Spectrum efficient optical transport system with superchannels

A method, performed by a computer device, may include determining that an available spectrum, associated with an optically switched light path, has been allocated for one or more superchannels and identifying a leftover spectrum, associated with the one or more superchannels allocated for the optically switched light path. The method may further include selecting a use for the leftover spectrum; selecting one or more devices to configure based on the selected use; configuring the selected one or more devices to use the leftover spectrum; and sending data via the leftover spectrum using the configured one or more devices.

BACKGROUND INFORMATION

An optical network may include optical fibers, which provide light path channels between devices of the network. A channel may originate at a first device, may pass through one or more intermediary devices, and may terminate at a second device. The one or more intermediary devices may switch the light path of the channel from one optical fiber to another optical fiber using a device such as an optical add-drop multiplexer (OADM). Multiple channels may be combined onto an optical fiber using wavelength division multiplexing (WDM). In WDM, each channel may be associated with a different wavelength band. Since an optical fiber has a limited bandwidth, efficient use of the bandwidth for allocating channels in an optical fiber is highly desirable.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

An implementation described herein relates to a spectrum efficient optical transport system with superchannels. An optical transport system, such as a Dense Wavelength Division Multiplexing (DWDM) network, may use channels of a fixed spectral width, which may enable the optical transport system to divide up an optical spectrum in an optical fiber into channels of a particular spectral width. For example, a 100 Gigabit/second (100 G) optical transport system may use a 50 Gigahertz (GHz) spectral width for channels. When channel speed exceeds 100 G, the channel structure may include superchannels. The term “superchannel” refers to a channel that includes multiple optical carriers. For example, a superchannel may include phase-locked carriers with independent modulation that overlap in frequency and are encoded using orthogonal frequency-division multiplexing (OFDM). An optical system that uses superchannels may be more spectrally efficient, because superchannels may allow optical carriers to be packed more tightly in the available optical spectrum.

In order to simplify network management, the spectral width of superchannels may be of a fixed spectral granularity times an integer. For example, the spectral granularity may correspond to 50 GHz and the spectral width of a superchannel may correspond to 50 GHz, 100 GHz, 150 GHz, etc. The use of superchannels with a fixed spectral granularity times an integer may result in a spectral gap between the available bandwidth, of an optically switched light path in an optical fiber, and the spectral width of a superchannel, which may result in a leftover spectrum in a light path.

An implementation described herein relates to using a leftover spectrum of available bandwidth in an optically switched light path in an optical system that uses superchannels. The leftover spectrum may be identified based on allocation of one or more superchannels for an available spectrum of the optically switched light path. A use for the leftover spectrum may be selected and equipment may be selected and configured based on the selected use. As an example, the leftover spectrum may be used as a data channel associated with a particular technology, such as an OFDM data channel. As another example, the leftover spectrum may be used as a network management channel that transmits network management messages and/or control plane messages.

As yet another example, multiple leftover spectra may exist in a light path that includes multiple superchannels. Each allocated superchannel may include an associated leftover spectrum of the available bandwidth in the light path. The multiple leftover spectra may be used in connection with a flexible channel that distributes signals into the multiple leftover spectra.

In some implementations, the use of the leftover spectrum, of the available bandwidth in an optically switched light path, may be flexible and/or adaptive. For example, the width of a carrier in a superchannel may change, the number of carriers in a superchannel may change, the bandwidth of a superchannel may change, and/or the number of superchannels in a light path may change. When a change in the light path configuration is detected, the use of the leftover spectrum may be adapted based on the detected change.

FIG. 1is a diagram of an exemplary system100according to an implementation described herein. As shown inFIG. 1, system100may include reconfigurable optical add-drop multiplexers (ROADMs)110-A through110-D (referred to herein collectively as “ROADMs110” and individually as “ROADM110”), superchannel systems120-A and120-B (referred to herein collectively as “superchannel systems120” and individually as “superchannel system120”), and leftover spectrum systems130-A and130-B (referred to herein collectively as “leftover spectrum systems130” and individually as “leftover spectrum system130”). WhileFIG. 1shows system100with a particular number of ROADMs110, superchannel systems120, and leftover spectrum systems130for illustrative purposes, in practice, system100may include a different number of ROADMs110, superchannel systems120, and/or leftover spectrum systems130.

ROADM110may include one or more devices configured to multiplex and/or route light channels into or out of an optical fiber. ROADM110may include light paths to other ROADMs110. For example, ROADM110-A may be connected to ROADM110-B via light path115-AB, to ROADM110-C via light path115-AC, and to ROADM110-D via light path115-AD. ROADM110-B may be connected to ROADM110-C via light path115-BC and to ROADM110-D via light path115-BD. ROADM110-C may be connected to ROADM110-D via light path115-CD. Thus, ROADMs110may form an interconnected mesh of light paths115.

ROADM110may be remotely reconfigurable. ROADM110may include colorless functionality. Colorless functionality may enable ROADM110to assign any wavelength (i.e., color) to any port. ROADM110may include directionless functionality. Directionless functionality may enable ROADM110to route any wavelength in any direction served by ROADM110. ROADM110may include contentionless functionality. When two wavelengths of the same color arrive at the same switching structure in ROADM110, network contention may result. Contentionless functionality may enable ROADM110to receive multiple copies of the same wavelength at the same switching, add, and/or drop structure. ROADM110may include gridless functionality. Gridless functionality may enable ROADM110to use adaptive channel widths that do not depend on the channel width of a particular optical network grid, such as a channel width specified by an International Telecommunications Union (ITU) standard.

Superchannel system120may include one or more devices that generate a superchannel and/or that retrieve signals from a superchannel. For example, superchannel system120may convert electrical signals into optical signals, and/or may receive optical signals from another device (not shown inFIG. 1), and may encode the optical signals into a superchannel optical signal. Superchannel system120may provide the superchannel optical signal to ROADM110. As another example, superchannel system,120may receive a superchannel optical signal from ROADM110and may decode the optical signal from the superchannel. Superchannel system120may provide a decoded optical signal to another device (not shown inFIG. 1), may convert a decoded optical signal into an electrical signal, and/or may perform other processing on the decoded optical signal.

Leftover spectrum system130may include one or more devices that select a use for a leftover spectrum, of an available bandwidth in an optically switched light path and resulting from an allocation of the available bandwidth for one or more superchannels, and may configure equipment for the selected use. In one implementation, leftover spectrum system130may obtain information relating to superchannel allocation, associated with a particular light path, from superchannel system120. In another implementation, leftover spectrum system130may monitor ROADM110to determine superchannel allocation associated with a particular light path.

As an example, superchannel system120-A may configure ROADM110-A to receive a superchannel (e.g., a range of wavelengths associated with the superchannel) from superchannel system120-A via a particular port and add the superchannel to light path115-AC. ROADM110-B may be configured to route light path115-AC from ROADM110-A to ROADM110-C. Superchannel system120-A may further configure ROADM110-C to provide the superchannel to superchannel system120-B. Leftover spectrum system130-A may configure ROADM110-A to receive an optical channel (e.g., a range of wavelengths associated with the optical channel), such as a data channel, a network management channel, and/or a flexible distributed channel, from leftover spectrum system130-A via a particular port and add the optical channel to the leftover spectrum of light path115-AC. Leftover spectrum system130-B may further configure ROADM110-C to provide the optical channel to leftover spectrum system130-B. If the superchannel allocation changes, resulting in a change in the leftover spectrum, leftover spectrum system130-A may reconfigure the optical channel based on the change in the leftover spectrum. For example, leftover spectrum system130-A may increase or decrease a bandwidth associated with the optical channel.

AlthoughFIG. 1shows exemplary components of system100, in other implementations, system100may include fewer components, different components, differently arranged components, or additional components than depicted inFIG. 1. Additionally or alternatively, one or more components of system100may perform functions described as being performed by one or more other components of system100.

FIG. 2is a diagram illustrating exemplary components of ROADM110ofFIG. 1. As shown inFIG. 2, ROADM110may include one or more wavelength selective switches (WSS)210(referred to herein collectively as “WSSes210” and individually as “WSS210”), one or more power splitters (PS)220(referred to herein collectively as “PSes220” and individually as “PS220”), an add module230, a drop module240, and a control unit250. WhileFIG. 2illustrates a particular number of WSSes210and PSes220, a single add module230, and a single drop module240for illustrative purposes, in practice, ROADM110may include a different number of WSSes210, PSes220, add modules230, and/or drop modules240. For example,FIG. 2illustrates ROADM110that receives optical signals from four directions and that transmits optical signals in four directions. In another example, ROADM110may receive and transmit optical signals in a different number of directions.

WSS210may select a particular wavelength, or range of wavelengths, from a first optical fiber for transmission onto a second optical fiber. For example, WSS210may receive the first optical fiber from a PSS220or add module230, may select an optical signal in a particular range of wavelength from the first optical fiber, and may divert the selected optical signal onto a second optical fiber that may connect to a remote ROADM110(or another type of device). In one implementation, WSS210may be implemented as an array of microelectromechanical system (MEMS) mirrors. In another implementation, WSS210may be implemented as a liquid crystal on Silicon (LCoS) system. In yet another implementation, WSS210may be implemented as a Liquid Crystal (LC) system. In yet another implementation, WSS210may be implemented as another type of system.

PS220may split an optical signal from a first optical fiber into multiple optical signals. For example, PS220may provide a received optical signal to WSSes210in ROADM110associated with other directions and/or may provide the received optical signal to drop module240. Add module230may receive an optical signal in a particular range of wavelengths from another device (not shown inFIG. 2) and may add the optical signal to a particular WSS210. Drop module240may receive an optical signal in a particular range of wavelengths from a particular PS220and may provide the optical signal to another device (not shown inFIG. 2).

AlthoughFIG. 2shows exemplary components of ROADM110, in other implementations, ROADM110may include fewer components, different components, additional components, or differently arranged components than depicted inFIG. 2. Additionally or alternatively, one or more components of ROADM110may perform one or more tasks described as being performed by one or more other components of ROADM110.

FIG. 3is a diagram illustrating exemplary components of a device300according to an implementation described herein. Superchannel system120, leftover spectrum system130, and/or control module250of ROADM110may each include one or more devices300. As shown inFIG. 3, device300may include a bus310, a processor320, a memory330, an input device340, an output device350, and a communication interface360.

Bus310may include a path that permits communication among the components of device300. Processor320may include any type of single-core processor, multi-core processor, microprocessor, latch-based processor, and/or processing logic (or families of processors, microprocessors, and/or processing logics) that interprets and executes instructions. In other embodiments, processor320may include an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), and/or another type of integrated circuit or processing logic.

Memory330may include any type of dynamic storage device that may store information and/or instructions, for execution by processor320, and/or any type of non-volatile storage device that may store information for use by processor320. For example, memory330may include a random access memory (RAM) or another type of dynamic storage device, a read-only memory (ROM) device or another type of static storage device, a content addressable memory (CAM), a magnetic and/or optical recording memory device and its corresponding drive (e.g., a hard disk drive, optical drive, etc.), and/or a removable form of memory, such as a flash memory.

Input device340may allow an operator to input information into device300. Input device340may include, for example, a keyboard, a mouse, a pen, a microphone, a remote control, an audio capture device, an image and/or video capture device, a touch-screen display, and/or another type of input device. In some embodiments, device300may be managed remotely and may not include input device340. In other words, device300may be “headless” and may not include a keyboard, for example.

Output device350may output information to an operator of device300. Output device350may include a display, a printer, a speaker, and/or another type of output device. For example, device300may include a display, which may include a liquid-crystal display (LCD) for displaying content to the customer. In some embodiments, device300may be managed remotely and may not include output device350. In other words, device300may be “headless” and may not include a display, for example.

Communication interface360may include a transceiver that enables device300to communicate with other devices and/or systems via wireless communications (e.g., radio frequency, infrared, and/or visual optics, etc.), wired communications (e.g., conductive wire, twisted pair cable, coaxial cable, transmission line, fiber optic cable, and/or waveguide, etc.), or a combination of wireless and wired communications. Communication interface360may include a transmitter that converts baseband signals to radio frequency (RF) signals and/or a receiver that converts RF signals to baseband signals. Communication interface360may be coupled to an antenna for transmitting and receiving RF signals.

As will be described in detail below, device300may perform certain operations relating to selecting a use for a leftover spectrum, of an available bandwidth in an optically switched light path and resulting from allocation of one or more superchannels for the available bandwidth, and relating to configuring equipment for the selected use. Device300may perform these operations in response to processor320executing software instructions contained in a computer-readable medium, such as memory330. A computer-readable medium may be defined as a non-transitory memory device. A memory device may be implemented within a single physical memory device or spread across multiple physical memory devices. The software instructions may be read into memory330from another computer-readable medium or from another device. The software instructions contained in memory330may cause processor320to perform processes described herein. Alternatively, hardwired circuitry may be used in place of, or in combination with, software instructions to implement processes described herein. Thus, implementations described herein are not limited to any specific combination of hardware circuitry and software.

AlthoughFIG. 3shows exemplary components of device300, in other implementations, device300may include fewer components, different components, additional components, or differently arranged components than depicted inFIG. 3. Additionally or alternatively, one or more components of device300may perform one or more tasks described as being performed by one or more other components of device300.

FIG. 4is a diagram of exemplary functional components of functional device400. Leftover spectrum system130and/or ROADM110may include functional device400. Functional device400may be implemented, for example, via processor320executing instructions from memory330. Alternatively, some or all of the functional components of leftover spectrum system130may be hardwired. As shown inFIG. 4, functional device400may include a leftover spectrum manager410. Leftover spectrum manager410may select a use for a leftover spectrum resulting from superchannel allocation and may configure equipment for the selected use. Leftover spectrum manager410may include a light paths monitor420, a light paths database430, a leftover spectrum use selector440, a leftover spectrum system controller450, and a ROADM controller460.

Light paths monitor420may monitor light paths associated with a ROADM associated with leftover spectrum system130. For example, light paths monitor420of leftover spectrum system130-A may monitor light paths associated with ROADM110-A. Light paths monitor420may monitor superchannel allocation associated with a particular light path and may determine a leftover spectrum associated with the superchannel allocation. Light paths database430may store information relating to superchannel allocation associated with particular light paths and/or may store information relating to leftover spectrums associated with the particular light paths.

Leftover spectrum use selector440may select a particular use for the leftover spectrum. For example, leftover spectrum selector440may select the particular use based on equipment associated with leftover spectrum system130. If the equipment associated with leftover spectrum system130is associated with different types of equipment, leftover spectrum selector440may select the particular use based on one or more other criteria. For example, leftover spectrum use selector440may select a use for the leftover spectrum based on a particular type of superchannel allocation. For example, if multiple superchannels have been allocated and each superchannel is associated with a leftover spectrum, leftover spectrum use selector440may select to use a flexible channel with a distributed spectral arrangement to utilize the multiple leftover spectra.

Leftover spectrum system controller450may configure leftover spectrum system130based on the selected use for the selected spectrum. For example, if leftover spectrum use selector440has selected that a particular data channel is to be transmitted via the leftover spectrum, leftover spectrum system controller450may configure leftover spectrum system130to receive (or generate) the data channel and convert the data channel to an optical signal at a wavelength range associated with the leftover spectrum. As another example, if leftover spectrum use selector440has selected that a network management channel is to be transmitted via the leftover spectrum, leftover spectrum system controller450may configure leftover spectrum system130to receive (or generate) the network management channel and convert the network management channel to an optical signal at a wavelength range associated with the leftover spectrum.

ROADM controller460may configure one or more ROADMs110based on the selected use for the leftover spectrum. For example, ROADM controller460may configure add module230and WSS210of a first ROADM110to add an optical signal at a wavelength range associated with the leftover spectrum onto a light path associated with the leftover spectrum and may configure drop module240of a second ROADM110to drop the optical signal at the end of the light path.

AlthoughFIG. 4shows exemplary functional components of leftover spectrum system130, in other implementations, leftover spectrum system130may include fewer functional components, different functional components, differently arranged functional components, or additional functional components than depicted inFIG. 4. Additionally or alternatively, one or more functional components of leftover spectrum system130may perform functions described as being performed by one or more other functional components of leftover spectrum system130.

FIG. 5is a flow chart of an exemplary process for using a leftover spectrum, when superchannels are allocated, according to an implementation described herein. In one implementation, the process ofFIG. 5may be performed by leftover spectrum system130. In other implementations, some or all of the process ofFIG. 5may be performed by another device or a group of devices separate from leftover spectrum system130and/or including leftover spectrum system130.

The process ofFIG. 5may include determining that an available spectrum associated with a light path has been allocated for one or more superchannels (block510). As an example, superchannel system120may send information relating to a superchannel allocation to leftover spectrum system130and light paths monitor420may store the information in light paths database430. As another example, light paths monitor420may monitor ROADM110for superchannel allocation. A leftover spectrum associated with the superchannel allocation may be identified (block520). For example, light paths monitor420may calculate a leftover spectrum for a particular optically switched light path based on the available spectrum and based on the bandwidth of the available spectrum taken up by the allocated superchannels.

A use for the leftover spectrum may be selected (block530). For example, leftover spectrum use selector440may select a particular use for the leftover spectrum based on one or more criteria. In one implementation, the particular use may be selected based on equipment associated with leftover spectrum system130. For example, if leftover spectrum system130includes a network management system, leftover spectrum use selector440may select to use the leftover spectrum as a network management channel. As another example, if leftover spectrum system130includes OFDM equipment, leftover spectrum use selector440may select to use the leftover spectrum as an OFDM channel.

In another implementation, the particular use may be selected based on a particular type of superchannel allocation. For example, if the superchannel allocation includes multiple superchannels, each superchannel may be associated with a leftover spectrum. Thus, the available spectrum may include multiple distinct unused wavelength ranges. Leftover spectrum use selector440may select to use a flexible channel with a distributed spectral arrangement and may distribute a channel across the multiple distinct unused wavelength ranges.

Equipment to configure may be selected based on the selected use (block540) and the selected equipment may be configured to use the leftover spectrum based on the selected use (block550). As an example, leftover spectrum system controller450may select particular devices associated with the selected use (e.g., a particular port that is to generate an optical signal to be provided onto the leftover spectrum). As another example, ROADM controller460may configure one or more ROADMs110based on the selected use.

Network configuration may be monitored (block560). For example, light paths monitor420may monitor the light path configuration of the network to determine whether a superchannel allocation associated with a light path has changed. A determination may be made as to whether the network configuration has changed (block570). If it is determined that the network configuration has not changed (block570—NO), processing may return to block560to continue to monitor the network configuration. If it is determined that the network configuration has changed (block570—YES), light paths which have changed may be identified (block580). For example, light paths monitor420may identify a particular light path for which the superchannel allocation has changed and processing may return to block520to identify a leftover spectrum associated with the changed superchannel allocation.

FIG. 6is a flow chart of an exemplary process for configuring equipment to use a leftover spectrum according to an implementation described herein. In one implementation, the process ofFIG. 6may be performed by leftover spectrum system130. In other implementations, some or all of the process ofFIG. 6may be performed by another device or a group of devices separate from leftover spectrum system130and/or including leftover spectrum system130.

The process ofFIG. 6may include configuring leftover spectrum equipment associated with a first ROADM at a first end of a light path (block610). For example, leftover spectrum system controller450may configure leftover spectrum system130-A to transmit information associated with a selected channel. Furthermore, leftover spectrum system130-A may configure a transceiver, such as a small form-factor (SFP) pluggable transceiver, to transmit an optical signal at a wavelength range associated with the leftover spectrum.

An add module of the first ROADM may be configured (block620) and a WSS of the first ROADM may be configured (block630). For example, ROADM controller460may configure add module230of ROADM110-A to add the channel from leftover spectrum system130-A to WSS210associated with the light path, associated with the leftover spectrum, and may configure the associated WSS210to add the channel to the light path.

A drop module of a second ROADM at a second end of the light path may be configured (block640). For example, ROADM controller460may configure drop module240of ROADM110-C to drop the channel from the light path. Leftover spectrum equipment associated with the second ROADM may be configured (block650). For example, leftover spectrum system controller450may send a message to leftover spectrum system130-B to configure leftover system130-B to receive the channel associated with the leftover spectrum.

FIG. 7is a diagram of a first example system700according to an implementation described herein. In system700, superchannel system120-A and superchannel system120-B may exchange optical signals using superchannel710. Furthermore, in system700, leftover spectrum system130-A may correspond to OFDM channel system720-A and leftover spectrum system130-B may correspond to OFDM channel system720-B. OFDM channel system720-A may select to use leftover spectrum, associated with a superchannel allocation generated by superchannel system120-A, as an OFDM channel.

OFDM channel system720may include a network device, such as a switch or a router, to receive an electrical signal from a computer device, such as a server device. OFDM channel system720may convert the electrical signal into an OFDM optical signal in a wavelength range associated with a leftover spectrum using an optical signal generator, such as, for example, a small form-factor (SFP) pluggable transceiver. Thus, the light path from ROADM110-A to ROADM110-C may include superchannel710, generated by superchannel system120-A, and OFDM channel730, generated by OFDM channel system720-A.

FIG. 8is a diagram of a second example system800according to an implementation described herein. In system800, superchannel system120-A and superchannel system120-B may exchange optical signals using superchannel810. Furthermore, in system800, leftover spectrum system130-A may correspond to network management system820-A and leftover spectrum system130-B may correspond to network management system820-B. Network management system820-A may select to use leftover spectrum, associated with a superchannel allocation generated by superchannel system120-A, as a network management channel.

Network management system820may include one or more network devices that perform control plane processing and/or network management for a network that includes ROADMs110. Control plane processing may include, for example, network topology discovery and/or management; network address assignment; routing table management; forwarding table manipulation; quality of service (QoS) table manipulation; connection set up, teardown, and/or restoration; assignment of wavelength; traffic engineering; etc. Network management may include, for example, management of control plane resources; fault management; performance management; security management; accounting management; policy management; etc.

Network management system820may generate a control plane and/or a network management message, may convert the message into an optical signal in a wavelength range associated with a leftover spectrum using an optical signal generator, such as, for example, an SFP pluggable transceiver. Thus, the light path from ROADM110-A to ROADM110-C may include superchannel810, generated by superchannel system120-A, and network management channel830, generated by network management system820-A.

FIG. 9is a diagram of a third example system900according to an implementation described herein. In system900, superchannel system120-A and superchannel system120-B may exchange optical signals using a first superchannel910-A, a second superchannel910-B, and a third superchannel910-C. Furthermore, in system900, leftover spectrum system130-A may correspond to a flexible channel system920-A and leftover spectrum system130-B may correspond to a flexible channel system920-B. Each of the three superchannels910may be associated with a distinct leftover spectrum and flexible channel system920-A may select to use a flexible channel930with a distributed spectral arrangement, in order to take advantage of the distinct leftover spectra.

FIG. 10is a diagram of a first example of spectrum allocation1000that may be associated with system900ofFIG. 9. Spectrum allocation may include first superchannel910-A, second superchannel910-B, and third superchannel910-C. Each of the three superchannels may be associated with a leftover spectrum. First superchannel910-A may be associated with first leftover spectrum1015-A, second superchannel910-B may be associated with second leftover spectrum1015-B, and third superchannel910-C may be associated with third leftover spectrum1015-C. Spectrum allocation1000may include flexible channel930with distributed spectral arrangement, which may be distributed onto first leftover spectrum1015-A, second leftover spectrum1015-B, and third leftover spectrum1015-C.

Flexible channel system920-A may receive electrical signals associated with a data stream and may encode the electrical signals onto flexible channel930. As an example, flexible channel system920-A may encode bits into symbols and may send encoded symbols alternately via a first wavelength range associated with first leftover spectrum1015-A, via a second wavelength range associated with second leftover spectrum1015-B, and via a third wavelength range associated with third leftover spectrum1015-C. Thus, optical signals may be distributed onto the leftover spectra through time division multiplexing. As another example, each time a new frame is to be transmitted, the information to be transmitted via flexible channel930may be distributed into three frames, each associated with one of the leftover spectra, and the three frames may be transmitted at a substantially same time.

FIG. 11is a diagram of a second example of spectrum allocation1100according to an implementation described herein. Spectrum allocation1100may change in response to a change in the superchannel allocation. For example, during a first time period, the superchannel allocation may include first superchannel1110-A may leave a leftover spectrum of 8 GHz. Thus, during the first time period, leftover spectrum channel1020-A may be configured with a bandwidth of 8 GHz. During a second time period, the superchannel allocation may change to include second superchannel1110-B, which may leave a leftover spectrum of 15 GHz. Thus, during the second time period, configuration of the leftover spectrum channel may change to leftover spectrum channel1020-B, which may include a bandwidth of 15 GHz.

For example, while series of blocks have been described with respect toFIGS. 5 and 6, the order of the blocks may be modified in other implementations. Further, non-dependent blocks may be performed in parallel.