Patent Publication Number: US-2023139142-A1

Title: Methods and apparatus to extend a timestamp range supported by a watermark

Description:
RELATED APPLICATION(S) 
     This patent arises from a continuation of U.S. patent application Ser. No. 17/332,636 (now U.S. Pat. No. ______), which is titled “METHODS AND APPARATUS TO EXTEND A TIMESTAMP RANGE SUPPORTED BY A WATERMARK,” and which was filed on May 21, 2021, which is a continuation of U.S. patent application Ser. No. 16/596,255 (now U.S. Pat. No. 11,025,995), which is titled “METHODS AND APPARATUS TO EXTEND A TIMESTAMP RANGE SUPPORTED BY A WATERMARK,” and which was filed on Oct. 8, 2019, which is a divisional of U.S. patent application Ser. No. 16/025,805 (now U.S. Pat. No. 10,448,123), which is titled “METHODS AND APPARATUS TO EXTEND A TIMESTAMP RANGE SUPPORTED BY A WATERMARK,” and which was filed on Jul. 2, 2018. Priority to U.S. patent application Ser. No. 17/332,636, U.S. patent application Ser. No. 16/596,255 and U.S. patent application Ser. No. 16/025,805 is claimed. U.S. patent application Ser. No. 17/332,636, U.S. patent application Ser. No. 16/596,255 and U.S. patent application Ser. No. 16/025,805 are hereby incorporated herein by reference in their respective entireties. 
    
    
     FIELD OF THE DISCLOSURE 
     This disclosure relates generally to media watermarking and, more particularly, to methods and apparatus to extend a timestamp range supported by a watermark. 
     BACKGROUND 
     Watermarks can be embedded or otherwise included in media to enable additional information to be conveyed with the media. For example, audio watermarks can be embedded or otherwise included in the audio data/signal portion of a media stream, file and/or signal to convey data, such as media identification information, copyright protection information, etc., with the media. Such watermarks enable monitoring of the distribution and/or use of media, such as by detecting watermarks present in television broadcasts, radio broadcasts, streamed multimedia, etc., to identify the particular media being presented to viewers, listeners, users, etc. Such information can be valuable to advertisers, content providers, and the like. 
     Some watermarks also include timestamps to represent time information associated with the media in which the watermark is embedded. For example, the timestamps can represent a broadcast time indicating when the media was broadcast, an access time indicated when the media was accessed (e.g., downloaded, streamed, etc.), a creation time of the media indicating when the media was created, etc. Such timestamps can be used to associate monitored media with a particular media broadcast, a particular media access, a particular media version, etc. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG.  1    is a block diagram of an example environment of use including an example media monitoring system structured to extend a time range supported by a watermark in accordance with teachings of this disclosure. 
         FIG.  2    is a block diagram of an example media watermark to be detected and processed by the example media monitoring system of  FIG.  1   . 
         FIG.  3    is a block diagram of an example media provider including an example watermark encoder structured to extend a time range supported by a watermark in accordance with teachings of this disclosure. 
         FIG.  4    is a block diagram of an example implementation of the watermark encoder of  FIG.  3   . 
         FIG.  5    is a block diagram of an example watermark decoder for use in the example media monitoring system of  FIG.  1    and structured to extend a time range supported by a watermark in accordance with teachings of this disclosure. 
         FIG.  6    is a flowchart representative of example computer readable instructions that may be executed to implement the example watermark encoder of  FIGS.  3  and/or  4   . 
         FIG.  7    is a flowchart representative of example computer readable instructions that may be executed to implement the example watermark decoder of  FIG.  5   . 
         FIG.  8    is a block diagram of an example processor platform structured to execute the example computer readable instructions of  FIG.  5    to implement the example watermark encoder of  FIGS.  3  and/or  4   . 
         FIG.  9    is a block diagram of an example processor platform structured to execute the example computer readable instructions of  FIG.  7    to implement the example watermark decoder of  FIG.  5   . 
         FIG.  10    is an example probability curve that may be used to configure operation of the example watermark decoder of  FIG.  5   . 
     
    
    
     The figures are not to scale. Wherever possible, the same reference numbers will be used throughout the drawing(s) and accompanying written description to refer to the same or like parts, elements, etc. 
     DETAILED DESCRIPTION 
     Methods, apparatus, systems and articles of manufacture (e.g., physical storage media) to extend a time range supported by a watermark are disclosed herein. Example watermark encoding apparatus disclosed herein include a timestamp cycle evaluator to determine which one of a plurality of timestamp cycles is to be represented by a timestamp of a watermark. The timestamp includes a set of timestamp symbols. Disclosed example watermark encoding apparatus also include a symbol modifier to modify a subset of data symbols of the watermark based on a further timestamp symbol not included in the set of timestamp symbols of the timestamp. The further timestamp symbol identifies the one of the plurality of timestamp cycles to be represented by the timestamp of the watermark, and the data symbols of the watermark are different from the timestamp symbols of the watermark. Disclosed example watermark encoding apparatus further include a watermark embedder to embed the watermark in a first piece of media. 
     In some disclosed examples, the timestamp has a timestamp range covering one timestamp cycle, and the watermark has a timestamp range covering the plurality of timestamp cycles. For example, one timestamp cycle can correspond to a time period of substantially 28 days. In some disclosed examples, a number of timestamp cycles in the plurality of timestamp cycles is two. Additionally or alternatively, in some disclosed examples, the data symbols represent an identifier of the piece of media. 
     Additionally or alternatively, in some disclosed examples, the subset of data symbols is a first subset of data symbols included in a set of data symbols of the watermark, and the set of data symbols also includes a second subset of data symbols, with respective ones of the second subset of data symbols being determined from corresponding ones of the first subset of data symbols based on another data symbol not included in the first and second subsets of data symbols. In some such disclosed examples, the symbol modifier is to modify the first subset of data symbols based on the further timestamp symbol, but is not to modify the second subset of data symbols based on the further timestamp symbol. 
     Additionally or alternatively, in some disclosed examples, to modify the subset of data symbols, the symbol modifier is to exclusive-OR (XOR) respective ones of the subset of data symbols with the further timestamp symbol. 
     Example watermark decoding apparatus disclosed herein include a watermark validator to determine whether a subset of data symbols of a watermark decoded from a first piece of media is valid. The watermark includes the data symbols and a timestamp, with the timestamp including a set of timestamp symbols different from the data symbols of the watermark. Disclosed example watermark decoding apparatus also include a symbol modifier to modify the subset of data symbols of the watermark based on a further timestamp symbol to determine a modified subset of data symbols when the subset of data symbols is not valid. In some disclosed examples, the further timestamp symbol is not included in the set of timestamp symbols of the timestamp. Disclosed example watermark decoding apparatus further include a timestamp cycle decoder to associate the watermark with a first one of a plurality of timestamp cycles when the subset of data symbols is valid, and when the subset of data symbols is not valid, associate the watermark with a second one of a plurality of timestamp cycles identified by the further timestamp symbol when the modified subset of data symbols is determined to be valid by the watermark validator. 
     In some disclosed examples, to modify the subset of data symbols, the symbol modifier is to exclusive-OR (XOR) respective ones of the subset of data symbols with the further timestamp symbol. 
     Additionally or alternatively, in some disclosed examples, the subset of data symbols is a first subset of data symbols included in a set of data symbols of the watermark, the set of data symbols also includes a second subset of data symbols. In some such examples, the watermark validator is to determine the first subset of data symbols is valid when respective ones of the second subset of data symbols are related to corresponding ones of the first subset of data symbols based on another data symbol not included in the set of data symbols, and is to determine the first subset of symbols is not valid when respective ones of the second subset of data symbols are not related to corresponding ones of the first subset of data symbols based on another symbol not included in the set of data symbols. In some such disclosed examples, the watermark validator is to determine the modified subset of data symbols is valid when respective ones of the second subset of data symbols are related to corresponding ones of the modified subset of data symbols based on another data symbol not included in the set of data symbols, and is to determine the modified subset of symbols is not valid when respective ones of the second subset of data symbols are not related to corresponding ones of the modified subset of data symbols based on another symbol not included in the set of data symbols. 
     Additionally or alternatively, in some disclosed examples, the timestamp has a timestamp range covering one timestamp cycle, and the watermark has a timestamp range covering the plurality of timestamp cycles. In some such disclosed examples, one timestamp cycle corresponds to a time period of substantially 28 days. In some disclosed examples, the data symbols represent an identifier of the piece of media. In some disclosed examples, a number of timestamp cycles in the plurality of timestamp cycles is two. 
     These and other example methods, apparatus, systems and articles of manufacture (e.g., physical storage media) to extend a timestamp ranges supported by a watermark are disclosed in further detail below. 
     Media watermarking is a technique used to identify media, such as television broadcasts, radio broadcasts, advertisements (television and/or radio), downloaded media, streaming media, prepackaged media, etc. Existing media watermarking techniques identify media by embedding one or more codes (e.g., one or more watermarks), such as media identifying information and/or an identifier that may be mapped to media identifying information, into an audio and/or video component of the media. In some examples, the audio or video component is selected to have a signal characteristic sufficient to hide the watermark. As used herein, the terms “code” or “watermark” are used interchangeably and are defined to mean any identification information (e.g., an identifier) that may be inserted or embedded in the audio or video of media (e.g., a program or advertisement) for the purpose of identifying the media or for another purpose such as tuning (e.g., a packet identifying header). As used herein “media” refers to audio and/or visual (still or moving) content and/or advertisements. To identify watermarked media, the watermark(s) are detected/decoded and used to obtain data that can be mapped to media identifying information. 
     Unlike media monitoring techniques based on codes and/or watermarks embedded or otherwise included in the monitored media, fingerprint or signature-based media monitoring techniques generally use one or more inherent characteristics of the monitored media during a monitoring time interval to generate a substantially unique proxy for the media. Such a proxy is referred to as a signature or fingerprint, and can take any form (e.g., a series of digital values, a waveform, etc.) representative of any aspect(s) of the media signal(s) (e.g., the audio and/or video signals forming the media presentation being monitored). A signature may be a series of signatures collected in series over a timer interval. Generally, a good signature is repeatable when processing the same media presentation, but is unique relative to other (e.g., different) presentations of other (e.g., different) media. Accordingly, the term “fingerprint” and “signature” are used interchangeably herein and are defined herein to mean a proxy for identifying media that is generated from one or more inherent characteristics of the media. 
     Signature-based media monitoring generally involves determining (e.g., generating and/or collecting) signature(s) representative of a media signal (e.g., an audio signal and/or a video signal) output by a monitored media device and comparing the monitored signature(s) to one or more references signatures corresponding to known (e.g., reference) media sources. Various comparison criteria, such as a cross-correlation value, a Hamming distance, etc., can be evaluated to determine whether a monitored signature matches a particular reference signature. When a match between the monitored signature and one of the reference signatures is found, the monitored media can be identified as corresponding to the particular reference media represented by the reference signature that with matched the monitored signature. Because attributes, such as an identifier of the media, a presentation time, a broadcast channel, etc., are collected for the reference signature, these attributes may then be associated with the monitored media whose monitored signature matched the reference signature. Example systems for identifying media based on codes and/or signatures are long known and were first disclosed in Thomas, U.S. Pat. No. 5,481,294, which is hereby incorporated by reference in its entirety. 
     As noted above, watermarks embedded in media may include timestamps to represent time information associated with the media in which the watermark is embedded. For example, the timestamps can represent a broadcast time indicating when the media was broadcast, an access time indicated when the media was accessed (e.g., downloaded, streamed, etc.), a creation time of the media indicating when the media was created, etc. Such timestamps can be used to associate monitored media with a particular media broadcast, a particular media access, a particular media version, etc. 
     The time period supported by a watermark timestamp is generally related to the number of symbols of the watermark payload used to represent the timestamp. (A symbol may include one or more bits.) As such, a timestamp supporting a long time period may require a relatively large number of symbols, whereas a timestamp supporting a short time period may require a fewer number of symbols. Thus, for a given payload size, there is a tradeoff between the number of data symbols conveying media identification (and/or other) information, and the number of timestamp symbols, which affects the corresponding time period that can be represented by the timestamp. For example, the Critical Band Encoding Technology (CBET) watermarks of The Nielsen Company (US), LLC., support a time period of substantially (e.g., on the order of) 28 days. 
     Although the time period supported by a watermark&#39;s timestamp may be sufficient for some purposes, such as monitoring presentations of live media broadcasts, such a time period may not be sufficient for other purposes. For example, the prevalence of digital video recorders, video-on-demand services, and other technologies have increased that likelihood that a monitored media presentation may have been time-shifted (e.g., presented at a different time than when the media was broadcast, accessed, etc.). Furthermore, the storage capacities of such technologies continue to increase, resulting in a corresponding increase in the duration of time by which media can be time-shifted. However, if media is time-shifted by a time duration exceeding the time period supported by the timestamp of a watermark embedded in the media, the time represented by the timestamp becomes ambiguous because the number of cycles of the timestamp period occurring from the time represented by the timestamp and the time when the media was presented (and when the watermark was decoded from the media) is unknown. This is because the value of timestamp rolls-over at the end of the timestamp period and, thus, different times separated by multiples of the timestamp period will all have the same timestamp value (similar to how different times separated by a 12-hour period all have the same values on a typical digital alarm clock). 
     One solution to enable a watermark to support a longer duration of time shifting is to increase the number of watermark symbols used to represent the watermark timestamp. However, such a solution can require a corresponding reduction in the number of data symbols able to be conveyed by the watermark if the watermark payload size remains unchanged, or can require a redesign of the watermark structure (and associated watermark encoder and decoder technology) to increase the size of the watermark payload to increase the number of timestamp symbols without decreasing the number of data symbols. In contrast, example watermarking techniques disclosed herein provide technical solutions to the problem of extending a timestamp range supported by a watermark, but without the need to increase the number of timestamp symbols and, thus, without decreasing the number of watermark data symbols or requiring a redesign of the watermark structure. Disclosed example watermarking techniques achieve this technical solution by modifying data symbols of the watermark based on an additional timestamp symbol to represent different timestamp cycles, with each timestamp cycle covering a corresponding period of the timestamp. A reversible operation, such as an exclusive-OR operation, is used to modify the data symbols based on the additional timestamp symbol to generate modified data symbols to be included in the watermark prior to encoding/embedding the watermark in a piece of media. Because the modification operation is reversible, both the original data symbols and the additional timestamp symbol can be recovered from the detected watermark by a watermark decoder. 
     For example, a first additional timestamp symbol, which may also be associated with no modification of the original watermark data symbols, may represent a first timestamp cycle covering a first period of the timestamp (e.g., a first 28 day period), whereas a second additional timestamp symbol used to modify at least some the data symbols of the watermark may represent a second timestamp cycle covering a subsequent second period of the timestamp (e.g., a subsequent second 28 day period). Similarly, a third additional timestamp symbol used to modify at least some the data symbols of the watermark may represent a third timestamp cycle covering a subsequent third period of the timestamp (e.g., a subsequent third 28 day period), and so on. Such a technical solution extends the range supported by watermark timestamp to be a multiple number of timestamp periods corresponding to the number of different possible values of the additional timestamp symbol. For example, if there are sixteen possible values of the additional timestamp symbol (e.g., corresponding to the additional timestamp symbol being a 4-bit symbol), then the range of the timestamp is extended to support sixteen (16) timestamp periods. As disclosed in further detail below, because the additional timestamp symbol is encoded in the watermark by modifying data symbols of the watermark, the number of data symbols and the watermark structure remain unchanged. However, because the symbol modification operation is reversible, a watermark decoder implemented in accordance with teachings of this disclosure can recover the original watermark data symbols of a detected watermark and determine which additional timestamp symbol was used to modify the data symbols to thereby determine which timestamp cycle is associated with the timestamp of the detected watermark. 
     Turning to the figures, a block diagram of an example environment of use including an example media monitoring system structured to extend a time range supported by a watermark in accordance with teachings of this disclosure is illustrated in  FIG.  1   . In the illustrated example of  FIG.  1   , an example media presentation environment  102  includes example panelists  104 ,  106 , an example media presentation device  110  that receives media from an example media source  112 , and an example meter  114 . The example meter  114  identifies the media presented by the example media presentation device  110  and reports media monitoring information to an example central facility  190  of an example audience measurement entity via an example gateway  140  and an example network  180 . In some examples, the meter  114  is referred to as an audience measurement device. In the illustrated example, the meter includes an example watermark decoder structured to extend a time range supported by a watermark in accordance with teachings of this disclosure. An example of such a watermark decoder is illustrated in  FIG.  5   , which is described in further detail below. 
     In the illustrated example of  FIG.  1   , the example media presentation environment  102  is a room of a household (e.g., a room in a home of a panelist, such as the home of a “Nielsen family”). In the illustrated example of  FIG.  1   , the example panelists  104 ,  106  of the household have been statistically selected to develop media ratings data (e.g., television ratings data) for a population/demographic of interest. People become panelists via, for example, a user interface presented on a media device (e.g., via the media presentation device  110 , via a website, etc.). People become panelists in additional or alternative manners such as, for example, via a telephone interview, by completing an online survey, etc. Additionally or alternatively, people may be contacted and/or enlisted using any desired methodology (e.g., random selection, statistical selection, phone solicitations, Internet advertisements, surveys, advertisements in shopping malls, product packaging, etc.). In some examples, an entire family may be enrolled as a household of panelists. That is, while a mother, a father, a son, and a daughter may each be identified as individual panelists, their viewing activities typically occur within the family&#39;s household. 
     In the illustrated example of  FIG.  1   , one or more panelists  104 ,  106  of the household have registered with an audience measurement entity (e.g., by agreeing to be a panelist) and have provided their demographic information to the audience measurement entity as part of a registration process to enable associating demographics with media exposure activities (e.g., television exposure, radio exposure, Internet exposure, etc.). The demographic data includes, for example, age, gender, income level, educational level, marital status, geographic location, race, etc., of a panelist. While the example media presentation environment  102  is a household in the illustrated example of  FIG.  1   , the example media presentation environment  102  can additionally or alternatively be any other type(s) of environments such as, for example, a theater, a restaurant, a tavern, a retail location, an arena, etc. 
     In the illustrated example of  FIG.  1   , the example media presentation device  110  is a television. However, the example media presentation device  110  can correspond to any type of audio, video and/or multimedia presentation device capable of presenting media audibly and/or visually. In some examples, the media presentation device  110  (e.g., a television) may communicate audio to another media presentation device (e.g., an audio/video receiver) for output by one or more speakers (e.g., surround sound speakers, a sound bar, etc.). As another example, the media presentation device  110  can correspond to a multimedia computer system, a personal digital assistant, a cellular/mobile smartphone, a radio, a home theater system, stored audio and/or video played back from a memory, such as a digital video recorder or a digital versatile disc, a webpage, and/or any other communication device capable of presenting media to an audience (e.g., the panelists  104 ,  106 ). 
     The media presentation device  110  receives media from the media source  112 . The media source  112  may be any type of media provider(s), such as, but not limited to, a cable media service provider, a radio frequency (RF) media provider, an Internet based provider (e.g., IPTV), a satellite media service provider, etc., and/or any combination thereof. The media may be radio media, television media, pay per view media, movies, Internet Protocol Television (IPTV), satellite television (TV), Internet radio, satellite radio, digital television, digital radio, stored media (e.g., a compact disk (CD), a Digital Versatile Disk (DVD), a Blu-ray disk, etc.), any other type(s) of broadcast, multicast and/or unicast medium, audio and/or video media presented (e.g., streamed) via the Internet, a video game, targeted broadcast, satellite broadcast, video on demand, etc. For example, the media presentation device  110  can correspond to a television and/or display device that supports the National Television Standards Committee (NTSC) standard, the Phase Alternating Line (PAL) standard, the Système Électronique pour Couleur avec Mémoire (SECAM) standard, a standard developed by the Advanced Television Systems Committee (ATSC), such as high definition television (HDTV), a standard developed by the Digital Video Broadcasting (DVB) Project, etc. Advertising, such as an advertisement and/or a preview of other programming that is or will be offered by the media source  112 , etc., is also typically included in the media. 
     In examples disclosed herein, an audience measurement entity provides the meter  114  to the panelist  104 ,  106  (or household of panelists) such that the meter  114  may be installed by the panelist  104 ,  106  by simply powering the meter  114  and placing the meter  114  in the media presentation environment  102  and/or near the media presentation device  110  (e.g., near a television set). In some examples, more complex installation activities may be performed such as, for example, affixing the meter  114  to the media presentation device  110 , electronically connecting the meter  114  to the media presentation device  110 , etc. The example meter  114  detects exposure to media and electronically stores monitoring information (e.g., a code detected with the presented media, a signature of the presented media, an identifier of a panelist present at the time of the presentation, a timestamp of the time of the presentation) of the presented media. The stored monitoring information is then transmitted back to the central facility  190  via the gateway  140  and the network  180 . While the media monitoring information is transmitted by electronic transmission in the illustrated example of  FIG.  1   , the media monitoring information may additionally or alternatively be transferred in any other manner, such as, for example, by physically mailing the meter  114 , by physically mailing a memory of the meter  114 , etc. 
     The meter  114  of the illustrated example combines audience measurement data and people metering data. For example, audience measurement data is determined by monitoring media output by the media presentation device  110  and/or other media presentation device(s), and audience identification data (also referred to as demographic data, people monitoring data, etc.) is determined from people monitoring data provided to the meter  114 . Thus, the example meter  114  provides dual functionality of an audience measurement meter that is to collect audience measurement data, and a people meter that is to collect and/or associate demographic information corresponding to the collected audience measurement data. 
     For example, the meter  114  of the illustrated example collects media identifying information and/or data (e.g., signature(s), fingerprint(s), code(s), tuned channel identification information, time of exposure information, etc.) and people data (e.g., user identifiers, demographic data associated with audience members, etc.). The media identifying information and the people data can be combined to generate, for example, media exposure data (e.g., ratings data) indicative of amount(s) and/or type(s) of people that were exposed to specific piece(s) of media distributed via the media presentation device  110 . To extract media identification data, the meter  114  of the illustrated example of  FIG.  1    monitors for watermarks (sometimes referred to as codes) included in the presented media. In examples disclosed herein, a watermark includes a sequence of symbols, with some symbols carrying portions of media-identifying information which, when concatenated into a first symbol sequence, form the media identification, and other symbols carrying portions of a timestamp which, when concatenated into a second symbol sequence, form the timestamp. As disclosed in further detail below, a disclosed example watermark decoder included in the meter  114  is also able to detect an additional timestamp symbol that was applied to or, in other words, used to modify the watermark data symbols and further associate a particular timestamp cycle with the watermark timestamp based on the additional timestamp symbol determined to have been applied to the watermark data symbols. 
     Depending on the type(s) of metering the meter  114  is to perform, the meter  114  can be physically coupled to the media presentation device  110  or may be configured to capture audio emitted externally by the media presenting device  110  (e.g., free field audio) such that direct physical coupling to the media presenting device  110  is not required. For example, the meter  114  of the illustrated example may employ non-invasive monitoring not involving any physical connection to the media presentation device  110  (e.g., via Bluetooth® connection, WIFI® connection, acoustic sensing via one or more microphone(s) and/or other acoustic sensor(s), etc.) and/or invasive monitoring involving one or more physical connections to the media presentation device  110  (e.g., via USB connection, a High Definition Media Interface (HDMI) connection, an Ethernet cable connection, etc.). 
     In examples disclosed herein, to monitor media presented by the media presentation device  110 , the meter  114  of the illustrated example senses audio (e.g., acoustic signals or ambient audio) output (e.g., emitted) by the media presentation device  110 . For example, the meter  114  processes the signals obtained from the media presentation device  110  to detect media and/or source identifying signals (e.g., audio watermarks) embedded in portion(s) (e.g., audio portions) of the media presented by the media presentation device  110 . To, for example, sense ambient audio output by the media presentation device  110 , the meter  114  of the illustrated example includes an example acoustic sensor (e.g., a microphone). In some examples, the meter  114  may process audio signals obtained from the media presentation device  110  via a direct cable connection to detect media and/or source identifying audio watermarks embedded in such audio signals. 
     To generate exposure data for the media, identification(s) of media to which the audience is exposed are correlated with people data (e.g., presence information) collected by the meter  114 . The meter  114  of the illustrated example collects inputs (e.g., audience identification data) representative of the identities of the audience member(s) (e.g., the panelists  104 ,  106 ). In some examples, the meter  114  collects audience identification data by periodically and/or a-periodically prompting audience members in the media presentation environment  102  to identify themselves as present in the audience. In some examples, the meter  114  responds to predetermined events (e.g., when the media presenting device  110  is turned on, a channel is changed, an infrared control signal is detected, etc.) by prompting the audience member(s) to self-identify. The audience identification data and the exposure data can then be compiled with the demographic data collected from audience members such as, for example, the panelists  104 ,  106  during registration to develop metrics reflecting, for example, the demographic composition of the audience. The demographic data includes, for example, age, gender, income level, educational level, marital status, geographic location, race, etc., of the panelist. 
     In some examples, the meter  114  may be configured to receive panelist information via an input device such as, for example, a remote control, an Apple® iPad®, a cell phone, etc. In such examples, the meter  114  prompts the audience members to indicate their presence by pressing an appropriate input key on the input device. The meter  114  of the illustrated example may also determine times at which to prompt the audience members to enter information to the meter  114 . In some examples, the meter  114  of  FIG.  1    supports audio watermarking for people monitoring, which enables the meter  114  to detect the presence of a panelist-identifying metering device in the vicinity (e.g., in the media presentation environment  102 ) of the media presentation device  110 . For example, the acoustic sensor of the meter  114  is able to sense example audio output (e.g., emitted) by an example panelist-identifying metering device, such as, for example, a wristband, a cell phone, etc., that is uniquely associated with a particular panelist. The audio output by the example panelist-identifying metering device may include, for example, one or more audio watermarks to facilitate identification of the panelist-identifying metering device and/or the panelist  104  associated with the panelist-identifying metering device. 
     The meter  114  of the illustrated example communicates with a remotely located central facility  190  of the audience measurement entity. In the illustrated example of  FIG.  1   , the example meter  114  communicates with the central facility  190  via a gateway  140  and a network  180 . The example meter  114  of  FIG.  1    sends media identification data and/or audience identification data to the central facility  190  periodically, a-periodically and/or upon request by the central facility  190 . 
     The example gateway  140  of the illustrated example of  FIG.  1    can be implemented by a router that enables the meter  114  and/or other devices in the media presentation environment (e.g., the media presentation device  110 ) to communicate with the network  180  (e.g., the Internet.) 
     In some examples, the example gateway  140  facilitates delivery of media from the media source(s)  112  to the media presentation device  110  via the Internet. In some examples, the example gateway  140  includes gateway functionality such as modem capabilities. In some other examples, the example gateway  140  is implemented in two or more devices (e.g., a router, a modem, a switch, a firewall, etc.). The gateway  140  of the illustrated example may communicate with the network  126  via Ethernet, a digital subscriber line (DSL), a telephone line, a coaxial cable, a USB connection, a Bluetooth connection, any wireless connection, etc. 
     In some examples, the example gateway  140  hosts a Local Area Network (LAN) for the media presentation environment  102 . In the illustrated example, the LAN is a wireless local area network (WLAN), and allows the meter  114 , the media presentation device  110 , etc., to transmit and/or receive data via the Internet. Alternatively, the gateway  140  may be coupled to such a LAN. 
     The network  180  of the illustrated example can be implemented by a wide area network (WAN) such as the Internet. However, in some examples, local networks may additionally or alternatively be used. Moreover, the example network  180  may be implemented using any type of public or private network such as, but not limited to, the Internet, a telephone network, a local area network (LAN), a cable network, and/or a wireless network, or any combination thereof. 
     The central facility  190  of the illustrated example is implemented by one or more servers. The central facility  190  processes and stores data received from the meter(s)  114 . For example, the example central facility  190  of  FIG.  1    combines audience identification data and program identification data from multiple households to generate aggregated media monitoring information. The central facility  190  generates reports for advertisers, program producers and/or other interested parties based on the compiled statistical data. Such reports include extrapolations about the size and demographic composition of audiences of content, channels and/or advertisements based on the demographics and behavior of the monitored panelists. 
     As noted above, the meter  114  of the illustrated example provides a combination of media metering and people metering. The meter  114  of  FIG.  1    includes its own housing, processor, memory and/or software to perform the desired media monitoring and/or people monitoring functions. The example meter  114  of  FIG.  1    is a stationary device disposed on or near the media presentation device  110 . To identify and/or confirm the presence of a panelist present in the media presentation environment  102 , the example meter  114  of the illustrated example includes a display. For example, the display provides identification of the panelists  104 ,  106  present in the media presentation environment  102 . For example, in the illustrated example, the meter  114  displays indicia (e.g., illuminated numerical numerals  1 ,  2 ,  3 , etc.) identifying and/or confirming the presence of the first panelist  104 , the second panelist  106 , etc. In the illustrated example, the meter  114  is affixed to a top of the media presentation device  110 . However, the meter  114  may be affixed to the media presentation device in any other orientation, such as, for example, on a side of the media presentation device  110 , on the bottom of the media presentation device  110 , and/or may not be affixed to the media presentation device  110 . For example, the meter  114  may be placed in a location near the media presentation device  110 . 
       FIG.  2    illustrates an example watermark  200  that the example meter  114  of  FIG.  1    may be configured to detect. The watermark  200  of the illustrated example is embedded or otherwise included in media to be presented by media device(s), such as the example media device  110 . For example, the watermark  200  may be embedded in an audio portion (e.g., an audio data portion, an audio signal portion, etc.) of the media, a video portion (e.g., a video data portion, a video signal portion, etc.) of the media, or a combination thereof. The example watermark  200  of  FIG.  2    includes an example first group of symbols  205  and an example second group of symbols  210 . In the illustrated example of  FIG.  2   , the first group of symbols  205  is repeated in successive watermarks  200  embedded/included in the media, whereas the second group of symbols  210  differs between successive watermarks  200  embedded/included in the media. 
     In the example watermark of  FIG.  2   , the first group of symbols  205  conveys media identification data (e.g., a media identifier) identifying the media watermarked by the watermark  200 . For example, the media identification data conveyed by the first group of symbols  205  may include data identifying a broadcast station providing the media, a name (e.g., program name) of the media, a source (e.g., a website) of the media, etc. Thus, in the illustrated example of  FIG.  2   , the first group of symbols  205  is also referred to as a first group of media identification symbols  205  (or simply the media identification symbols  205  or media identification payload  205 ). In some examples, the first group of symbols  205  includes any type of data, which may or may not include media identification information. In such examples, the first group of symbols  205  may be referred to as the data symbols  205 , or data payload  205 , or data  205  of the watermark  200 . In the illustrated example, the media identification data conveyed by the first group of symbols  205  (e.g., the media identification symbols  205 ) is repeated in successive watermarks  200  embedded/included in the media. 
     In some examples, the first group of symbols  205  of the watermark  200  includes example marker symbols  215 A-B to assist the watermark detector  145  in detecting the start of the watermark  200  in the watermarked media, and example data symbols  220 A-F to convey the media identification data. Also, in some examples, corresponding symbols pairs in similar respective locations after the first marker symbol  215 A and the second marker symbol  215 B are related by an offset. For example, the value of data symbol  220 D may correspond to the value of data symbol  220 A incremented by an offset, the value of data symbol  220 E may correspond to the value of data symbol  220 B incremented by the same offset, and the value of data symbol  220 F may correspond to the value of data symbol  220 C incremented by the same offset, as well. In such examples, the symbols pairs  220 A/D,  220 B/E and  220 C/F are referred to as symbol offset pairs, or offset pairs, and the offset used to generate the symbol offset pairs forms an additional data symbol that can be used to convey the media identification data. 
     For example, the watermark payload of example watermark  200  of  FIG.  2    has the following structure: 
       [ M 1  S 1  S 2  S 3  M 2  S 4  S 5  S 6  T 1  T 2  T 3  T 4] 
     where the symbols [S4 S5 S6] are related to the symbols [S1 S2 S3] according to the following first system of relationships: 
         S 4=( S 1+ S 0)mod 16 
         S 5=( S 2+ S 0)mod 16, and 
         S 6=( S 3+ S 0)mod 16, 
     with “mod” representing the modulo operation. In this example, the symbol S0 is another symbol represented by the offset between symbols [S1 S2 S3] and symbols [S4 S5 S6]. In this example, the symbols [S0 S1 S2 S3] are data symbols representing a value of a media identifier, such as a source identifier (SID). 
     In the example watermark  200  of  FIG.  2   , the second group of symbols  210  conveys timestamp data (e.g., a timestamp) identifying, for example, a broadcast time of the watermarked media, an access time of the watermarked media, a creation time of the watermarked media, a particular elapsed time within the watermarked media, etc. Thus, in the illustrated example of  FIG.  2   , the second group of symbols  210  is also referred to as the second group of timestamp symbols  210  (or simply the timestamp symbols  210 , or timestamp payload  210 , or timestamp  210 ). Furthermore, the timestamp data conveyed by the second group of symbols  210  (e.g., the timestamp symbols  210 ) differs in successive watermarks  200  embedded/included in the media (e.g., as the elapsed time of the watermarked media increases with each successive watermark  200 ). 
     In the illustrated example of  FIG.  2   , the watermark  200  is embedded/included in media at a repetition interval of T seconds (or, in other words, at a repetition rate of 1/T seconds), with the first group of symbols  205  remaining the same in successive watermarks  200 , and the second group of symbols  205  varying in successive watermarks  200 . For example, the repetition interval T may correspond to T=4.8 seconds. As there are 12 symbols in the example watermark  200  (e.g., 8 symbols in the first group of symbols  205  and 4 symbols in the second group of symbols  210 ) each watermark symbol in the illustrated example has a duration of 4.8/12=0.4 seconds. However, other values for the repetition interval T may be used in other examples. 
     In some examples, a watermark symbol included in the watermark  200  is able to take on one of several possible symbol values. For example, if a symbol in the watermark  200  represents 4 bits of data, then the symbol is able to take on one of 16 different possible values. For example, each possible symbol value may correspond to a different signal amplitude, a different set of code frequencies, etc. In some such examples, to detect a watermark symbol embedded/included in watermarked media, the example meter  114  processes monitored media data/signals output from the example media device  110  to determine measured values (e.g., signal-to-noise ratio (SNR) values) corresponding to each possible symbol value the symbol may have. The meter  114  then selects the symbol value corresponding to the best (e.g., strongest, largest, etc.) measured value (possibly after averaging across multiple samples of the media data/signal) as the detected symbol value for that particular watermark symbol. 
     In the illustrated example, the meter  114  further uses the relationships between the symbols [S1 S2 S3] and the symbols [S4 S5 S6] specified above to decode the other symbol S0 and further determine whether the decoded symbols correspond to a valid symbol sequence. For example, let [A1 A2 A3 A4 A5 A6] represent the respective values of the watermark symbols [S1 S2 S3 S4 S5 S6] detected by the meter  114 . The detected watermark symbols [A1 A2 A3 A4 A5 A6] are related to the original watermark symbols [S1 S2 S3 S4 S5 S6] according to the following second system of relationships: 
         A 1= S 1+ε1
 
         A 2= S 2+ε2
 
         A 3= S 3+ε3
 
         A 4= S 4+ε4
 
         A 5= S 5+ε5
 
         A 6= S 6+ε6
 
     where [ε1 ε2 ε3 ε4 ε5 ε6] represent respective errors in the [A1 A2 A3 A4 A5 A6] relative to the original watermark symbols [S1 S2 S3 S4 S5 S6] (e.g., introduced by transmission errors, sensing errors, etc.) and the additions are modulo additions (e.g., modulo 16 additions in this example, but in other example, the modulo addition will be based on the number of different values each symbol can have, which corresponds to the number of bits represented by the symbol). To decode the symbol S0 and further validate the decoded symbols, the meter  114  attempts to find a single offset value that relates [A1 A2 A3] to [A4 A5 A6] by modulo addition according to the first system of relationships given above. To do this, the meter  114  assumes the values of the detected watermark symbols [A1 A2 A3] are correct and correspond to the original watermark symbols [S1 S2 S3]. The meter  114  then evaluates the first system of relationships above using different offset values to attempt to find one offset value that when added to each of [A1 A2 A3] by modulo addition results in [A4 A5 A6]. If the meter  114  is able to find one such offset value, that offset value is set to be the decoded value of S0, and the resulting sequence of decoded watermark data symbols [S0 S1 S2 S3] is considered valid. If the meter  114  is unable to find such a single offset value that relates each of [A1 A2 A3] to [A4 A5 A6] by modulo addition, the meter  114  determines the decoded watermark symbols are not valid. (In some examples, if two of the three decoded symbol pairs are related by the same offset, the resulting decoded symbols are not considered as invalid but are indicated as having a lower reliability score.) 
     A block diagram of an example media provider  300  providing watermarked media in accordance with teachings of this disclosure is illustrated in  FIG.  3   . For example, the media provider  300  can correspond to any type of media provider, such as a television station, a cable network, a satellite network (e.g., television or radio), a radio station, a streaming media service (e.g., such as Hulu™, Netflix®, etc.), etc. As such, the media distributed by the media provider  200  can correspond to any type of media, such as television programming, radio programming, multimedia (e.g., audio and/or visual) content, etc. In the illustrated example, the media provider  300  can distribute a particular piece of media (e.g., such as a particular television program, a particular radio program, a particular movie, etc.) to recipients (e.g., television viewers, radio listeners, computer users, electronic device users, etc.) via one or more program broadcasts, distribution channels, etc. (e.g., such a one or more radio frequency, cable and/or satellite television and/or radio channels, one or more networks carrying one or more digital transport channels, etc.). The example media provider  300  can correspond to the media source  114  of  FIG.  1   . 
     In the illustrated example of  FIG.  3   , the media provider  300  includes an example media database  305  to store pieces of media (e.g., media content, media advertisements/commercials, etc.) to be distributed by the media provider  300 . The media provider  300  can be implemented by any type or combination of one or more memories and/or storage devices. For example, the media provider  300  can be implemented by the mass storage device  828  and/or the volatile memory  814  in the example processing system  800  of  FIG.  8   , which is described in further detail below. 
     The example media provider  300  of  FIG.  3    also includes an example watermark encoder  310  to retrieve a piece of media stored in the media database  305  and encode (e.g., embed) a sequence of watermarks into the media. For example, the sequence of watermarks encoded by the watermark encoder  310  in the piece of media can be a sequence of audio watermarks, such as the watermark  200  of  FIG.  2   , encoded in audio portion(s) of the media at successive intervals of time (e.g., such as every 4.8 seconds or any other constant or changing interval of time) using any appropriate audio watermarking technique. Additionally or alternatively, the sequence of watermarks encoded in the piece of media by the watermark encoder  210  can be a sequence of video watermarks encoded in video portion(s) of the media content at successive intervals of time using any appropriate video watermarking technique. In some examples, the watermarks can include or otherwise convey media identifying payload data (e.g., the data payload  205 ) that identifies, for example, a source of the media content (e.g., such as the particular media provider  300 ) and/or the media itself (e.g., such as a title of the media content, an episode number, etc.). In some examples, the watermarks can include or otherwise convey timestamp payload data (e.g., the timestamp payload  210 ) representing a timestamp associated with the watermark. As disclosed in further detail below, the watermark encoder  210  is also structured to extend a timestamp range supported by the watermarks in accordance with teachings of this disclosure. 
     A block diagram of an example implementation of the watermark encoder  310  of  FIG.  3    is illustrated in  FIG.  4   . The example watermark encoder  310  of  FIG.  4    is structured to extend a range of a watermark timestamp, such as the timestamp  210 , included in a watermark, such as the watermark  200 , to be embedded in media. The example watermark encoder  310  of  FIG.  4    includes an example data generator  405  to generate or otherwise obtain (e.g., download, retrieve from memory, etc.) the data symbols for the media identification payload  205  or data payload  205  of the watermark  200  described above. As such, the data generator  405  is an example of means for generating the media identification or data payload of a watermark to be embedded in media. The example watermark encoder  310  of  FIG.  4    includes an example timestamp generator  410  to generate or otherwise obtain (e.g., from a clock, counter or other timing source) the timestamp symbols for the timestamp payload  210  of the watermark  200  described above. As such, the timestamp generator  410  is an example of means for generating the timestamp payload of a watermark to be embedded in media. 
     In the illustrated example, the watermark encoder  310  includes an example timestamp cycle evaluator  415  and an example encoded symbol modifier  420  to extend a range of the watermark timestamp  210 . The timestamp cycle evaluator  415  of the illustrated example determines which one of a group of timestamp cycles is to be represented by the timestamp  210  generated by the timestamp generator  410 . In the illustrated example, beginning with a starting reference time, a group of two or more timestamp cycles may be defined to correspond to a respective two or more successive periods of the timestamp  210 , which repeat after a number of timestamp periods corresponding to the number of timestamp cycles included in the group. For example, for a group of timestamp cycles including two timestamp cycles, the two timestamp cycles correspond to alternating periods of the timestamp  210 . As another example, for a group of timestamp cycles including sixteen (16) timestamp cycles, the 16 timestamp cycles correspond to 16 successive periods of the timestamp  210 . In the illustrated example, the timestamp cycle evaluator  415  compares a time to be represented by the timestamp  210  (e.g., such as a current time) with the starting reference time to determine in which one of the group of timestamp cycles the time to be represented by the timestamp falls. The identified timestamp cycle is then determined by the timestamp cycle evaluator  415  to be represented by the timestamp  210  and, thus, associated with the watermark  200 . As such, the timestamp cycle evaluator  415  is an example of means for determining which one of a plurality of timestamp cycles is to be represented by a timestamp of a watermark. 
     By associating the timestamp  210  with a particular one of the group of timestamp cycles, the time value represented by the timestamp  210  becomes the value of the timestamp  210  offset by a number of timestamp periods represented by the particular timestamp cycle associated with the timestamp  210 . For example, for a group of timestamp cycles including two timestamp cycles, the time represented by the timestamp  210  may be the value of the timestamp  210  when the timestamp  210  represents (is associated with) the first timestamp cycle of the group, and may be the value of the timestamp  210  offset by one timestamp period when the timestamp  210  represents (is associated with) the second timestamp cycle of the group. As another example, for a group of timestamp cycles including 16 timestamp cycles, the time represented by the timestamp  210  may be the value of the timestamp  210  when the timestamp  210  represents (is associated with) the first timestamp cycle of the group, and may be the value of the timestamp  210  offset by one timestamp period when the timestamp  210  represents (is associated with) the second timestamp cycle of the group, and may be the value of the timestamp  210  offset by two timestamp periods when the timestamp  210  represents (is associated with) the third timestamp cycle of the group, and so on, up to the time represented by the timestamp  210  being the value of the timestamp  210  offset by fifteen (15) timestamp periods when the timestamp  210  represents (is associated with) the fifteenth timestamp cycle of the group. In this manner, the range of time represented by the watermark (e.g., the timestamp range of the watermark) is extended from the timestamp&#39;s range of one timestamp period covering one timestamp cycle to a range corresponding to a number of timestamp periods covered by the group of timestamp cycles. For example, for a group of timestamp cycles including two timestamp cycles, the timestamp range of the watermark is extended from one timestamp period to two timestamp periods, and for a group of timestamp cycles including 16 timestamp cycles, the timestamp range of the watermark is extended from one timestamp period to 16 timestamp periods. 
     The encoded symbol modifier  420  of the illustrated example is included in the watermark encoder  310  to encode the timestamp cycle that is to be represented by the timestamp  210  into the watermark  200  to be encoded in the media. To do this, the encoded symbol modifier  420  modifies symbols of the media identification payload  205  or data payload  205  of the watermark  200  based on a further timestamp symbol (referred to as timestamp symbol T0 herein) to encode different ones of the group of timestamp cycles that can be represented by the timestamp  200  generated by the timestamp generator  410 . In some examples, the encoded symbol modifier  420  uses a first value of the further timestamp symbol T0, which corresponds to no modifying of symbols of the data payload  205  to encode a first one of the possible timestamp cycles in the watermark  200 , a second value of the further timestamp symbol T0 to modify symbols of the data payload  205  to encode a second one of the possible timestamp cycles in the watermark  200 , a third value of the further timestamp symbol T0 to modify symbols of the data payload  205  to encode a third one of the possible timestamp cycles in the watermark  200 , etc. As disclosed in further detail below, the encoded symbol modifier  420  employs a reversible operation to modify symbols of the data payload  205  based on the further timestamp symbol T0 such that the value of the timestamp symbol T0 is conveyed implicitly by the modified symbols of the data payload  205 , and the original symbols of the data payload  205  and the further timestamp T0 can be recovered from the modified symbols of the data payload  205 . As such, the encoded symbol modifier  420  is an example of means for modifying a subset of data symbols  205  of a watermark  200  based on a further timestamp symbol T0 not included in a set of timestamp symbols of a timestamp  210  of the watermark  200 , with the further timestamp symbol T0 identifying the one of a group of timestamp cycles to be represented by the timestamp  210  of the watermark  200 . 
     In some examples, the encoded symbol modifier  420  employs an exclusive-OR (XOR) operation as the reversible operation to modify symbols of the data payload  205  based on the further timestamp symbol T0 to enable the modified symbols to convey the value of the timestamp symbol T0 implicitly without modifying the structure of the watermark  200 . For example, the encoded symbol modifier  420  can be structured to modify a first subset of symbols of the data payload  205 , which include the data symbols [S1 S2 S3] based on the further timestamp symbol T0 to determine a modified subset of data symbols [S1* S2* S3*] according to the following third system of relationships: 
         S 1*= S 1 xor  T 0 
         S 2*= S 2 xor  T 0 
         S 3*= S 3 xor  T 0 
     where “xor” represents the bitwise XOR operation (or, in other words, bitwise modulo 2 addition). The encoded symbol modifier  420  then replaces the original subset of data symbols [S1 S2 S3] with the modified subset of data symbols [S1* S2* S3*] before the watermark  200  is embedded in the media. The properties of the XOR operation allow the original subset of data symbols [S1 S2 S3] from the modified subset of data symbols [S1* S2* S3*] by again performing an XOR operation on the modified subset of data symbols [S1* S2* S3*] using the further timestamp symbol T0 as given by the following fourth system of relationships: 
         S 1* xor  T 0= S 1 xor  T 0 xor  T 0= S 1 
         S 2* xor  T 0= S 2 xor  T 0 xor  T 0= S 2 
         S 3* xor  T 0= S 3 xor  T 0 xor  T 0= S 3 
     As such, the properties of the XOR operation enable the further timestamp symbol T0 to be conveyed in the watermark  200  which still retaining the original watermark message structure [M1 S1* S2* S3* M2 S4 S5 S6 T1 T2 T3 T4], retaining the original range of symbol values (e.g., [0-15]), retaining the original Hamming distances between the group of data symbols [S0 S1 S2 S3], etc. 
     In the illustrated example, beginning with a starting reference time, the encoded symbol modifier  420  changes the value of the further timestamp symbol T0 to represent each subsequent timestamp cycle in the group of timestamp cycles to be supported. The value of the further timestamp symbol T0 then loops back to its original starting value when the group of timestamp cycles. For example, if the further timestamp symbol T0 supports a group of 16 timestamp cycles, the encoded symbol modifier  420  may loop through 16 values corresponding to the 16 timestamp cycles and then restart for the next group of 16 timestamp cycles. In some examples, the encoded symbol modifier  420  starts with an initial value of 0 (corresponding to no symbol modification when the XOR operation is used) for the further timestamp T0 to represent a first timestamp cycle in the group of timestamp cycles, increments the value of the further timestamp T0 by one for each subsequent timestamp cycle in the group, and then returns the value of the further timestamp T0 to 0 when the next timestamp cycle group starts. In some examples, the encoded symbol modifier  420  varies the further timestamp symbol T0 for each subsequent timestamp cycle in the group according to a pattern, such as the example pattern shown in Table 1: 
                                         TABLE 1                       Binary   Decimal   Hamming distance   Decimal           Value   Value   T0(n) − T0(n − 1)   Difference                                                        T0(0)   ‘0000’   0   3   7       T0(1)   ‘1111’   15   4   15       T0(2)   ‘0001’   1   3   14       T0(3)   ‘1110’   14   4   13       T0(4)   ‘0010’   2   3   12       T0(5)   ‘1101’   13   4   11       T0(6)   ‘0011’   3   3   10       T0(7)   ‘1100’   12   4   9       T0(8)   ‘1011’   11   3   1       T0(9)   ‘0100’   4   4   7       T0(10)   ‘1010’   10   3   6       T0(11)   ‘0101’   5   4   5       T0(12)   ‘1001’   9   2   4       T0(13)   ‘0110’   6   4   3       T0(14)   ‘1000’   8   3   2       T0(15)   ‘0111’   7   4   1                    
In Table 1, T0(n) represents the n th  value of T0, the binary value is the bit representation for the given value of T0(n), the decimal value is the decimal representation for the given value of T0(n), the Hamming distance is the bitwise difference between adjacent values of T0(n) and T0(n−1), and the decimal difference is the difference between the decimal values of T0(n) and T0(n−1) (modulo 16).
 
     In some examples, the permitted combinations of the symbols included in the media identification payload  205  or data payload  205  of the watermark  200  are pruned (e.g., disallowed) to ensure that the resulting payload after data symbol modification by the encoded symbol modifier  420  satisfies one or more criteria. For example, analysis of the possible resulting payloads after data symbol modification may reveal that one or more resulting combinations of modified symbols do not satisfy a Hamming distance requirement and, thus, such symbol combinations may be removed as possible media identifiers, information values, etc. In some such examples, the data generator  405  is configured to block the generation of combination of symbols that have been pruned. 
     The example watermark encoder  310  of  FIG.  4    further includes an example watermark embedder  425  to embed the watermark  200  (e.g., after any data symbol modification performed by the encoded symbol modifier  420 ) in media (e.g., obtained from the media database  305 ). For example, the watermark embedder  425  may use any appropriate watermark embedding technique to embed the watermark  200  in an audio portion/signal and/or video portion/signal of the media. As such, the watermark embedder  425  is an example of means for embedding a watermark (e.g., after any symbol modification) in a first piece of media. 
     An example watermark decoder  500  that may be included in the example meter  114  of  FIG.  1    to decode watermarks embedded in media is illustrated in  FIG.  5   . The watermark decoder  500  of the illustrated example is structured to extend a range of a watermark timestamp, such as the timestamp  210 , included in a watermark, such as the watermark  200 , embedded in monitored media. The example watermark decoder  500  includes an example symbol decoder  505  to decode symbols of a watermark detected in monitored media. For example, the symbol decoder  505  may use any appropriate watermarking detection technique to decode symbols of the watermark  200  detected as embedded in an audio portion/signal and/or video portion/signal of the media. The symbols detected by the symbol decoder  500  of the illustrated example include the detected symbols [A1 A2 A3 A4 A5 A6] of the watermark payload  205  described above, as well as detected versions of the symbols [T1 T2 T3 T4] of the timestamp payload  210  of the watermark  200 . As such, the watermark decoder  500  is an example of means for decoding symbols of a watermark embedded in monitored media. 
     The watermark decoder  500  also includes an example watermark validator  510  to validate a decoded set or subset watermark symbols obtained by the symbol decoder  505 . In some examples, the watermark validator  510  is structured to validate the set of decoded symbols corresponding to the data payload  205  of the watermark  210 . In some such examples, to validate the set of decoded symbols corresponding to the data payload  205 , the watermark validator  510  attempts to find a single offset value that relates [A1 A2 A3] to [A4 A5 A6] by modulo addition according to the first system of relationships describes above. As described above, this single offset value corresponds to another symbol, S0. As described above, to perform such a validation, the watermark validator  510  assumes the values of the decoded watermark symbols [A1 A2 A3] obtained by the symbol decoder  505  are correct and correspond to the original subset of watermark symbols [S1 S2 S3]. The watermark validator  510  then evaluates the first system of relationships described above using different possible offset values to attempt to find one offset value that when added to each of [A1 A2 A3] by modulo addition results in [A4 A5 A6]. If the watermark validator  510  is able to find one such offset value, that offset value is set to be the decoded value of S0, and the resulting subset of decoded watermark data symbols [S0 S1 S2 S3] are considered valid. Otherwise, the watermark validator  510  determines this subset of decoded watermark symbols obtained by the symbol decoder  505  is not valid. As such, the watermark validator  510  is an example of means for determining whether given subsets of symbols of a watermark decoded from a piece of media is valid. 
     In the illustrated example, the watermark decoder  500  includes an example decoded symbol modifier  515 , an example timestamp cycle decoder  520  and an example watermark reported  525  to extend a range of the watermark timestamp  210 . As described above, a subset of data symbols of the watermark  200  may have been modified by the watermark encoder  310  using a reversible operation, such as the XOR operation, to implicitly encode, in the modified data symbols, a further timestamp symbol T0 identifying a particular timestamp cycle to be represented by the timestamp  210  of the watermark  200 . The example decoded symbol modifier  515  takes advantage of the reversible nature of the operation to modify the subset of data symbols  205  of the decoded watermark based on different possible values of the further timestamp symbol T0 that can be employed by the watermark encoder  310  to find the correct value of T0 in the event the watermark validator  510  determines a given subset of decoded watermark data symbols  205  is not valid. For example, if the watermark validator  510  determines the subset of decoded symbols corresponding to the data payload  205  without any modification (e.g., corresponding to a first value of the further timestamp symbol T0) is valid, the decoded symbol modifier  515  does not perform any modification of the decoded data symbols  210  and the decoded timestamp  210  is determined to represent the timestamp cycle corresponding to the first value of the further timestamp symbol T0. However, if the watermark validator  510  determines the decoded symbols corresponding to the data payload  205  without any modification (e.g., corresponding to the first value of the further timestamp symbol T0) is not valid, the decoded symbol modifier  515  modifies the subset of decoded symbols of the data payload  205  based on another value of the further timestamp symbol T0 that could be employed by the watermark encoder  310 . The watermark validator  510  then attempts to validate the resulting modified subset of decoded watermark data symbols  205 . If the resulting modified subset of decoded watermark data symbols  205  is valid, the decoded timestamp  210  is determined to represent the particular timestamp cycle corresponding to the value of the further symbol T0 used to determine the modified subset of data symbols. However, if the resulting modified subset of decoded watermark data symbols is still not valid, the decoded symbol modifier  515  can continue to modify the subset of decoded symbols of the data payload  205  based on other value of the further timestamp symbol T0 that could be employed by the watermark encoder  310  to determine if any of those values in a valid subset of modified decoded symbols for the data payload  210  of the watermark  200 . As such, the decoded symbol modifier  515  is an example of means for modifying a subset of data symbols  210  of a watermark  200  based on a further timestamp symbol T0 to determine a modified subset of data symbols  210  when the subset of data symbols is not valid. In some examples, if none of the possible values of the further timestamp symbol T0 result in a valid subset of modified symbols for the data payload  210 , the watermark validator  510  determines the decoded watermark symbols should be discarded as invalid. 
     An example probability curve  1000  that may be used by the example decoded symbol modifier  515  to select value of the further timestamp symbol T0 to use to modify subset of data symbols  210  of a watermark  200  is illustrated in  FIG.  10   . The example probability curve  10  represents a probability of time-shifted viewing of media. According to the example probability curve  1000 , for the monitoring of the time-shifted viewing, there is a high probability that the value of the timestamp  210  of the watermark  200  decoded from monitored media will correspond to the current timestamp cycle (as defined from a starting reference time). The probability then drops off monotonically for the value of the timestamp  210  of the watermark  200  corresponding to each successive earlier timestamp cycle. This means that, in this example, the time-shifted viewing of media is most likely to occur within 1 timestamp period from when the media was broadcast/accessed, with the probability dropping off for each additional timestamp period that occurs between the media broadcast/access time and the time-shifted viewing time. Accordingly, in some examples, the example decoded symbol modifier  515  initially attempts to decode the subset of subset of data symbols  210  of a decoded watermark  200  by modifying the subset of data symbols  210  based on the value of the further timestamp symbol T0 corresponding to the current timestamp cycle. If decoding is unsuccessful, the decoded symbol modifier  515  then tries successive values of the further timestamp symbol T0 corresponding to respective successive earlier timestamp cycles relative to the current timestamp cycle. 
     For example, assume the current timestamp cycle corresponds to the value T0(3) of the further timestamp symbol T0 in Table 1. In the preceding example, the decoded symbol modifier  515  can initially modify the subset of detected watermark data symbols [A1 A2 A3] based on the further timestamp symbol value T0(3) to determine a modified subset of detected watermark data symbols [S1′ S2′ S3′] according to the following fifth system of relationships: 
         S 1′= A 1 xor  T 0(3)
 
         S 2′= A 2 xor  T 0(3)
 
         S 3′= A 3 xor  T 0(3)
 
     If the further timestamp symbol value T0(3) is the same value used by the watermark encoder  310  when encoding the watermark, then the modified subset of decoded watermark data symbols [S1′ S2′ S3′] will correspond to the original encoded subset of watermark data symbols [S1 S2 S3] due to the XOR property that y=y XOR x XOR x for any values of y and x. Thus, if the watermark validator  510  determines the modified decoded watermark data symbols [S1′ S2′ S3′] are related to the decoded watermark data symbols [A4 A5 A6] by the same offset value and, thus, are valid, then the decoded timestamp  210  is determined to represent the timestamp cycle corresponding the value T0(3) of the further timestamp symbol. However, if the watermark validator  510  determines the modified decoded watermark data symbols [S1′ S2′ S3′] are not valid (e.g., are not related to the decoded watermark data symbols [A4 A5 A6] by the same offset value), then the decoded symbol modifier  515  tries modifying the subset of detected watermark data symbols [A1 A2 A3] based on the further timestamp symbol value T0(2) corresponding to the preceding timestamp cycle, and the process repeats. 
     In some examples, the watermark validator  510  indicates that the decoded watermark data symbols [A1 A2 A3] (or the modified decoded watermark data symbols [S1′ S2′ S3′]) are valid if some (e.g., 2) of the decoded watermark data symbols [A1 A2 A3] (or [S1′ S2′ S3′]) are related to the corresponding symbols [A4 A5 A6] by the same offset. In some such examples, the decoded symbol modifier  515  initially modifies the subset of decoded watermark data symbols [A1 A2 A3] based on the value of the further timestamp symbol T0 corresponding to the current timestamp cycle. If the resulting modified decoded watermark data symbols [S1′ S2′ S3′] yield a validation with all symbols related by the same offset, the process stops and the decoded timestamp  210  is determined to represent the timestamp cycle corresponding the value of the further timestamp symbol T0. However, if the resulting modified decoded watermark data symbols [S1′ S2′ S3′] yield a validation with just some, but not all, symbols related by the same offset, the decoded symbol modifier  515  tries modifying the subset of decoded watermark data symbols [A1 A2 A3] based on other values of the further timestamp symbol T0 (e.g., in order of preceding timestamp cycles) to attempt to find one that yield a validation with all symbols related by the same offset. However, if no value of the further timestamp symbol T0 yields a validation with all symbols related by the same offset, then value of the further timestamp symbol T0 corresponding to the first validation having some, but not all, symbols being related by the same offset is used to identify the particular timestamp cycle represented by the timestamp  210 . 
     The timestamp cycle decoder  520  of the illustrated example is included in the watermark decoder  500  to decode the particular timestamp cycle to be represented by the timestamp  210  decoded by the symbol decoder  505  for a detected watermark  200 . In the illustrated example, the timestamp cycle decoder  520  determines that the detected watermark  200  is identified by the particular one of the group of possible timestamp cycles corresponding to the particular value of the further timestamp symbol T0 that the yielded a valid subset of decoded (and potentially modified) symbols for the data payload  210  of the watermark  200 . For example, if the decoded symbols obtained for the data payload  210  are determined to be valid when the symbols are modified based on a first value of the further timestamp symbol T0, the timestamp cycle decoder  520  determines the detected watermark  200  is associated with a first timestamp cycle corresponding to the first value of the further timestamp symbol T0. However, if the decoded symbols obtained for the data payload  210  is determined to be valid when the symbols are modified based on a second value of the further timestamp symbol T0, the timestamp cycle decoder  520  determines the detected watermark  200  is associated with a second timestamp cycle corresponding to the second value of the further timestamp symbol T0. Likewise, if the decoded symbols obtained for the data payload  210  are determined to be valid when the symbols are modified based on a third value of the further timestamp symbol T0, the timestamp cycle decoder  520  determines the detected watermark  200  is associated with a third timestamp cycle corresponding to the first value of the further timestamp symbol T0, and so on. As such, the timestamp cycle decoder  520  is an example of means for associating a watermark with a first one of a plurality of timestamp cycles when a first subset of decoded watermark data symbols is valid, and when the first subset of decoded watermark data symbols is not valid, associating the watermark with a second one of a plurality of timestamp cycles identified by the further timestamp symbol when a modified subset of the decoded watermark data symbols (which are modified based on the further timestamp symbol) is determined to be valid. 
     The watermark reporter  525  of the illustrated example is included in the watermark decoder  500  to report the final version of the watermark  200  decoded from the monitored media. For example, the watermark reporter  525  reports the data payload  205  of the decoded watermark  200  to be the set of decoded data symbols with any modification that was performed to yield a valid data payload  205  as determined by the watermark validator  510 . The watermark reporter  525  of the illustrated example reports the timestamp payload  210  of the watermark  200  as the time value represented by the decoded symbols of the timestamp  210  adjusted, if appropriate, by a number of timestamp periods corresponding to the timestamp cycle encoded in the watermark  200 , as described above. For example, watermark reporter  525  may report the time represented by the decoded timestamp  210  to be the value of the timestamp  210  when the timestamp cycle decoder  520  determines the timestamp  210  represents (is associated with) the first timestamp cycle of the group of possible timestamp cycles, and may report the time represented by the decoded timestamp  210  to be the value of the timestamp  210  offset by one timestamp period when the timestamp cycle decoder  520  determines the timestamp  210  represents (is associated with) the second timestamp cycle of the group, etc. As such, watermark reporter  525  is an example of means for constructing final watermark data from watermark symbols decoded from a detected watermark and modified according to a particular further timestamp symbol identifying to particular timestamp cycle represented by the timestamp of the watermark. The watermark reporter  525  then reports the decoded watermark  200  to the central facility  190 , as described above. 
     While example manners of implementing the watermark encoder  310  and the watermark decoder  500  are illustrated in  FIGS.  3 - 5   , one or more of the elements, processes and/or devices illustrated in  FIGS.  3 - 5    may be combined, divided, re-arranged, omitted, eliminated and/or implemented in any other way. Further, the example data generator  405 , the example timestamp generator  410 , the example timestamp cycle evaluator  415 , the example encoded symbol modifier  420 , the example watermark embedder  425 , the example symbol decoder  505 , the example watermark validator  510 , the example decoded symbol modifier  515 , the example timestamp cycle decoder  520 , the example watermark reported  525  and/or, more generally, the example watermark encoder  310  and the example watermark decoder  500  of  FIGS.  3 - 5    may be implemented by hardware, software, firmware and/or any combination of hardware, software and/or firmware. Thus, for example, any of the example data generator  405 , the example timestamp generator  410 , the example timestamp cycle evaluator  415 , the example encoded symbol modifier  420 , the example watermark embedder  425 , the example symbol decoder  505 , the example watermark validator  510 , the example decoded symbol modifier  515 , the example timestamp cycle decoder  520 , the example watermark reported  525  and/or, more generally, the example watermark encoder  310  and the example watermark decoder  500  could be implemented by one or more analog or digital circuit(s), logic circuits, programmable processor(s), programmable controller(s), graphics processing unit(s) (GPU(s)), digital signal processor(s) (DSP(s)), application specific integrated circuit(s) (ASIC(s)), programmable logic device(s) (PLD(s)) and/or field programmable logic device(s) (FPLD(s)). When reading any of the apparatus or system claims of this patent to cover a purely software and/or firmware implementation, at least one of the example watermark encoder  310 , the example watermark decoder  500 , the example data generator  405 , the example timestamp generator  410 , the example timestamp cycle evaluator  415 , the example encoded symbol modifier  420 , the example watermark embedder  425 , the example symbol decoder  505 , the example watermark validator  510 , the example decoded symbol modifier  515 , the example timestamp cycle decoder  520  and/or the example watermark reported  525  is/are hereby expressly defined to include a non-transitory computer readable storage device or storage disk such as a memory, a digital versatile disk (DVD), a compact disk (CD), a Blu-ray disk, etc. including the software and/or firmware. Further still, the example watermark encoder  310  and/or the example watermark decoder  500  may include one or more elements, processes and/or devices in addition to, or instead of, those illustrated in  FIGS.  3 - 5   , and/or may include more than one of any or all of the illustrated elements, processes and devices. As used herein, the phrase “in communication,” including variations thereof, encompasses direct communication and/or indirect communication through one or more intermediary components, and does not require direct physical (e.g., wired) communication and/or constant communication, but rather additionally includes selective communication at periodic intervals, scheduled intervals, aperiodic intervals, and/or one-time events. 
     Flowcharts representative of example hardware logic, machine readable instructions, hardware implemented state machines, and/or any combination thereof for implementing the example watermark encoder  310  and the example watermark decoder  500  are shown in  FIGS.  6 - 7   . In these examples, the machine readable instructions may be one or more executable programs or portion(s) thereof for execution by a computer processor, such as the processor  812  and/or the processor  912  shown in the example processor platform  800  and/or the example processor platform  900  discussed below in connection with  FIGS.  8 - 9   . The one or more programs, or portion(s) thereof, may be embodied in software stored on a non-transitory computer readable storage medium such as a CD-ROM, a floppy disk, a hard drive, a DVD, a Blu-ray disk™, or a memory associated with the processor  812  and/or the processor  912 , but the entire program or programs and/or parts thereof could alternatively be executed by a device other than the processor  812  and/or the processor  912  and/or embodied in firmware or dedicated hardware (e.g., implemented by an ASIC, a PLD, an FPLD, discrete logic, etc.). Further, although the example program(s) is(are) described with reference to the flowcharts illustrated in  FIGS.  6 - 7   , many other methods of implementing the example watermark encoder  310  and the example watermark decoder  500  may alternatively be used. For example, with reference to the flowcharts illustrated in  FIGS.  6 - 7   , the order of execution of the blocks may be changed, and/or some of the blocks described may be changed, eliminated, combined and/or subdivided into multiple blocks. Additionally or alternatively, any or all of the blocks may be implemented by one or more hardware circuits (e.g., discrete and/or integrated analog and/or digital circuitry, a Field Programmable Gate Array (FPGA), an ASIC, a comparator, an operational-amplifier (op-amp), a logic circuit, etc.) structured to perform the corresponding operation without executing software or firmware. 
     As mentioned above, the example processes of  FIGS.  6 - 7    may be implemented using executable instructions (e.g., computer and/or machine readable instructions) stored on a non-transitory computer and/or machine readable medium such as a hard disk drive, a flash memory, a read-only memory, a compact disk, a digital versatile disk, a cache, a random-access memory and/or any other storage device or storage disk in which information is stored for any duration (e.g., for extended time periods, permanently, for brief instances, for temporarily buffering, and/or for caching of the information). As used herein, the term non-transitory computer readable medium is expressly defined to include any type of computer readable storage device and/or storage disk and to exclude propagating signals and to exclude transmission media. Also, as used herein, the terms “computer readable” and “machine readable” are considered equivalent unless indicated otherwise. 
     “Including” and “comprising” (and all forms and tenses thereof) are used herein to be open ended terms. Thus, whenever a claim lists anything following any form of “include” or “comprise” (e.g., comprises, includes, comprising, including, etc.), it is to be understood that additional elements, terms, etc. may be present without falling outside the scope of the corresponding claim. As used herein, when the phrase “at least” is used as the transition term in a preamble of a claim, it is open-ended in the same manner as the term “comprising” and “including” are open ended. The term “and/or” when used, for example, in a form such as A, B, and/or C refers to any combination or subset of A, B, C such as (1) A alone, (2) B alone, (3) C alone, (4) A with B, (5) A with C, (6) B with C, and (7) A with B and with C. 
     An example program  600  that may be executed to implement the example watermark encoder  310  of  FIGS.  3  and/or  4    is illustrated in  FIG.  6   . With reference to the preceding figures and associated written descriptions, the example program  600  of  FIG.  6    begins execution at block  605  at which the example watermark embedder  425  of the watermark encoder  310  obtains a piece of media be watermarked, such as from the example media database  305 , as described above. At block  610 , the example data generator  405  of the watermark encoder  310  obtains, as described above, the data symbols of the data payload  205  of the watermark  200  to be embedded in the media. Also at block  610 , the example timestamp generator  410  of the watermark encoder  310  obtains, as described above, the timestamp symbols of the timestamp payload  210  of the watermark  200  to be embedded in the media. At block  615 , the example timestamp cycle evaluator  415  of the watermark encoder  310  determines, as described above, which one of a group of timestamp cycles is to be represented by the timestamp  210  obtained at block  610 . 
     At block  620 , the example encoded symbol modifier  420  of the watermark encoder  310  determines whether the particular timestamp cycle to be represented by the timestamp  210  is to be encoded in the watermark  200  by modifying data symbols of the data payload  205  of the watermark  200  based on a further timestamp symbol T0, as described above. If symbol modification is to be performed (at block  620 ), the encoded symbol modifier  420  modifies data symbols of the data payload  205  of the watermark  200  based on the value of the further timestamp symbol T0 identifying the particular timestamp cycle to be represented by the timestamp  210 , as described above. At block  630 , the watermark embedder  425  embeds the watermark  200  in the media, as described above. 
     An example program  700  that may be executed to implement the example watermark decoder  500  of  FIG.  5    is illustrated in  FIG.  7   . With reference to the preceding figures and associated written descriptions, the example program  700  of  FIG.  7    begins execution at block  705  at which the example symbol decoder  505  of the watermark decoder  500  accesses monitored media. At block  710 , the symbol decoder  505  detects a watermark  200  embedded in the monitored media. At block  715 , the example timestamp cycle decoder  520  of the watermark decoder  500  initializes the timestamp cycle to be associated with a timestamp of the watermark  200  to be an initial timestamp cycle, as described above. In some examples, at block  715 , timestamp cycle decoder  520  sets the initial timestamp cycle to be the one of the group of possible timestamp cycles corresponding to a current time, as described above. At block  715 , the example decoded symbol modifier  515  of the watermark decoder  500  initializes the value of the further timestamp symbol T0 to be the value identifying the initialized timestamp cycle to be evaluated, as described above. 
     At block  720 , the symbol decoder  505  decodes the symbols of the detected watermark  200 , including the decoded data symbols for the data payload  205  of the watermark  200  and the decoded timestamp symbols for the timestamp payload of the watermark  200 , after the decoded data symbols have been modified based on the further timestamp symbol T0, as described above. At block  725 , the example watermark validator  510  determines, as described above, whether the sequence of decoded data symbols for the data payload  205  is valid. If the sequence of decoded data symbols is not valid (block  725 ), at block  730  the decoded symbol modifier  515  modifies, as described above, symbols of the decoded data payload  205  based on another value of the further timestamp symbol T0 corresponding to another possible timestamp cycle that can be represented by the decoded timestamp  210 , as described above. Blocks  725  and  730  are repeated until the watermark validator  510  determines a particular value of the further timestamp symbol T0 yields valid decoded data symbols for the data payload  205 , as described above. At block  735 , the timestamp cycle decoder  520  associates the detected watermark  200  with the particular timestamp cycle identified by the particular value of the further timestamp symbol T0 that yielded valid decoded data symbols for the data payload  205 , as described above. At block  740 , the example watermark reported  525  of the watermark decoder  500  reports, as described above, the final version of the detected watermark  200 , which includes the final sequence of decoded data symbols for the data payload  205  (e.g., with symbols modified based on the value of the further timestamp symbol T0 determined to be valid) and the timestamp payload  210  adjusted based on the particular timestamp cycle determined to be associated with the detected watermark  200 . 
       FIG.  8    is a block diagram of an example processor platform  800  structured to execute the instructions of  FIG.  6    to implement the example watermark encoder  310  of  FIGS.  3  and/or  4   . The processor platform  800  can be, for example, a server, a personal computer, a workstation, a self-learning machine (e.g., a neural network), a mobile device (e.g., a cell phone, a smart phone, a tablet such as an iPad™), a personal digital assistant (PDA), an Internet appliance, a DVD player, a CD player, a digital video recorder, a Blu-ray player, a gaming console, a personal video recorder, a set top box, a digital camera, a headset or other wearable device, or any other type of computing device. 
     The processor platform  800  of the illustrated example includes a processor  812 . The processor  812  of the illustrated example is hardware. For example, the processor  812  can be implemented by one or more integrated circuits, logic circuits, microprocessors or controllers from any desired family or manufacturer. The hardware processor  812  may be a semiconductor based (e.g., silicon based) device. In this example, the processor  812  implements the example data generator  405 , the example timestamp generator  410 , the example timestamp cycle evaluator  415 , the example encoded symbol modifier  420  and/or the example watermark embedder  425 . 
     The processor  812  of the illustrated example includes a local memory  813  (e.g., a cache). The processor  812  of the illustrated example is in communication with a main memory including a volatile memory  814  and a non-volatile memory  816  via a link  818 . The link  818  may be implemented by a bus, one or more point-to-point connections, etc., or a combination thereof. The volatile memory  814  may be implemented by Synchronous Dynamic Random Access Memory (SDRAM), Dynamic Random Access Memory (DRAM), RAMBUS® Dynamic Random Access Memory (RDRAM®) and/or any other type of random access memory device. The non-volatile memory  816  may be implemented by flash memory and/or any other desired type of memory device. Access to the main memory  814 ,  816  is controlled by a memory controller. 
     The processor platform  800  of the illustrated example also includes an interface circuit  820 . The interface circuit  820  may be implemented by any type of interface standard, such as an Ethernet interface, a universal serial bus (USB), a Bluetooth® interface, a near field communication (NFC) interface, and/or a PCI express interface. 
     In the illustrated example, one or more input devices  822  are connected to the interface circuit  820 . The input device(s)  822  permit(s) a user to enter data and/or commands into the processor  812 . The input device(s) can be implemented by, for example, an audio sensor, a microphone, a camera (still or video), a keyboard, a button, a mouse, a touchscreen, a track-pad, a trackball, a trackbar (such as an isopoint), a voice recognition system and/or any other human-machine interface. Also, many systems, such as the processor platform  800 , can allow the user to control the computer system and provide data to the computer using physical gestures, such as, but not limited to, hand or body movements, facial expressions, and face recognition. 
     One or more output devices  824  are also connected to the interface circuit  820  of the illustrated example. The output devices  824  can be implemented, for example, by display devices (e.g., a light emitting diode (LED) display, an organic light emitting diode (OLED) display, a liquid crystal display (LCD), a cathode ray tube (CRT) display, an in-place switching (IPS) display, a touchscreen, etc.), a tactile output device, a printer and/or speakers(s). The interface circuit  820  of the illustrated example, thus, typically includes a graphics driver card, a graphics driver chip or a graphics driver processor. 
     The interface circuit  820  of the illustrated example also includes a communication device such as a transmitter, a receiver, a transceiver, a modem, a residential gateway, a wireless access point, and/or a network interface to facilitate exchange of data with external machines (e.g., computing devices of any kind) via a network  826 . The communication can be via, for example, an Ethernet connection, a digital subscriber line (DSL), connection, a telephone line connection, coaxial cable system, a satellite system, a line-of-site wireless system, a cellular telephone system, etc. 
     The processor platform  800  of the illustrated example also includes one or more mass storage devices  828  for storing software and/or data. Examples of such mass storage devices  828  include floppy disk drives, hard drive disks, compact disk drives, Blu-ray disk drives, redundant array of independent disks (RAID) systems, and digital versatile disk (DVD) drives. 
     The machine executable instructions  832  corresponding to the instructions of  FIG.  6    may be stored in the mass storage device  828 , in the volatile memory  814 , in the non-volatile memory  816 , in the local memory  813  and/or on a removable non-transitory computer readable storage medium, such as a CD or DVD  836 . 
       FIG.  9    is a block diagram of an example processor platform  900  structured to execute the instructions of  FIG.  7    to implement the example watermark decoder  500  of  FIG.  5   . The processor platform  900  can be, for example, a server, a personal computer, a workstation, a self-learning machine (e.g., a neural network), a mobile device (e.g., a cell phone, a smart phone, a tablet such as an iPad™), a PDA, an Internet appliance, a DVD player, a CD player, a digital video recorder, a Blu-ray player, a gaming console, a personal video recorder, a set top box, a digital camera, a headset or other wearable device, or any other type of computing device. 
     The processor platform  900  of the illustrated example includes a processor  912 . The processor  912  of the illustrated example is hardware. For example, the processor  912  can be implemented by one or more integrated circuits, logic circuits, microprocessors or controllers from any desired family or manufacturer. The hardware processor  912  may be a semiconductor based (e.g., silicon based) device. In this example, the processor  912  implements the example symbol decoder  505 , the example watermark validator  510 , the example decoded symbol modifier  515 , the example timestamp cycle decoder  520  and/or the example watermark reported  525 . 
     The processor  912  of the illustrated example includes a local memory  913  (e.g., a cache). The processor  912  of the illustrated example is in communication with a main memory including a volatile memory  914  and a non-volatile memory  916  via a link  918 . The link  918  may be implemented by a bus, one or more point-to-point connections, etc., or a combination thereof. The volatile memory  914  may be implemented by SDRAM, DRAM, RDRAM® and/or any other type of random access memory device. The non-volatile memory  916  may be implemented by flash memory and/or any other desired type of memory device. Access to the main memory  914 ,  916  is controlled by a memory controller. 
     The processor platform  900  of the illustrated example also includes an interface circuit  920 . The interface circuit  920  may be implemented by any type of interface standard, such as an Ethernet interface, a USB interface, a Bluetooth® interface, an NFC interface, and/or a PCI express interface. 
     In the illustrated example, one or more input devices  922  are connected to the interface circuit  920 . The input device(s)  922  permit(s) a user to enter data and/or commands into the processor  912 . The input device(s) can be implemented by, for example, an audio sensor, a microphone, a camera (still or video), a keyboard, a button, a mouse, a touchscreen, a track-pad, a trackball, a trackbar (such as an isopoint), a voice recognition system and/or any other human-machine interface. Also, many systems, such as the processor platform  900 , can allow the user to control the computer system and provide data to the computer using physical gestures, such as, but not limited to, hand or body movements, facial expressions, and face recognition. 
     One or more output devices  924  are also connected to the interface circuit  820  of the illustrated example. The output devices  924  can be implemented, for example, by display devices (e.g., an LED display, an OLED display, an LCD display, a CRT display, an IPS display, a touchscreen, etc.), a tactile output device, a printer and/or speakers(s). The interface circuit  920  of the illustrated example, thus, typically includes a graphics driver card, a graphics driver chip or a graphics driver processor. 
     The interface circuit  920  of the illustrated example also includes a communication device such as a transmitter, a receiver, a transceiver, a modem, a residential gateway, a wireless access point, and/or a network interface to facilitate exchange of data with external machines (e.g., computing devices of any kind) via a network  926 . The communication can be via, for example, an Ethernet connection, a DSL, connection, a telephone line connection, coaxial cable system, a satellite system, a line-of-site wireless system, a cellular telephone system, etc. 
     The processor platform  900  of the illustrated example also includes one or more mass storage devices  928  for storing software and/or data. Examples of such mass storage devices  928  include floppy disk drives, hard drive disks, compact disk drives, Blu-ray disk drives, RAID systems, and DVD drives. 
     The machine executable instructions  932  corresponding to the instructions of  FIG.  7    may be stored in the mass storage device  928 , in the volatile memory  914 , in the non-volatile memory  916 , in the local memory  913  and/or on a removable non-transitory computer readable storage medium, such as a CD or DVD  936 . 
     From the foregoing, it will be appreciated that example methods, apparatus and articles of manufacture have been disclosed that extend a time range supported by a media watermark. Example watermarking techniques disclosed herein provide technical solutions to the problem of extending a timestamp range supported by a watermark, but without the need to change the number of timestamp symbols or restructure the watermark. Disclosed example watermarking techniques achieve this technical solution by modifying data symbols of the watermark based on different values of further timestamp symbol to implicitly encode different possible timestamp cycles to be represented by the watermark timestamp. 
     Although certain example methods, apparatus and articles of manufacture have been disclosed herein, the scope of coverage of this patent is not limited thereto. On the contrary, this patent covers all methods, apparatus and articles of manufacture fairly falling within the scope of the claims of this patent.