SIGNAL CODING

Technical Field

The present invention relates to methods for encoding and decoding signals. Processing data may include, but is not limited to, obtaining, deriving, outputting, receiving and reconstructing data.

Background

There is a need to create flexible solutions to signal encoding and decoding schemes, particularly in the field of video encoding and decoding. Also, it is important to provide the highest quality video output to viewers wherever possible, and to do so in a way that is backward compatible with existing technologies and decoder hardware.

It is an aim of this disclosure to provide a solution to one or more of these needs.

WO 2014/170819 Al describes computer processor hardware that parses a data stream into first portions of encoded data and second portions of encoded data. The computer processor hardware implements a first decoder to decode the first portions of encoded data into a first rendition of a signal and a second decoder to decode the second portions of encoded data into reconstruction data. The reconstruction data specifies how to modify the first rendition of the signal. The computer processor hardware and applies the reconstruction data to the first rendition of the signal to produce a second rendition of the signal.

Summary

There is provided a method, computer program, computer-readable medium, and encoder as set out in the appended claims.

Brief Description of Figures

Figure 1 is a schematic illustration showing an embodiment associated with the methods of encoding and decoding.

Figures 2 and 3 are flow charts showing methods of encoding. Detailed Description

In the present disclosure, a method of encoding and decoding is described. Figure 1 shows one embodiment associated with the methods of encoding and decoding.

In Figure 1, an input signal 100 is received by an encoding system. The encoding system consists of a down-sampler 105, a baseline encoder 110, a baseline decoder 115 and an enhancement encoder 125. The baseline encoder 110 and the baseline decoder 115 may be implemented in hardware (FtW) and the enhancement encoder 125 may be implemented using software (SW). The input signal 100 may be a video sequence, i.e. a sequence of frames where each frame comprises a two-dimensional array of signal elements such as pixels.

In Figure 1, the input signal 100 is received by both the down-sampler 105 and the enhancement encoder 125. The input signal 100 is initially down-sampled using the down- sampler 105. Here the term“down-sampling” is to be understood as used in the art of signal processing, e.g. reducing a resolution or dimensionality of the input signal 100. For a video sequence, this may comprise generating a version of an original frame of video that has a resolution in one or more directions that is less than the original frame. For example, down- sampling a 640 by 480 frame by a factor of 2 may generate a 320 by 240 frame. In another way, down-sampling may be seen as reducing a number of sample elements within the signal by a defined factor. Down-sampling may be performed for one or more dimensions of an n- dimensional signal.

Returning to Figure 1, the resulting down-sampled version of the input signal is fed to the baseline encoder 110. The baseline encoder 110 encodes the down-sampled version of the input signal to generate an encoded base data stream 120. This may be considered a first encoded signal. The encoded base data stream 120 is outputted from the baseline encoder 115. The encoded base data stream 120 may form a first portion of a bitstream, e.g. for transmission or communication to a decoder. The encoded base data stream 120 output from the baseline encoder is also fed to the baseline decoder 115 within the encoding system. The output of the baseline decoder 115 is then fed to the enhancement encoder 125. The baselines decoder 115 may be thought of as providing a signal output that simulates decoding by a decoding system. The enhancement encoder 125 receives the input signal 100 and the output of the baseline decoder 115. Optionally, the enhancement encoder 125 may receive the down-sampled version of the input signal. The enhancement encoder processes the various inputs to generate an encoded added data stream 130. The encoded added data stream 130 may be seen as an enhancement data stream. The encoded added data stream 130 may be output as a second portion of a bitstream. In certain cases, the first and second portions of a bitstream, i.e. the encoded base stream 120 and the encoded added data stream 130 may be combined into a single bit stream. In other cases, the first and second portions of a bitstream, i.e. the encoded base stream 120 and the encoded added data stream 130 may be transmitted as independent bit streams (e.g. two bit streams). In certain cases, the two portions of the bitstream (or to independent bit streams) may be identified using respective identifiers, e.g. the first portion may be identified using a first identifier and the second portion may be identified using a second identifier.

Figure 1 also shows a corresponding decoding system. The corresponding decoding system comprises a baseline decoder 135 and an enhancement decoder 140. As for the encoding system, the baselines decoder 135 may be implemented in hardware (HW) and the enhancement decoder 140 may be implemented in software (SW). At the decoding system, the encoded base data stream 120 is fed to the baseline decoder 135 which decodes said stream to generate a baseline decoded stream. The baseline decoded stream is fed to the enhancement decoder 140, which also receives the encoded added data stream 130. The enhancement decoder 140 processes the baseline decoded stream and the encoded added data stream 130 to generate a decoded data stream 145. This may comprise, for example, a decoded video sequence for display.

The baseline decoder 135 may be a version of, or identical to, the baseline decoder 115 within the encoding system. As such, the output of the baseline decoder 115 that is received by the enhancement encoder 125 may resemble the output of the baseline decoder 135 that is received by the enhancement decoder 140. The enhancement encoder 125 uses the output of the baseline decoder 115 to generate the encoded added data stream 130.

In one case, the baseline encoder 110 and/or the baseline decoder or decoders 115 and 135 are preferably implemented using hardware blocks, for example digital signal processing modules on a chipset. The enhancement encoder 125 and/or the enhancement decoder 140 are preferably implemented in software.

Figure 1 shows an example encoding system. Figure 2 shows a method of encoding a signal that may be enacted by this system. The signal may be a video signal. The method comprises encoding a version of the signal to produce a first encoded signal 210, decoding said first encoded signal to produce a first decoded signal 220, up-sampling said first decoded signal to obtain a first up-sampled decoded signal 230, obtaining a first residual signal by taking a difference between said first up-sampled decoded signal and a first reference signal 240, and encoding said first residual signal to produce a first encoded residual signal 250.

Figure 3 shows a variation of the method of Figure 2. The method of Figure 3 includes an initial down-sampling step. The method may be performed or controlled by the enhancement encoder 125 or the encoding system. The method of Figure 3 comprises down-sampling the signal to generate a version of the signal 310, instructing the encoding of said version of the signal to produce a first encoded signal 320, instructing the decoding of said first encoded signal to produce a first decoded signal 330, up-sampling said first decoded signal to obtain a first up-sampled decoded signal 340, obtaining a first residual signal by taking a difference between said first up-sampled decoded signal and a first reference signal 350, and encoding said first residual signal to produce a first encoded residual signal 360. In the method of Figure 3, the first reference signal corresponds to the signal prior to down-sampling. The version of the signal is obtained by down-sampling the signal prior to encoding it. The first reference signal corresponds to the signal prior to down-sampling it.

To be more explicit in relating the methods of Figures 2 and 3 to Figure 1, the signal down- sampled at step 310 comprises the input signal 100, the version of the signal produced at step 310 is the output of the down-sampler 105, the first encoded signal produced at step 210 or 320 is the encoded base data stream 120, the first up-sampled decoded signal is generated based on the output of the baseline decoder 115 that is received by the enhancement encoder 125, and the encoded first residual signal produced at step 250 or 360 is the encoded added data stream 130. The term“instructing” is used because the enhancement encoder 125 or another entity may instruct a digital chip that implements the baseline encoder 110 and the baseline decoder 115 to perform steps 210 and 220 of Figure 2. The enhancement encoder 125 may also control the upsampling of the output of the baseline decoder 115 and the generation of a residual signal, e.g. by subtracting the upsampled output of the baseline decoder 115 from the input signal 105.

In the embodiment of Figure 1, the first encoded signal (i.e. in the form of the encoded base data stream 120) may be seen to be produced using a first encoding algorithm. The first encoding algorithm may be a method implemented by the baseline encoder 110. Following this, the first encoded residual signal (i.e. in the form of the encoded added data stream 130) may be seen to be produced by using a second encoding algorithm. In this case, the second encoding algorithm may be a method implemented by the enhancement encoder 125. In certain cases, the first and second encoding algorithms are different.

In certain cases, the method of encoding a signal may be seen to encode the signal using at least two levels of encoding. A first level is encoded using a first encoding algorithm and a second level is encoded using a second encoding algorithm. In this case, the first level may correspond to a“baseline” level comprising the baseline encoder 110 and decoders 115, 120 and the second level may correspond to an“enhancement” level comprising the enhancement encoder 125 and the enhancement decoder 140. Each level may be seen to have corresponding signals. For example, the encoded base data stream 120 may comprise a first portion of a bitstream that is obtained by encoding the first level of the signal (e.g. a down- sampled version of the input signal 100), and the encoded added data stream 130 may comprise a second portion of a bitstream that is obtained by encoding the second level of the signal (e.g. a residual or difference signal that is generated by comparing an upsampled decoded signal from the baseline decoder 115 and the input signal 100).

The first and second portion of the bitstream may be combined to form a combined bytestream. The method may further comprise sending this combined bytestream to a decoder, e.g. encoded base data stream 120 and the encoded added data stream 130 may be combined in one bytestream that is decoded by the decoder, e.g. the decoder directs each portion of the bitstream to an appropriate one of the baseline decoder 135 and the enhancement decoder 140. In another case, the first portion of the bitstream and the second portion of the bitstream may be sent as two independent bitstreams. The encoded data may be sent as either a bitstream or a bytestream, depending on configurations. Similarly to the description of encoding above, the first portion of the bitstream may be decoded using a first decoding algorithm, which may be implemented by the baseline decoder 135, and the second portion of the bitstream may be decoded using a second decoding algorithm, which may be implemented by the enhancement decoder 140. The first decoding algorithm may be implemented by a legacy decoder that is implemented using legacy hardware, wherein“legacy” here has its normal meaning of old or relating to a superseded model of decoder.

In certain examples, the“enhancement” level may be extended to generate multiple levels of residual signals. In this case, the method may further comprise decoding said first encoded residual signal to obtain a second decoded signal, obtaining a second residual signal by taking a difference between said second decoded signal and a second reference signal; and encoding said second residual signal to produce a second encoded residual signal. In this case, the second encoded residual signal may be produced by using the second encoding algorithm, e.g. as embodied within the enhancement encoder 125. Alternatively, the method may also further comprise decoding said first encoded residual signal to obtain a second decoded signal, up-sampling said second decoded signal to obtain a second up-sampled decoded signal, obtaining a second residual signal by taking a difference between said second up- sampled decoded signal and a second reference signal; and encoding said second residual signal to produce a second encoded residual signal. In this case, the second reference signal may correspond to the signal prior to down-sampling (i.e. the input signal 100), wherein the down-sampling of the second reference signal results in the first reference signal.

Referring back to Figures 2 and 3, corresponding decoding methods may also be provided. A method of decoding a signal may comprise: receiving a first encoded signal (e.g. the base data stream 120) and a first encoded residual signal (e.g. the added data stream 130), decoding said first encoded signal to obtain a first decoded signal (e.g. the output of the baseline decoder 135), up-sampling said first decoded signal to obtain a first up-sampled decoded signal (e.g. this may occur within the enhancement decoder 140), decoding said first encoded residual signal to obtain a first decoded residual signal (e.g. the enhancement decoder 140 decoding the encoded added data stream 130); and combining at least said first up-sampled decoded signal and said first decoded residual signal to obtain a first combined decoded signal (e.g. at the enhancement decoder 140 to output reconstructed signal 145, which is a reconstructed version of input signal 100). Hence, the methods applied at the decoder may correspond to the methods applied at the encoder.

In cases where a second encoded residual signal is generated, this may be received and decoded to obtain a second decoded residual signal. The first combined decoded signal and the second decoded residual signal may be combined to obtain a second combined decoded signal.

When the bitstream comprises first and second portions as described above, the method of decoding may further comprise selecting the first portion of the bitstream, decoding the first portion of the bitstream using a first decoding algorithm to obtain a first decoded portion of the signal, selecting the second portion of the bitstream, decoding the second portion of the bitstream using a second decoding algorithm to obtain a second decoded portion of the signal, and combining at least the first decoded portion and the second decoded portion to obtain a decoded combined signal. For example, the decoding system may be configured to parse a combined bit or byte stream and extract the various portions relating the encoded base data stream 120 and the encoded added data stream 130.

In certain cases, the portions of a bitstream, e.g. the signals at each layer may be identified using corresponding identifiers, e.g. the first portion is identified using a first identifier and the second portion is identified using a second identifier. The selection of the portions by the decoding system may then be performed by using said identifiers and determining the corresponding portions.

In one case, a method of decoding an encoded signal may be applied when the signal is encoded using at least two levels of encoding, where a first level is encoded using a first encoding algorithm (e.g. a“base” or“baseline” algorithm) and a second level is encoded using a second encoding algorithm (e.g. an“enhancement” algorithm). The method in this case may comprise obtaining a first bitstream, wherein the first bitstream is derived using the first encoding algorithm and corresponds to the first level of encoding, decoding said first bitstream using a first decoding algorithm to obtain a first decoded portion of the signal, obtaining a second bitstream, wherein the second bitstream is derived using the second encoding algorithm and corresponds to the second level of encoding, decoding said second bitstream using a second decoding algorithm to obtain a second decoded portion of the signal, and combining at least the first decoded portion and the second decoded portion to obtain a decoded combined signal. Decoding of the first portion may be performed by existing dedicated hardware designed to decode accordingly to the first decoding algorithm. Decoding the second portion may be performed using a software implementation (e.g. as implemented using a processor and memory) designed to decode accordingly to the second decoding algorithm, and wherein the combination of the first decoded portion and the second decoded portion is performed using the software implementation.

Given the example embodiments of Figures 1, 2 and 3, further variations will now be described.

A first variation relates to down-sampling, e.g. as performed by the down-sampler 105 or the down-sampling step 310. In one embodiment, the down-sampling operation is performed by a down-sampler which implements a separable filter with two or more separate kernels. For example, a two-dimensional filtering operation may be applied by applying a two- dimensional filter to a frame of video data. The two-dimensional filter may have a two- dimensional kernel, typically implemented as a matrix that is multiplied or convolved with elements of the frame. In certain cases, e.g. where the filter is separable, the two-dimensional filtering operation may be decomposed into multiple one-dimensional filtering operations. For example, a two-dimensional kernel may be defined as a product of two one-dimensional kernels. The two-dimensional filtering operation may be decomposed into a series of one dimensional filtering operations using each of the one-dimensional kernels.

In the present case, a filtering kernel may be formed of two or more separate kernels, i.e. a plurality of separate kernels. Each kernel may relate to a different direction. In one case, each of the separate kernels may be capable of better preserving a specific direction when down- sampling. These directions may be, for example, vertical, horizontal, diagonal etc. The directions may be defined in relation to a two-dimensional frame, e.g. of video.

In one example, the plurality of separate kernels may be weighted by way of one or more weighting factors. This can be useful to ensure that certain directions are filtered more accurately than others. For example, if a frame contains mainly vertical direction elements (for example, a handrail) then the kernel which preserves better the vertical elements may be weighted more than the kemel(s) preserving other directions, so that the vertical elements are better preserved in the down-sampled frame. On the other hand, if a frame contains mainly horizontal directional elements (for example, a long shot of a savannah) then the kernel which preserves better the horizontal elements may be weighted more than the kemel(s) preserving other directions, so that the horizontal elements are better preserved in the down- sampled frame. A kernel that is weighted more than other kernels may be multiplied by a weighting factor that is greater than a weighting factor for the other kernels. The weighting factors for the separate kernels may be determined by analysing each frame. The weighting factors may be determined per frame. The kernels are weighted to differentially preserve different specific directions within the version of the signal, i.e. a first direction in the version of the signal may be preserved differently to a second direction in the version of the signal, e.g. by weighting a first kernel relating to the first direction using a weighting factor that is greater than a weighting factor for a second kernel relating to the second direction. In certain cases, two or more of the specific directions may be orthogonal (e.g. as is the case in two- dimensions for the horizontal and vertical directions).

Performing down-sampling according to this variation may help enhance the signal that is supplied to the base encoder 110. For example, emphasising or retaining certain directions within the video signal, may improve one or more of the encoded base data stream 120 and the encoded added data stream 130. Down-sampling in this manner may enable certain directions to be better preserved in the signal output by the baseline decoder 115, which in turn may influence the residual data generated by the enhancement encoder 125. For example, if edges in a particular direction are preserved or enhanced, and these are preserved in the output of the baseline decoder 115, this may lead to a reduced difference between an original reference and reconstructed frame, thus increasing the number of 0 or near 0 residual values, which may allow residual data to be efficiently compressed. By adapting the weighting factor or factors based on the content of the signal (e.g. of a frame of video), the signal sent to the baseline encoder 110 may be adapted to improve end appearance of the reconstructed signal (e.g. signal 145). This is somewhat unusual, as the baseline encoder 110 may be a legacy hardware encoder that is expecting normal lower-resolution video without enhancement (e.g. just standard video). However, it has been observed to provide improvements in certain situations. A second variation relates to a transform operation that may be performed on the residual data generated by the enhancement encoder 125. In certain examples, the method comprises using a transform operation in order to process residuals planes in the enhancement layer, i.e. to generate planes of transformed residual data that represent the output of different directional transforms. As described above, the“enhancement” layer corresponds to the layer processed by the enhancement encoder 125 and the enhancement decoder 140. Residual data, e.g. the data that forms part of the residual signals discussed above (including the first residual signal), may be generated by comparing a reference frame and a reconstructed frame, e.g. by taking a difference between a reference frame and a reconstructed frame (e.g., an up- sampled decoded frame like that coming from the baseline decoder 115). The difference may be computed using element-wise subtraction (e.g. matrix subtraction if each of the two frames is represented as a two-dimensional array).

In the present variation, an (untransformed) residual plane may include residual information being the difference between a reference frame and a reconstructed frame. The frames may be frames of video. The enhancement layer may operate on a frame-by-frame basis, e.g. may determine residual data for a present frame from the input signal 100. In the case of a frame, such as a frame of video, this residual information may include edges, contours and details. For example, a reconstructed frame derived from the down-sampled signal, following encoding by the base encoder 110, decoding by the baseline decoder 115, and up-sampling by the enhancement encoder 125 may resemble a blurred version of the reference frame from the original input signal 100. The difference between the reference frame and the reconstructed frame may thus include detail for the higher resolution that is not present in the reconstructed frame. This detail typically appears as lines representing the fine edges of objects, texture details and points that act to sharpen the more blurred contours in the reconstructed frame.

In the second variation, the residual plane is processed by way of a transform which decomposes the residual plane into one or more transformed planes. The transformation converts the original residual values within the frame of residual data (the residual plane) into transformed values. These are then able to be encoded in a more efficient way. These transforms can correspond, for example, to the directional transforms described in PCT patent publication WO2013/171173 Al or European patent publication No. EP2850829, by the same applicant and included herein by reference. The directional transform may be referred to as a directional decomposition. A directional transform may include, for example, four different kernels, each preserving better a specific direction in the residual plane, for example, horizontal, vertical and diagonal. One known example of such a kernel is a Hadamard transform. The directional transform may be applied to small coding blocks of residual data, e.g. 2x2 or 4x4 blocks. In these cases, the kernel of the directional transform may comprise a matrix that is multiplied with a flattened version of the coding blocks to generate a transformed block. For example, a 2x2 block may be flattened into a four-element vector and multiplied by a 4x4 matrix representing the kernel. In this case, each kernel may represent a row or column of the matrix that has matrix coefficients that are applied to the elements of the flattened vector to generate an output value for the specific direction (e.g. in an output vector of length 4, each element may represent a different direction of the transform). The output of applying the kernel, if it is provided as a one-dimensional vector, may be reshaped into a two-dimensional block. The output transformed residual plane may thus comprise tiled sets of transformed blocks. In one case, the output of each different kernel (e.g. representing a different direction) may be structured as an individual plane of residual data associated with that kernel (e.g. that direction). In this case, a frame of residual data may be transformed into four planes of transformed residual data. Either approach may be used.

In the present second variation, there is a proposed additional processing operation, e.g. that is in addition to the processing operation described in the patent publications referenced above. In this variation, the additional processing operation comprises weighting the different kernels by different weights. These different weights may be based, for example, on which direction is to be preserved better than other. Similar to the weighted down-sampling of the first variation, the weights may comprise one or more weighting factors that are applied to respective kernels. For example, if the residual plane has mainly vertical elements (e.g., vertical edges or contours), then the vertical transform may be weighted more than the other transform(s) so as to better preserve the vertical elements and, ultimately, obtain a more accurate reconstructed image when the residuals are decoded and added to the decoded frame. Applying weights may comprise multiplying rows or columns of a kernel matrix representing the different“direction” kernels by a determined factor value. A value greater than one may enhance the elements of the residual data and a value less than one may reduce the impact of the elements of the residual data. A value of 0 may remove the elements of that direction altogether. In certain case, the weights may be selected to sum to one across the set of directions. In one example, the weights for each directional transform (e.g. for each kernel associated with each direction) are generated and then applied to the directional transforms. This may be performed by weighting the kernel itself, or by weighting the resultant transformed residual values.

Weighted down-sampling as per the first variation may be applied in combination with weighted transformation as per the second variation. These two variations may combine synergistically. This is because the preservation of certain details in the signal input to the baseline encoder 110, may lead to modified transformed residual values in a particular direction. Even though the baseline encoder 110 may encode the down-sampled signal in a complex non-linear manner, the linear weighting applied during down-sampling and transformation operations may provide an element of control, e.g. in the form of what directional aspects to preserve into the resultant encoded added data stream 130.

In one or more of the first and second variations, the weights may be chosen, for example, by an analysis of a frame to identify how many elements are in specific directions. For example, the method may include analysing one or more frames (or residual planes in the case the weights are applied to the transform), estimating the number of directional elements present and, based on this estimate, generating weights for the corresponding directions. By way of example, if the analysis determines that the relative percentage of elements is 70% horizontal and 30% vertical, then the weights may be 0.7 for the filter or transform preserving the horizontal dimension, and 0.3 for the filter or transform preserving the vertical dimension.

In the examples described herein, the encoding method may be seen as consisting of separating, in a signal, a structured component from a non- structured component. The structured component is encoded using a first encoding algorithm (a“base” or“baseline” algorithm), said algorithm being designed to optimally encode structured information. The unstructured component is encoded using a second encoding algorithm (an“enhancement” algorithm), said algorithm being designed to optimally encode unstructured information.

The structured component may correspond, for example, to a down-sampled image, audio signal or video frame, wherein the elements in the component are significantly spatially and/or temporally correlated. For example, a normal frame of video data has many elements that are spatially and/or temporally correlated. Many comparative encoding and decoding methods, such as the High Efficiency Video Coding (HEVC) standard, also known as H.265 and MPEG-H Part 2, or the Advanced Video Coding (AVC) standard, also referred to as H.264 or MPEG-4 Part 10, are designed to apply motion compensation for temporally correlated elements and to predict spatial elements within a frame based on spatially correlated elements. Hence, these approaches are based on structed components, and the corresponding encoding and decoding algorithms are optimised for these components. To supply a second data stream at a higher resolution that the encoded base stream 120 would require the baseline encoder 110 to be applied again to the higher resolution stream (e.g. at the resolution of the original input signal 100). This leads to a high required bitrate for transmissions.

On the other hand, the presently described examples encode an additional unstructured component using a second encoding approach that is optimised for unstructured data. This leads to a lower bitrate, and greater efficiencies, in supplying both a low-resolution and high- resolution encoded data stream. As described herein, an unstructured component may correspond, for example, to residual data. This may have some spatial and/or temporal correlation but, in general, resembles more a sparse set of data. It has properties that are quite different to a conventional frame of (structured) video. For example, because the residual data is based on a difference between an original input signal (e.g. an input or reference frame) and an up-sampled version of a previously down-sampled signal (e.g. a reconstructed frame), in many cases the difference may be 0, which means statistical measures like the signal mean and median are near 0. The unstructured component may be determined on a frame basis and may thus not require dependencies across multiple frames (e.g. as found in motion compensation encoding) and also do not require complex spatial prediction within frames, which may lead to artifacts and instabilities. This provides advantages as compared to encoding two structured components using the same encoding strategy but at different resolutions. The transforms that are described herein are applied to the unstructured or sparse data. The transformations may be particularly adapted for this form of data.

As described herein, both the encoder and decoder may be implemented within a variety of devices, including, for example, a streaming server or a client device, or server or client device that decodes from a data store. As described, various methods and processes described herein can be embodied as code (e.g., software code) and/or data. The encoder and decoder may be implemented in hardware or software as is well-known in the art of data compression. For example, hardware acceleration using a specifically programmed Graphical Processing Unit (GPU) or a specifically designed FPGA may provide certain efficiencies. Reference to software as used herein also applies to a hardware computer system processing said software, e.g. a memory to store computer program code and one or more processors to execute the computer program code. For completeness, such code and data can be stored on one or more computer-readable media, which may include any device or medium that can store code and/or data for use by a computer system. When a computer system reads and executes the code and/or data stored on a computer-readable medium, the computer system performs the methods and processes embodied as data structures and code stored within the computer- readable storage medium. In certain embodiments, one or more of the steps of the methods and processes described herein can be performed by a processor (e.g., a processor of a computer system or data storage system). Generally, any of the functionality described in this text or illustrated in the figures can be implemented using software, firmware (e.g., fixed logic circuitry), programmable or nonprogrammable hardware, or a combination of these implementations. The terms“component” or“function” as used herein generally represents software, firmware, hardware or a combination of these. For instance, in the case of a software implementation, the terms“component” or“function” may refer to program code that performs specified tasks when executed on a processing device or devices. The illustrated separation of components and functions into distinct units may reflect any actual or conceptual physical grouping and allocation of such software and/or hardware and tasks.