descriptions of tape drives included herein, in various embodiments. The controller128may be coupled to a memory136of any known type, which may store instructions executable by the controller128. Moreover, the controller128may be configured and/or programmable to perform or control some or all of the methodology presented herein. Thus, the controller128may be considered to be configured to perform various operations by way of logic programmed into one or more chips, modules, and/or blocks; software, firmware, and/or other instructions being available to one or more processors; etc., and combinations thereof.

The cable130may include read/write circuits to transmit data to the head126to be recorded on the tape122and to receive data read by the head126from the tape122. An actuator132controls position of the head126relative to the tape122.

An interface134may also be provided for communication between the tape drive100and a host (internal or external) to send and receive the data and for controlling the operation of the tape drive100and communicating the status of the tape drive100to the host, all as will be understood by those of skill in the art.

FIG. 2Billustrates an exemplary tape cartridge150according to one embodiment. Such tape cartridge150may be used with a system such as that shown inFIG. 2A. As shown, the tape cartridge150includes a housing152, a tape122in the housing152, and a nonvolatile memory156coupled to the housing152. In some approaches, the nonvolatile memory156may be embedded inside the housing152, as shown inFIG. 2B. In more approaches, the nonvolatile memory156may be attached to the inside or outside of the housing152without modification of the housing152. For example, the nonvolatile memory may be embedded in a self-adhesive label154. In one preferred embodiment, the nonvolatile memory156may be a Flash memory device, ROM device, etc., embedded into or coupled to the inside or outside of the tape cartridge150. The nonvolatile memory is accessible by the tape drive and the tape operating software (the driver software), and/or other device.

FIG. 3shows, in detailed form, a conceptual data flow300in a tape drive with K simultaneously written tracks via K write channels. The data flow300includes passing host data through a cyclic redundancy check (CRC) error detection encoder302, a compression module304, an optional encryption module306, an error correction code (ECC) encoder308(which includes a C1 encoder and a C2 encoder, arranged as C1/C2, or C2/C1), and a tape layout module310, according to one embodiment. The header insertion module312may be positioned as shown, feeding into the tape layout module310, or may be positioned feeding into the ECC encoder308, thereby allowing the headers to receive some amount of ECC encoding, in one embodiment. The tape layout module310splits the data into individual feeds for each channel 1, . . . , K to write to the tracks of the tape medium. The data flow300also includes scrambling the data (data randomization)314, . . . ,316, modulation encoding318, . . . ,320, synchronization insertion326, . . . ,328, and multiplexing322, . . . ,324for each simultaneously written track 1, . . . , K.

In the following descriptions, most of these operations are not shown, in order to simplify descriptions. However, any of the descriptions herein may include additional operations not depicted, as would be understood by one of ordinary skill in the art upon reading the present descriptions. The number of tracks that may be written simultaneously depends on the tape drive being used, with the value of K ranging from 1 to 64 or more.

FIG. 4shows a logical data array400that may be used to organize data in a sub data set (SDS), according to one embodiment. As shown, the data array includes a plurality of rows402and columns404. Each row402in the data array400is a codeword interleave (CWI) that includes a plurality of C1 codewords. When the CWI includes four interleaved codewords, it is referred to as a CWI-4. The data in the SDS is protected by C1 encoding across each row402to produce C1 row parity (not shown as it is modified later to produce the data array400), and by C2 encoding across each column404to produce C2 column parity408.

As shown, the headers406for each row402may be encoded using a C1 encoding scheme by modifying the C1 parity (computed for the data in the row402only) to account for the headers406to produce C1′ parity410. In this embodiment, the headers406are protected by one-level ECC (C1′ parity410only), whereas the data is protected by two-level ECC (C1′ parity410and C2 parity408).

Each data set includes multiple sub data sets and each sub data set may be represented by a logical two-dimensional array. Usually hundreds of headers are assigned to a single data set because each data set includes multiple SDSs and each row (CWI) of a column-encoded SDS is assigned a header.

Currently-used linear tape drives simultaneously write and read up to 32 tracks to and/or from a magnetic tape medium. C1 row codewords of a product code are written in a byte-interleaved fashion onto individual tracks of the magnetic tape medium. Due to differences in performance of the individual transducers writing and reading the parallel tracks of the magnetic tape medium, the raw error-rate of individual tracks may vary significantly from track to track, and across time for each individual track.

In order to address this variability of the raw error-rate of individual tracks, a track-dependent decoding scheme may be used, according to one embodiment that is configured to adapt to the time-varying signal quality of all tracks read simultaneously from the magnetic tape medium.

In a further embodiment, erasure pointers (that signal that a C1 codeword should be erased, instead of relying on the decoded bytes therein during C2 decoding) are generated in a manner that accounts for the track signal quality. In one approach, erasure pointers for C2 decoding are enabled if, and only if, C1 codewords include a large number of byte errors with a relatively high probability. Each erasure pointer may have a coefficient associated therewith, the coefficient indicating a belief/likelihood/probability that the C2 decoder should treat the corresponding C1 bytes as erasures, and not rely on the decoded information therein.

Now referring toFIG. 5, a system500configured for priority-based decoding is shown according to one embodiment. As shown, the system500includes, for each of K tracks (Track 0, Track 1, . . . , Track K−1), read channel architecture508, a RLL decoder506(or some other suitable decoder of a type known in the art), a C1 decoder504, and track-dependent erasure coefficient logic502. These various components may be included in each track, or some or all of the various components may be centralized and implemented for each track from a central implementation thereof.

The track-dependent erasure coefficient logic502may use side information about the reliability of detected bytes within C1 codewords of each track to determine the probability that a C1 codeword has a number of byte errors that exceeds a predetermined threshold. In this embodiment, erasure pointers for C2 decoding are utilized if and only if there is a high probability that one or more C1 codewords in a specific track contain a large number of byte errors. By a large number of byte errors, what is meant is that the number of byte errors exceeds the amount of correctable byte errors within a single C1 codeword. The probability of an amount by which the number of byte errors within a single C1 codeword exceeds the maximum number of correctable byte errors is indicated with erasure coefficients wi, e.g., w0, w1, w2, for each erasure pointer. This decision as to what the likelihood or probability of the amount by which the number of byte errors within a single C1 codeword exceeds the maximum number of correctable byte errors may be based on side information. This side information provides insight into the reliability of the detected bytes within the C1 codewords for each track, Track 0 to Track K−1.

Each erasure coefficient is associated with an erasure flag for C2 decoding indicated by the C1 decoder, with the erasure coefficient, wi, being in a range from 0 to 1, e.g., (0≦wi≦1). The erasure coefficient may correlate with the number of byte errors within a C1 codeword, thus representing a belief/likelihood/probability that the C2 decoder should treat the corresponding C1 bytes as erasures, and not rely on the decoded information therein.

Each erasure coefficient may be selected such that it correlates with the number of byte errors within a C1 codeword. This is, for example, the case when the side information about erasure coefficients is obtained from the number of RLL decoding failures within a C1 codeword. A high number of RLL decoding failures within a C1 codeword indicates a high number of actual byte errors within a C1 codeword. In this case all erasure coefficients in a C1 codeword may have the same value and they are approximately proportional to the number of byte errors in a C1 codeword. However, erasure coefficients may also be obtained in other ways, such as from SNR, mean squared error (MSE) measurements, a single RLL decoding failure, etc., in which case the erasure coefficients of each byte in a C1 codeword may be different and reflect the probability that a particular byte may be in error.

The computation of the erasure coefficients in the track-dependent erasure coefficient logic502may utilize side information about the reliability of detected bytes within C1 codewords of each track. Any potential source of side information may be used, such as statistics of channel/track performance that may be monitored by the firmware514, e.g., calibration data, runtime statistics, etc.; C1 decoder504statistics, e.g., a number of C1 uncorrectable codewords after C1 decoding; read channel508metrics, e.g., MSE, SNR, etc.; RLL decoder506metrics, e.g., a number of error detection flag(s), etc. Of course, other sources of side information may be used as would be apparent to one of skill in the art upon reading the present descriptions.

In one embodiment, the erasure coefficients may be used in a determination to enable erasure decoding on a per decoded C1 codeword basis. Any erased C1 row codeword bytes may then be used as erasures during C2 error-and-erasure column codeword decoding. Once the erasure coefficients, wi, of all bytes in a decoded C1 row codeword are computed and/or estimated, there will be N1 erasure coefficients in the C1 row codeword, one for each byte in the codeword.

These erasure coefficients may be summed over all N1 decoded bytes of the C1 codeword (note: a C1 codeword has N1 bytes) to obtain the sum S, where S=Σ1N1wi. In response to a determination that this sum S is greater than a predetermined configurable threshold, all the N1 bytes of the C1 codeword may be erased (e.g., the erase pointer is enabled for the decoded C1 codeword which is then used to erase a row of decoded C1 bytes during C2 error-and-erasure column decoding).

The predetermined configurable threshold may have any positive value, such as 0.1, 0.2, 0.25, 0.5, 0.6, 0.75, 1.0, 2.0, 5.0, 10.0, etc., determined based on a desired amount of errors in a codeword that causes an erasure pointer to be set and a value of a typical erasure coefficient wi.

In one embodiment, K=32, e.g., there may be 32 tracks in the system500. In some other embodiments, K may equal 16, 64, or some other positive integer.

After the erasure pointers are either enabled and set, or disabled and not used, the C1 codewords, or the erasure-enabled C1 codewords (with at least one C1 codeword having an erasure pointer enabled) are passed to a de-interleaver/buffer510to revert the interleaving of the data in the encoded data and to store the data prior to passing the data to the C2 decoder512for C2 decoding thereof. The C2 decoding may be error-only decoding (in response to the erasure pointers not being enabled) or error-and-erasure decoding (in response to the erasure pointers being enabled, as shown inFIG. 5by the darkened rows of the array in the C2 decoder512).

In one embodiment, the track-dependent erasure coefficient logic502may be in communication with firmware514of a tape drive, a tape library, or some other suitable system capable of directing the track-dependent erasure coefficient logic502before/during/after erasure enabling procedures.

Track-dependent erasure coefficient logic502is configured to compute erasure coefficients, wi, with (0.0≦wi≦1.0) for each individual erasure pointer for C2 decoding. The erasure coefficients, wi, may correlate with the number of byte errors within C1 codewords, thus representing a probability and/or belief and/or likelihood that the C2 decoder512should treat the corresponding C1 bytes as erasures. In this approach, each erasure coefficient, reflects a probability that a particular byte in a C1 codeword is in error.

Therefore, these coefficients may be used to determine a priority for C2 decoding performing an error-and-erasure decoding algorithm that depends on all the erasure pointers and erasure coefficients that are placed in a C2 codeword.

In one embodiment, the track-dependent erasure coefficient logic502is configured to create an erasure coefficient list, W, that includes the individual erasure coefficients, wi, associated with all symbols in a C1 codeword (and therefore in all C2 codewords).

The C1 decoder504and C2 decoder512are each configured to utilize either a RS(N,K) code with minimum Hamming distance dmin=N−K+1 or a block code with minimum Hamming distance dmin. For example, the code may be the C2 column code in a product code.

An erasure coefficient list, W, may be constructed according to one embodiment by the track-dependent erasure coefficient logic502. The erasure coefficient list, W, includes N coefficients that are arranged in a monotonically increasing arrangement, e.g., W={w1, w2, w3, . . . , wN}, where 0.0≦wi≦1.0 and wi≦wi+1. In a further approach, the coefficients wimay be q-level quantized, but this is not necessary in all embodiments.

In the erasure coefficient list, W, according to one embodiment, an erasure coefficient of zero, e.g., wi=0, corresponds to a case where no erasure pointer is being raised, e.g., a corresponding symbol is obtained from successful C1 decoding in a previous decoding step. A second erasure coefficient list W′ is obtained from the initial erasure coefficient list, W, by removing all erasure coefficients having a value of zero, e.g., removing all wi=0. In response to there being several coefficients in the second erasure coefficient list W′ that are equal to max {W′}, one coefficient may be picked arbitrarily such that wi=max {W′}, and the processing may continue in the loop until the number of erasures per codeword, E, is equal to an adaptive limit to a number of erased symbols, L, e.g., |E|=L, or |W′|=0.

In one embodiment, an erasure coefficient having a value of 1, e.g., wi=1, corresponds to a case where an erasure pointer is being raised without an associated symbol, and therefore must be erased in subsequent decoding, as no byte value is available with which to base decoding on.

A third erasure coefficient list W″={wj, wj+1, wj+2, . . . , wm} is obtained from the erasure list W by excluding all the coefficients that are zero or one where 1≦j and m≦N.

The priority-based decoding logic516of the C2 decoder512is configured to determine whether error-and-erasure decoding is to be used during C2 decoding of the codewords provided to the C2 decoder from the de-interleaver/buffer510. This determination may be based on several factors, including, but not limited to, the erasure coefficient list W, the number of symbols to erase, L, the minimum Hamming distance dmin, the number of symbols in a codeword, N, and the minimum margin, M, reserved for correcting at least floor(M/2) symbols, as described in more detail later.

According to one embodiment, a tape drive may include a magnetic head having a plurality of read sensors. Each read sensor is configured to read data simultaneously from one track of a magnetic tape medium, thereby allowing a plurality of tracks to be read simultaneously from the magnetic tape medium, the number capable of being read simultaneously being equal to the number of read sensors of the magnetic head. Of course, some read sensors may be configured to read servo tracks for head alignment, and/or for other purposes, but for the sake of these descriptions, it is assumed that the read sensors are each capable of reading data from the magnetic tape medium.

The tape drive also includes a hardware processor and logic integrated with and/or executable by the hardware processor. The hardware processor may be a hardware processing unit and/or circuit, such as a central processing unit (CPU), an application specific integrated circuit (ASIC), a field programmable gate array (FPGA), etc., combinations thereof, or any other suitable computing device known in the art. The logic may be implemented in software, hardware, or some combination thereof. The logic is configured to read, using the plurality of read sensors, encoded data from a plurality of tracks of the magnetic tape medium simultaneously. The number of tracks that may be read simultaneously is determined by the number of read sensors of the magnetic head. The logic is also configured to perform track-dependent erasure decoding on the encoded data based on detection of one or more time-varying signal quality issues associated with at least one of the plurality of tracks read simultaneously from the magnetic tape medium, with priority-based decoding based on coefficients assigned to each erasure pointer.

Now referring toFIG. 6, an erasure coefficient list W600is shown in which the coefficients, wi, for each symbol in a codeword have been arranged according to their respective coefficient values, with coefficients of zero (indicating the associated symbol is not to be erased) on the left side, and coefficients of one (indicating the associated symbol is to be erased) on the right side, e.g., a monotonically increasing arrangement. Because each coefficient is associated with one symbol in the codeword, it may be assumed that these symbols are logically arranged along with the coefficients.

Using the erasure coefficient list W600, the adaptive number of erased symbols, L, may be calculated based on the minimum Hamming distance, dmin, the length of the codeword, N, and the minimum margin, M, reserved for correcting at least floor(M/2) symbols.

Referring again toFIG. 6, according to one embodiment, the number of erased symbols, L, may be computed according to the following equation, L=D+H=D+floor((F−D)B/(A+B)), which may be notated as L=f(dmin,M,N,W).

The maximum number of erased symbols, F, is equal to dmin−1−M, and the term D is defined as D=min{F, N−m} where D is the total number of symbols in a C1 codeword that have erasure coefficient 1. We assumed that D is less than or equal to F. If D>F, then the decoder either declares decoding failure or attempts to correct F or more erased bytes by accepting the risk of higher probability of miscorrection. The maximum number of erased bytes that can be corrected is F+M=dmin−1. Furthermore, the sum of the terms A+B is the sum of the coefficients in the third erasure coefficient list W″ where the value of the coefficients are between 0 and 1, e.g., 0<wi<1, with A+B=Σi=jmwi, with B being the sum of the coefficients in the area defined by F where the value of the coefficients are not equal to 1, e.g., wi≠1, where B=Σi=N−F+1N−Dwi. The number of erased symbols, L, is adaptive, i.e., it depends on channel conditions, e.g., the erasure coefficients wi, among other variables.

Now referring toFIG. 7, a method700is shown according to one embodiment. The method700may be performed in accordance with the present invention in any of the environments depicted inFIGS. 1-6, among others, in various embodiments. Of course, more or less operations than those specifically described inFIG. 7may be included in method700, as would be understood by one of skill in the art upon reading the present descriptions.

In method700, W is the erasure list comprising the erasure coefficients corresponding to all symbols in a C2 codeword generated by track-dependent erasure coefficient logic, with a C2 code being a (N,K) RS code, |W|=N, W′ is the second erasure list having of all nonzero coefficients from W, |W′|=number of coefficients in W′, E is the erasure list of symbols to erase, |E|=number of entries in E, and M is the minimum margin reserved for correcting at least floor(M/2) symbols.

As shown inFIG. 7, method700may initiate with operation702, where an erasure coefficient list, W, is created for a codeword. The erasure coefficient list includes all erasure coefficients for each decoded symbol in the codeword, each erasure coefficient being a measure of the reliability of the associated decoded symbol of the codeword. Also, the erasure list, E, is set to empty. This erasure list will be populated during the method700.

In operation704, a second erasure coefficient list, W′, is created based on the erasure coefficient list, W. The second erasure coefficient list is equal to all erasure coefficients from the erasure coefficient list less any erasure coefficients equal to zero, e.g., W′=W\{wi|wi=0}.

In operation706, a number of symbols of the codeword to erase, L, is computed based on minimum Hamming distance, dmin, a length of the codeword, N, a minimum margin, M, reserved for correcting at least floor(M/2) symbols of the codeword, and the erasure coefficient list (W), where L=f(dmin,M,N,W).

In one embodiment, L=D+H=D+floor((F−D) B/(A+B)). The maximum number of erased symbols, F, is equal to dmin−1−M, and the term D is defined as D=min{F, N−m} where D is the total number of symbols in a C1 codeword that have erasure coefficient 1. We assumed that D is less than or equal to F. If D>F, then the decoder either declares decoding failure or attempts to correct F or more erased bytes by accepting the risk of higher probability of miscorrection. The maximum number of erased bytes that may be corrected is F+M=dmin−1. Furthermore, the sum of the terms A+B is the sum of the coefficients in the third erasure coefficient list W″ where the value of the coefficients are between 0 and 1, e.g., 0<wi<1, with A+B=Σi=jmwi, with B being the sum of the coefficients in the area defined by F where the value of the coefficients are not equal to 1, e.g., wi≠1, where B=Σi=N−F+1N−Dwi.

In operation708, it is determined whether the number of erasure coefficients (and therefore a number of associated symbols) in the second erasure coefficient list is greater than zero, e.g., |W′|>0. In response to a determination that the number of erasure coefficients in the second erasure coefficient list is greater than zero, method700continues to operation710; otherwise, method700jumps to operation718.

In operation710, an erasure coefficient having a maximum value is selected, e.g., wi=max {W′}. In operation712, the second erasure coefficient list has this erasure coefficient wiremoved therefrom, e.g., W′=W′\{wi}. Then, in operation714, the symbol corresponding to this erasure coefficient wi, is added to the erasure list E, e.g., E=E∪{wi}.

In operation716, it is determined whether the number of symbols in the erasure list E is equal to the number of symbols to erase L. In response to a determination that the number of symbols in the erasure list E is equal to the number of symbols to erase L, method700continues to operation718; otherwise, method700returns to operation708so that more symbols may be added to the erasure list E.

In operation718, C2 decoding is performed on the codeword using erasure pointers associated with erasure coefficients from the erasure list E, such that the symbols corresponding to the entries in the erasure list E are erased during C2 error-and-erasure decoding.

According to method700, a predetermined number of symbols may be added to the erasure list, E, and sent for C2 error-and-erasure decoding using the erasure pointers provided by the C1 decoder. The symbols selected will all be associated with the highest erasure coefficients, and therefore are the most probable candidates to be erased in C2 decoding, as the confidence in the decoded symbol is lowest for these symbols.

Now referring toFIG. 8, a method800is shown according to one embodiment. The method800may be performed in accordance with the present invention in any of the environments depicted inFIGS. 1-6, among others, in various embodiments. Of course, more or less operations than those specifically described inFIG. 8may be included in method800, as would be understood by one of skill in the art upon reading the present descriptions.

In method800, W is the erasure list comprising the erasure coefficients corresponding to all symbols in a C2 codeword generated by track-dependent erasure coefficient logic, with a C2 code being a (N,K) RS code, |W|=N, E is the erasure list of symbols to erase, |E|=number of entries in E, M is the minimum margin reserved for correcting at least floor(M/2) symbols, and the erasure coefficients are three-level quantized such that wiε{0, g1, 1}. In this embodiment, the list of all coefficients W is partitioned into three mutually exclusive sets: P0, P1 and P2, where W=P0∪P1∪P2.

According to one embodiment, P0 is the set of all erasure coefficients wihaving an erasure coefficient of zero indicating no erasure flag being raised by the C1 decoder (C1 decoding success), e.g., P0={wiεW|wi=0}, P1 is the set of all erasure coefficients wi, that correspond to a case where the C1 decoder has raised an erasure flag (a C1 decoding failure), e.g., {wiεW|wi=g1}, and P2 is the set of all erasure coefficients wihaving an erasure coefficient of one indicating either an erasure flag is raised by the RLL decoder or no decoded C1 codeword is provided by the C1 decoder, e.g., P2={wiεW|wi=1}.

As shown inFIG. 8, method800may initiate with operation802, where an erasure coefficient list, W, is created having the erasure coefficients for all decoded symbols of a codeword. Also, the erasure list, E, is set to empty. This erasure list will be populated during the method800.

In operation804, a number of symbols of the codeword to erase, L, is computed based on minimum Hamming distance, dmin, a length of the codeword, N, a minimum margin, M, reserved for correcting at least floor(M/2) symbols of the codeword, and the erasure coefficient list (W), where L=f(dmin,M,N,W).

In one embodiment, L=D+H=D+floor((F−D) B/(A+B)). The maximum number of erased symbols, F, is equal to dmin−1−M, and the term D is defined as D=min{F, N−m} where D is the total number of symbols in a C1 codeword that have erasure coefficient 1. We assumed that D is less than or equal to F. If D>F, then the decoder either declares decoding failure or attempts to correct F or more erased bytes by accepting the risk of higher probability of miscorrection. The maximum number of erased bytes that may be corrected is F+M=dmin−1. Furthermore, the sum of the terms A+B is the sum of the coefficients in the third erasure coefficient list W″ where the value of the coefficients are between 0 and 1, e.g., 0<wi<1, with A+B=Σi=jmwi, with B being the sum of the coefficients in the area defined by F where the value of the coefficients are not equal to 1, e.g., wi≠1, where B=Σi=N−F+1N−Dwi.

In operation806, P1 and P2 are computed, where P1 includes all erasure coefficients (and associated symbols) that correspond to a situation where the C1 decoder has raised an erasure flag (a C1 decoding failure), e.g., {wiεW|wi=g1}. Also, P2 includes the set of all erasure coefficients wihaving an erasure coefficient of one indicating either an erasure flag is raised by the RLL decoder or no decoded C1 codeword is provided by the C1 decoder, e.g., P2={wiεW|wi=1}.

In operation808, it is determined whether the number of symbols in P2 is greater than the number of symbols to erase L. In response to a determination that the number of symbols in P2 is greater than the number of symbols to erase L, method800jumps to operation816; otherwise, method800continues to operation810.

In operation810, it is determined whether the sum of the number of symbols in P1 and P2 is greater than the number of symbols to erase L. In response to a determination that the sum of the number of symbols in P1 and P2 is greater than the number of symbols to erase L, method800jumps to operation814; otherwise, method800continues to operation812.

In operation812, the erasure list E is set to be the union of P1 and P2.

In operation814, the erasure list E is set to be P2.

In operation816, C2 decoding is performed on the codeword using erasure pointers associated with erasure coefficients from the erasure list E, such that the symbols corresponding to the entries in the erasure list E are erased during C2 error-and-erasure decoding.

In an alternate embodiment of method800, exactly L symbols may be erased, the L symbols having the highest corresponding erasure coefficients in the erasure coefficient list W.

Now referring toFIG. 9, a method900is shown according to one embodiment. The method900may be performed in accordance with the present invention in any of the environments depicted inFIGS. 1-6, among others, in various embodiments. Of course, more or less operations than those specifically described inFIG. 9may be included in method900, as would be understood by one of skill in the art upon reading the present descriptions.

In method900, W is the erasure list comprising the erasure coefficients corresponding to all symbols in a C2 codeword generated by track-dependent erasure coefficient logic, with a C2 code being a (N,K) RS code, |W|=N, E is the erasure list of symbols to erase, |E|=number of entries in E, M is the minimum margin reserved for correcting at least floor(M/2) symbols, and the erasure coefficients are four-level quantized such that wiε{0, g1, g2, 1}. In this embodiment, the list of all coefficients W is partitioned into four mutually exclusive sets: P0, P1 P2, and P3 where W=P0 ∪P1 ∪P2 ∪P3.

According to one embodiment, P0 is the set of all erasure coefficients wihaving an erasure coefficient of zero indicating no erasure flag being raised by the C1 decoder (C1 decoding success), e.g., P0={wiεW|wi=0}, P1 is the set of all erasure coefficients withat correspond to a case where the C1 decoder has raised an erasure flag (a C1 decoding failure), e.g., {wiεW|wi=g1}, P2 is the set of all erasure coefficients withat correspond to a case where the RLL decoder has raised an erasure flag (a RLL decoding failure), e.g., {wiεW|wi=g2}, and P3 is the set of all erasure coefficients wihaving an erasure coefficient of one indicating no decoded C1 codeword is provided by the C1 decoder, e.g., P3={wiεW|wi=1}.

As shown inFIG. 9, method900may initiate with operation902, where an erasure coefficient list, W, is created having the erasure coefficients for all decoded symbols of a codeword. Also, the erasure list, E, is set to empty. This erasure list will be populated during the method900.

In operation904, a number of symbols of the codeword to erase, L, is computed based on minimum Hamming distance, dmin, a length of the codeword, N, a minimum margin, M, reserved for correcting at least floor(M/2) symbols of the codeword, and the erasure coefficient list (W), where L=f(dmin,M,N,W).

In one embodiment, L=D+H=D+floor((F−D) B/(A+B)). The maximum number of erased symbols, F, is equal to dmin−1−M, and the term D is defined as D=min{F, N−m} where D is the total number of symbols in a C1 codeword that have erasure coefficient 1. We assumed that D is less than or equal to F. If D>F, then the decoder either declares decoding failure or attempts to correct F or more erased bytes by accepting the risk of higher probability of miscorrection. The maximum number of erased bytes that may be corrected is F+M=dmin−1. Furthermore, the sum of the terms A+B is the sum of the coefficients in the third erasure coefficient list W″ where the value of the coefficients are between 0 and 1, e.g., 0<wi<1, with A+B=Σi=jmwi, with B being the sum of the coefficients in the area defined by F where the value of the coefficients are not equal to 1, e.g., wi≠1, where B=Σi=N−F+1N−Dwi.

In operation906, P1, P2, and P3 are computed, where P1 includes all erasure coefficients (and associated symbols) that correspond to a situation where the C1 decoder has raised an erasure flag (a C1 decoding failure), e.g., {wiεW|wi=g1}. Also, P2 includes the set of all erasure coefficients withat correspond to a case where the RLL decoder has raised an erasure flag (a RLL decoding failure), e.g., {wiεW|wi=g2}. Moreover, P3 includes the set of all erasure coefficients having an erasure coefficient of one indicating no decoded C1 codeword is provided by the C1 decoder, e.g., P3={wiεW|wi=1}.

In operation908, it is determined whether the sum of the number of symbols in P2 and P3 is greater than the number of symbols to erase L. In response to a determination that the sum of the number of symbols in P2 and P3 is greater than the number of symbols to erase L, method900jumps to operation916; otherwise, method900continues to operation910.

In operation910, it is determined whether the sum of the number of symbols in P1, P2, and P3 is greater than the number of symbols to erase L. In response to a determination that the sum of the number of symbols in P1, P2, and P3 is greater than the number of symbols to erase L, method900jumps to operation914; otherwise, method900continues to operation912.

In operation912, the erasure list E is set to be the union of P1, P2, and P3.

In operation914, the erasure list E is set to be the union of P2 and P3.

In operation916, the erasure list E is set to be P3.

In operation918, C2 decoding is performed on the codeword using erasure pointers associated with erasure coefficients from the erasure list E, such that the symbols corresponding to the entries in the erasure list E are erased during C2 error-and-erasure decoding.

In an alternate embodiment of method900, exactly L symbols may be erased, the L symbols having the highest corresponding erasure coefficients in the erasure coefficient list W.

Now referring toFIG. 10, a method1000is shown according to one embodiment. The method1000may be performed in accordance with the present invention in any of the environments depicted inFIGS. 1-6, among others, in various embodiments. Of course, more or less operations than those specifically described inFIG. 10may be included in method1000, as would be understood by one of skill in the art upon reading the present descriptions.

As shown inFIG. 10, method1000may initiate with operation1002, where encoded data read from a plurality of tracks of a magnetic tape medium simultaneously is received, such as by track-dependent erasure coefficient logic of a tape drive, or some other suitable component or device.

In operation1004, priority-based decoding is performed on the encoded data based on erasure coefficients associated with at least one codeword of the encoded data.

Any of the embodiments described previously, particularly inFIGS. 7-9may be used for performing the priority-based decoding. In on embodiment, performing the priority-based decoding may include calculating an erasure coefficient for each symbol in the at least one codeword, each erasure coefficient being a measure of a reliability of an associated decoded symbol in the at least one codeword, generating an erasure coefficient list comprising the erasure coefficients associated with each symbol of the at least one codeword, generating an erasure list comprising a subset of symbols from the at least one codeword based on the erasure coefficient list, and performing error-and-erasure C2 decoding using erasure pointers corresponding to the subset of symbols in the erasure list.

In this embodiment, the erasure list may include a predetermined number of symbols having erasure coefficients not lower than erasure coefficients of symbols not selected for the erasure list, where a lower erasure coefficient indicates smaller confidence that an associated symbol is to be erased.

In another embodiment, performing priority-based decoding may include computing the predetermined number of symbols in the erasure list as a function of minimum Hamming distance, a length of the at least one codeword, a minimum margin reserved for correcting an integer number of bytes at least half the minimum margin, and the erasure coefficient list.

In a further embodiment, any symbols having a corresponding erasure coefficient equal to zero may be excluded from the erasure list.

In another embodiment, the erasure coefficients in the erasure coefficient list may be quantized into at least three levels, e.g., P0, P1, P2, etc. In one embodiment, the at least three levels may include a first level (P0) having all erasure coefficients equal to zero, a second level (P1) having all erasure coefficients where an erasure flag is raised by a C1 decoder, and a third level (P2) having all erasure coefficients equal to one. In this embodiment, the erasure list includes symbols of the at least one codeword corresponding to erasure coefficients in the second and third levels in response to a determination that a number of symbols corresponding to erasure coefficients in the second and third levels does not exceed a predetermined number of symbols. Moreover, the erasure list includes symbols of the at least one codeword corresponding to erasure coefficients in the third level in response to a determination that a number of symbols corresponding to erasure coefficients in the second and third levels exceed the predetermined number of symbols.

According to another embodiment, the at least three levels may include a first level (P0) having all erasure coefficients equal to zero, a second level (P1) having all erasure coefficients where an erasure flag is raised by a C1 decoder, a third level (P2) having all erasure coefficients where an erasure flag is raised by a RLL decoder, and a fourth level (P3) having all erasure coefficients equal to one. In this embodiment, the erasure list includes symbols of the at least one codeword corresponding to erasure coefficients in the second, third, and fourth levels in response to a determination that a number of symbols corresponding to erasure coefficients in the second, third, and fourth levels does not exceed a predetermined number of symbols. Moreover, the erasure list includes symbols of the at least one codeword corresponding to erasure coefficients in the third and fourth levels in response to a determination that the number of symbols corresponding to erasure coefficients in the second, third, and fourth levels exceed the predetermined number of symbols and a number of symbols corresponding to erasure coefficients in the third and fourth levels does not exceed the predetermined number of symbols. Furthermore, the erasure list includes symbols of the at least one codeword corresponding to erasure coefficients in the fourth level in response to a determination that a number of symbols corresponding to erasure coefficients in the third and fourth levels exceed the predetermined number of symbols.