Generally, a data communications system is defined by its architectural model, the protocols that instantiate each layer of that model, and then by the physical embodiments of those protocol layers. Thus, it is typical to say, “this system implements layers 1 through 7 of the OSI network model, incorporating a custom application program communicating over TCP/IP, with a MAC/PHY later optimized for transmission over printed circuit traces.” However, in practical systems, the details of the lower-level transport, e.g. the wires and the physical signals they carry, may significantly impact the overall performance and capabilities of the system. Thus, a substantial technological corpus has developed to facilitate operation of the PHY or physical level transport on which the network depends.
As examples, optimized line drivers and line receivers may be used to initiate and detect wire transmissions, and in long wire paths intermediary amplifiers may be introduced to mitigate the effects of wire attenuation by restoring the original signal amplitude.
However, if the physical medium (wire or optical fiber) has any dispersive characteristic, the amplitude of signal transitions will not only be attenuated but the rise and fall times of those transitions will also be affected, generally described as a spreading or softening of pulse edges that a receiver may interpret as timing variations. Thus, intermediary devices such as “retimers” both amplify and reclock the signal being regenerated, in an attempt to reconstitute not only the original signal amplitude, but also its pulse edge timing characteristics.
The PHY/MAC layers of the network may impose additional constraints, typically having to do with identification of the start and end of a message block or “packet”, and optionally including an interactive procedure that arbitrates access to a shared communications medium. A “repeater” is generally considered to be an amplifier and pulse regenerator/retimer also having awareness of and participating in those media access behaviors.
Even though intermediate devices such as retimers and repeaters may operate by passing along individual bits without regard to higher-level protocol behavior, they themselves may need to receive and respond to said protocol messages, as part of its general compliance with management, configuration, or other operational system requirements.
In some USB support devices, it may be problematic to provide sufficient internal memory and/or processing power to fully buffer an entire USB message frame. Such buffering is generally considered necessary, as a conventional implementation relies on the state of sync bits received near the end of the message to facilitate parsing message segments (super symbols) earlier in the message.
In an alternative embodiment, a pattern matching operation is used to identify particular USB messages incrementally during data reception, with the eventual reception of sync bits and/or error correction checksum used to confirm the identified message patterns. The amount of local memory used to buffer, compare, and flag identified pattern matches is significantly less than required to buffer an entire frame. In a further embodiment, the need to perform a full forward error correction computation in the event of a detected error may be avoided, further reducing the necessary computational capabilities required.
The Universal Serial Bus (USB) specification has evolved significantly since its inception in 1996. Originally a mechanism for host-to-peripheral device attachment, it has grown to support far more elaborate use cases, ranging from high speed peer-to-peer connection to raw power delivery. Advanced versions of the USB specification have also incorporated other protocol standards, one significant example being Apple's Thunderbolt.
The evolutionary nature of the USB specification, along with the need for each advancement to provide backwards compatibility with earlier versions, have resulted in a layering of multiple data encoding and data integrity functions onto the basic data stream, with a corresponding number of special cases to be handled.
The USB 4 specification describes channels carrying a 10 or 20 Gigabit/second data stream. To facilitate receive clock recovery, the transmitted stream is scrambled using a conventional cyclic sequence generator (typically referred to as a pseudo-random number generator, or a PRNG) initialized at link startup, with data integrity maintained by a forward-error-correction (FEC) code capable of correcting up to two byte errors per message block and detecting larger errors.
As USB receivers often use decision feedback equalization (DFE) to counteract the effects of inter-symbol interference, a single received bit error is likely to result in a block or “burst” of incorrectly decoded bits, as feedback of the incorrect data value through the DFE computation will steer sampling thresholds away from correct levels until the stream of errors finally is flushed from the DFE history. To mitigate this effect, advanced versions of the USB 4 standard specify a pre-coding operation that performs a bitwise integration operation on the transmit data stream, and a complementary differentiation operation on the received data stream. This pre-coding has the effect of converting a block data error into two single-bit errors, one at the start and one at the end of the block. As this is within the correction capability of the FEC code, the result is significantly improved data integrity.
The protocol format for a USB 4 frame is shown in
The two-byte sync field includes four reserved bits and 12 flag bits, each flag bit corresponding to one super symbol of the current frame. A flag set to ‘1’ may indicate that a super symbol in a corresponding index or location of the data frame contains a scrambled or an unscrambled ordered set.
In previous USB protocol versions, each super symbol contained 8 bytes or 64 bits. For compatibility between those legacy versions and the larger 128 byte super symbols of the most recent specification version, two copies of the same 64 bit UOS control message are always transmitted together in USB 4, thus introducing a 128 bit gap or pause in the normal progression of the scrambler. In current USB implementations, the UOS control messages SKIP and TSNOS will periodically be interleaved with scrambled data messages. The UOS control message CL_WAKE2 may also be received at CLOs exit.
A conventional (i.e. prior art) software-oriented parsing of the resulting frame would proceed as:
Receive 192+2+4 bytes into a message buffer
Compute the ECC parity across the entire message. As is well understood in the art, this may entail re-computing the parity as transmitted across the first 194 bytes of the message and comparing the computed result and the 4 byte received FEC parity word. Alternatively, it is known that the same calculation may be configured such that computing the parity over the entire 198 byte message including the received FEC parity word produces a zero result if no error was found. For convenience, the latter computation mode will be assumed without implying limitation.
If errors were found, perform the FEC error recovery procedure to identify the message byte(s) containing errors, and the bits to be corrected in those bytes. (If uncorrectable errors remain, exit this message parsing procedure and initiate whatever resynchronization/recovery procedures are defined for error correction failure.)
For each super symbol in the message, determine if it is scrambled or unscrambled. The sync flags identify super symbols containing ordered sets.
This procedure is straightforward for a typical host computer system or a client device with moderate memory and processing capabilities. However, several aspects of it are intractable or awkward for a low-level embedded device such as a repeater or retimer. First, sufficient memory is needed to store an entire frame, whereas an embedded hardware device may be limited to buffering or storage of no more than tens of bytes. Second, if the FEC parity check indicates an error, the full FEC recovery process must be run to identify where in the frame the error occurs, such computation requiring significant memory and processing capabilities. In the worst case, the sync bits may be in error, which would lead to an inability to identify unscrambled ordered set super symbols, thus leading to a failure to maintain the scrambler synchronization needed to parse subsequent messages.
In contrast, the embodiment described herein may parse super symbols in the received data frame “on the fly”, i.e. as they are received, and process the super symbols as they are received as opposed to buffering the entire frame. In some embodiments, this parsing includes pattern matching of the as-received data to known SOS and UOS messages to identify potential SOS and UOS candidates, which in turn allows dynamic decision making as to whether the descrambler should be advanced or halted as appropriate for the type of super symbol detected, and furthermore direct other elements of the chip to take various other actions such as enter a low-power mode responsive to identifying certain SOS.
In practice, there are only a limited number of possible UOS messages to be identified (in some embodiments, as few as two or three) thus a finite state machine may be used to perform the pattern matching operations. Without implying limitation, the following descriptions assume that the comparison or matching operation occurs for each eight bits (i.e. byte) received, each operation successively comparing eight received bits against corresponding portions of one or more known values representing known UOS message patterns that may be stored in e.g., memory or some other storage circuit. In one such embodiment, an explicit “XOR” comparison is made of the received data byte and a byte of each possible message; in another embodiment, the comparison incorporates “don't care” elements that force a match for those elements regardless of value, allowing two or more messages differing only in a few bit locations to be detected by the same comparison operations. Similarly, known message patterns not extending over the entire 128 (or, for earlier protocol versions, 64) bits of a super symbol may judiciously apply said “don't care” elements to skip the redundant or inapplicable portions of the message.
As shown in
One embodiment buffers and compares incoming data in 8 bit (e.g. byte) increments, and compares using pattern compare circuit 220 each received byte to corresponding byte locations of one or more known UOS stored in storage circuit 230. If the raw (e.g. not unscrambled) contents of the received data stream match one of those detectable message patterns of a given known UOS, a “match counter” maintained e.g., by controller 280 is incremented associated with that message pattern.
If at least six bytes match in a given 64 bit received sequence, the matched sequence is identified as an unscrambled ordered set candidate (UOS candidate.) In a further embodiment, said matching operations are continued across an entire 128 bit super symbol (rather than only the 64 bits of a legacy message length), with a match count of at least 14 bytes out of the potential 16 bytes being considered as a UOS candidate. As the protocol's FEC capabilities allow correction of up to two byte errors per frame, this “6 or more out of 8” or “14 or more out of 16” byte match procedure will detect an incoming message of the desired format, even in the presence of two separate byte errors, e.g. one or more bit errors occurring in each of two different received message bytes. The likelihood of false identification of one of the limited set of detectable UOS messages due to such partial matching is exceedingly small, and in the worst case would result in the need to resynchronize the descrambler before the embedded device can receive a subsequent scrambled message. Statistically, the probability of false identification is estimated as:
which is on the order of 4.6×10−32
In some embodiments, this bit- or byte-wise comparison of buffered super symbols to known UOS messages for identifying UOS candidates may overlap in time or occur essentially in parallel with a similar comparison process identifying known SOS messages. This latter operation includes incrementally descrambling 240 received message data (thus advancing the state of the scrambler by some number of bit intervals) and then performing a pattern comparison operation using a pattern compare circuit 250 that may be similar to that of pattern compare circuit 220 as described above against known SOS message patterns 260. It is possible that by the time that an UOS candidate is identified, the descrambler operating to identify concurrent SOS message comparison operation may have incorrectly advanced by some number of bit times. This would cause the receiver's descrambler state to lose synchronization with the transmitter's scrambler state, impeding further scrambled data reception.
Some embodiments may restore descrambler synchronization by halting advancement of the descrambling operation of descrambler 240 for a predetermined number of bit intervals, e.g. 128 bit intervals for the most recent frame format or 64 bit intervals for older versions, responsive to identifying a UOS candidate by the pattern matching function. Alternative embodiments may remember the value of the scrambler syndrome at the beginning of a super symbol, and then may restore that state to a descrambler that has been clocked or advanced unnecessarily upon detection of a false UOS candidate.
The receive FEC parity check 270 may also be calculated dynamically as the message is received and, if no errors are found and the previously-identified message pattern matches confirmed by the sync bit flags, the actions identified through pattern matching may be acted upon. In some embodiments, said actions may include suspending advancement of the scrambler state for the duration of a super symbol, and executing the USB command associated with the identified UOS message. It should be noted that in some embodiments FEC parity check 270 may compare the locally generated FEC parity word to the received FEC parity word and notify controller 280 of whether or not errors occurred.
It should be reiterated that the FEC parity check 270 is computed over the as-received data bits, thus its computation and verification are independent of the synchronization state of the scrambler, or whether the descrambler 240 is being advanced or halted.
If the number of set sync flag bits does not match the number of UOS super symbols identified by pattern matching, it is possible that a false UOS candidate was identified, thus unnecessarily suspending advancement of the descrambler state. Alternatively, it is possible that one or more of the sync flag bits were received in error.
In one embodiment, if the receive FEC parity check identifies the presence of errors, the pattern matching results are given precedence over the values of the sync flag bits, in both determining the state of the descrambler 240, and in executing the USB commands identified by identifying true UOS and SOS messages. Statistically, the probability of a received sync flag bit error is significantly greater than the probability of a false pattern match as performed by the described embodiment. Although this probability computation assumes the synergistic benefits of pre-coding constraining the creation of blocks of data errors with the two-byte correction offered by FEC, the described message parsing remains functional in the absence of one or both of those protocol functions.
In a further embodiment, if the receive FEC parity check verifies that no errors occurred in a received frame and the number of UOS candidates determined by pattern matching does not correspond with the number of sync flag bits set in that frame, it may be determined that one or more false UOS candidates were detected, and precedence given to the set sync flags over the pattern matching results, suggesting that the scrambler state may have been unnecessarily frozen during on-the-fly UOS pattern matching. Furthermore, the position of the UOS candidates in the received data frame may be checked against the position of the sync bits to determine if a UOS candidate is a true or false UOS candidate. In such an event, the scrambler state may subsequently be re-advanced by the number of bit intervals (64 or 128 per super symbol, depending on the protocol version in use) in the event that the sync bits indicate a false UOS candidate was identified.
As the synchronization of descrambler 240 is maintained at the start of each received frame of symbols, SOS pattern compare 250 may accurately identify various SOS and notify controller 280 to take specific actions within the retimer chip 200 itself. As described above, the retimer chip 200 of
As the retimer in between them has maintained synchronization within its own local descrambler 240, the retimer can accurately identify these SOS messages being conveyed between device 1 and 2. As such, the controller 280 in retimer 200 may configure its own Rx and Tx elements in either direction to enter low-power modes of operation to save power within the chip.
While the above example is given for a low-power initiation handshake protocol, it should be noted that the controller 280 may be configured to take various other actions via identification of SOS messages identified using descrambler 240 and SOS pattern compare circuit 250.
A high-level process description for one embodiment performing such parsing is:
In some embodiments, identifying the UOS candidate includes performing a byte-wise comparison using e.g., pattern compare circuit 220, of bytes in each super symbol of the set of super symbols to corresponding bytes in the one or more known UOS values 230. In some such embodiments, identifying the UOS candidate includes determining that a predetermined number of bytes in a given super symbol are exact matches to the corresponding bytes in a known UOS value. In some embodiments, each super symbol includes 8 bytes, and the pattern compare circuit 220 determines that at least 6 bytes of the given super symbol are matches to the corresponding bytes in the known UOS value 230 to identify the UOS candidate. Alternatively, each super symbol may include 16 bytes, and the pattern compare circuit 220 may determine that at least 14 bytes of the given super symbol are matches to the corresponding bytes in the known UOS value 230 to identify the UOS candidate.
In some embodiments, at least one scrambled super symbol in the subsequent data frame corresponds to a low-power mode initiation command.
In some embodiments, the method 300 includes identifying a second UOS candidate in a set of super symbols of a second received data frame by comparing portions of each super symbol in the second received data frame to corresponding portions of the one or more known UOS values and halting advancement of the descrambling operation for the second UOS candidate responsive to the identification of the second UOS candidate.
In some embodiments, the method includes calculating a second local FEC parity word based on the second received data frame and comparing the second local FEC parity word to a second received FEC parity word.
In some embodiments, the second UOS candidate may be determined to be a true UOS, and thus no advancement of the descrambling operation is required. Two examples of determining the second UOS is a true UOS are described below. In a first embodiment, the second UOS candidate is verified against a corresponding sync bit received in the second received data frame responsive to determining no errors are present according to a comparison of the second local FEC parity word to a second received FEC parity word. In a second embodiment, the second UOS candidate is determined to be a true UOS by determining a bit error is present according to a comparison of the second local FEC parity word to a second received FEC parity word.
In some embodiments similar to those described above, the method 300 may further include determining that the second UOS candidate is another false UOS candidate by determining no errors are present according to a comparison of the second local FEC parity word to a second received FEC parity word, and validating the second UOS candidate against a corresponding sync bit in the second received data frame. Such embodiments may similarly advance the descrambling operation responsive to determining the second UOS candidate is a false UOS candidate to maintain descrambler synchronization.
In some embodiments, a method parses incoming data to identify a message as it is being received. As the USB 4 message FEC can correct up to two independent byte errors per frame, as many as two comparisons each of size (match segment) may fail to match out of the total number of matches per message segment
sizeof(message segment)/sizeof(match segment)
while still identifying that particular received message with high probability.
Various embodiments in accordance with the invention may utilize different criteria as to how accurate a pattern match is acceptable (e.g. how many elements of super-symbol must match a pattern) whether identified matches must be confirmed by association with a properly set sync flag, and under what conditions a FEC parity check error may be ignored. Similarly, different embodiments may choose to pattern match one instance of a 64 bit UOS control message (thus treating actual 128 bit UOS super symbols as two back-to-back control messages) or may pattern match the entire 128 bit sequence consisting of two repeats of the same 64 bit message (with substantially lower risk of false positive identification.) Within the scope of the described embodiments, these criteria may be chosen based on expected correctable and uncorrectable error rates, statistical estimates of match success and match failure, implementation complexity, cost, and power consumption, and the relative benefits and risks of positive or negative match failure rates in identification of particular messages for that particular system and instance.
This application is a continuation of U.S. application Ser. No. 17/834,628, filed Jun. 7, 2022, naming Filippo Borlenghi, entitled “Error-Tolerant Forward Error Correction Ordered Set Message Decoder”, which is a continuation of U.S. application Ser. No. 17/207,565, filed Mar. 19, 2021, now U.S. Pat. No. 11,356,197, granted Jun. 7, 2022, naming Filippo Borlenghi, entitled “Error-Tolerant Forward Error Correction Ordered Set Message Decoder”, which is hereby incorporated herein by reference in its entirety for all purposes.
Number | Name | Date | Kind |
---|---|---|---|
3629824 | Bossen | Dec 1971 | A |
3965418 | Bauer et al. | Jun 1976 | A |
4112264 | Abramson et al. | Sep 1978 | A |
4486739 | Franaszek et al. | Dec 1984 | A |
4772845 | Scott | Sep 1988 | A |
4864303 | Ofek | Sep 1989 | A |
5168509 | Nakamura et al. | Dec 1992 | A |
5566193 | Cloonan | Oct 1996 | A |
5825808 | Hershey et al. | Oct 1998 | A |
5875202 | Venters et al. | Feb 1999 | A |
5881130 | Zhang | Mar 1999 | A |
6097732 | Jung | Aug 2000 | A |
6119263 | Mowbray et al. | Sep 2000 | A |
6128330 | Schilling | Oct 2000 | A |
6163284 | Munakata | Dec 2000 | A |
6175230 | Hamblin et al. | Jan 2001 | B1 |
6188497 | Franck et al. | Feb 2001 | B1 |
6404820 | Postol | Jun 2002 | B1 |
6473877 | Sharma | Oct 2002 | B1 |
6650638 | Walker et al. | Nov 2003 | B1 |
6690739 | Mui | Feb 2004 | B1 |
6865234 | Agazzi | Mar 2005 | B1 |
6963622 | Eroz et al. | Nov 2005 | B2 |
6973613 | Cypher | Dec 2005 | B2 |
6976194 | Cypher | Dec 2005 | B2 |
6982954 | Dhong et al. | Jan 2006 | B2 |
7057546 | Secatch et al. | Jun 2006 | B1 |
7080288 | Ferraiolo et al. | Jul 2006 | B2 |
7082557 | Schauer et al. | Jul 2006 | B2 |
7231558 | Gentieu et al. | Jun 2007 | B2 |
7269130 | Pitio | Sep 2007 | B2 |
7335976 | Chen et al. | Feb 2008 | B2 |
7346819 | Bansal et al. | Mar 2008 | B2 |
7362130 | Broyde et al. | Apr 2008 | B2 |
7362697 | Becker et al. | Apr 2008 | B2 |
7370264 | Worley et al. | May 2008 | B2 |
7643588 | Visalli et al. | Jan 2010 | B2 |
7694204 | Schmidt et al. | Apr 2010 | B2 |
7698088 | Sul et al. | Apr 2010 | B2 |
7734191 | Welch et al. | Jun 2010 | B1 |
7882413 | Chen et al. | Feb 2011 | B2 |
7933770 | Krueger et al. | Apr 2011 | B2 |
8091006 | Prasad et al. | Jan 2012 | B2 |
8185807 | Oh et al. | May 2012 | B2 |
8209580 | Varnica et al. | Jun 2012 | B1 |
8233544 | Bao et al. | Jul 2012 | B2 |
8245102 | Cory et al. | Aug 2012 | B1 |
8279094 | Abbasfar | Oct 2012 | B2 |
8279957 | Tsai et al. | Oct 2012 | B2 |
8341492 | Shen et al. | Dec 2012 | B2 |
8365035 | Hara | Jan 2013 | B2 |
8429492 | Yoon et al. | Apr 2013 | B2 |
8429495 | Przybylski | Apr 2013 | B2 |
8462891 | Kizer et al. | Jun 2013 | B2 |
8521020 | Welch et al. | Aug 2013 | B2 |
8539318 | Shokrollahi et al. | Sep 2013 | B2 |
8578246 | Mittelholzer et al. | Nov 2013 | B2 |
8601340 | Farhoodfar et al. | Dec 2013 | B2 |
8693570 | Wang et al. | Apr 2014 | B2 |
8711919 | Kumar | Apr 2014 | B2 |
8773964 | Hsueh et al. | Jul 2014 | B2 |
8775892 | Zhang et al. | Jul 2014 | B2 |
8949693 | Ordentlich et al. | Feb 2015 | B2 |
9152495 | Losh et al. | Oct 2015 | B2 |
9172412 | Kim et al. | Oct 2015 | B2 |
9178536 | Lee et al. | Nov 2015 | B2 |
9183085 | Northcott | Nov 2015 | B1 |
9300503 | Holden et al. | Mar 2016 | B1 |
9385755 | Petrov | Jul 2016 | B2 |
9444654 | Hormati et al. | Sep 2016 | B2 |
9450612 | Hu et al. | Sep 2016 | B2 |
9455744 | George et al. | Sep 2016 | B2 |
9564926 | Farhoodfar et al. | Feb 2017 | B2 |
9588715 | Staelin et al. | Mar 2017 | B2 |
9608669 | Song et al. | Mar 2017 | B2 |
9667379 | Cronie et al. | May 2017 | B2 |
9852806 | Stauffer et al. | Dec 2017 | B2 |
10243614 | Ulrich et al. | Mar 2019 | B1 |
10396819 | Myung et al. | Aug 2019 | B1 |
10601574 | Hormati | Mar 2020 | B2 |
10873373 | Suh et al. | Dec 2020 | B2 |
20010000219 | Agazzi et al. | Apr 2001 | A1 |
20020154633 | Shin et al. | Oct 2002 | A1 |
20020163881 | Dhong et al. | Nov 2002 | A1 |
20030016770 | Trans et al. | Jan 2003 | A1 |
20030185310 | Ketchum et al. | Oct 2003 | A1 |
20060245757 | Elahmadi et al. | Nov 2006 | A1 |
20060291571 | Divsalar et al. | Dec 2006 | A1 |
20070076871 | Renes | Apr 2007 | A1 |
20070204205 | Niu et al. | Aug 2007 | A1 |
20070283210 | Prasad et al. | Dec 2007 | A1 |
20080016432 | Lablans | Jan 2008 | A1 |
20090110106 | Wornell et al. | Apr 2009 | A1 |
20090141827 | Saito et al. | Jun 2009 | A1 |
20090150754 | Dohmen et al. | Jun 2009 | A1 |
20090316730 | Feng et al. | Dec 2009 | A1 |
20100146363 | Birru et al. | Jun 2010 | A1 |
20100287438 | Lakkis | Nov 2010 | A1 |
20110051854 | Kizer et al. | Mar 2011 | A1 |
20110072330 | Kolze | Mar 2011 | A1 |
20110299555 | Cronie et al. | Dec 2011 | A1 |
20120036415 | Shafrir et al. | Feb 2012 | A1 |
20120272117 | Stadelmeier et al. | Oct 2012 | A1 |
20130223552 | Okada | Aug 2013 | A1 |
20130259113 | Kumar | Oct 2013 | A1 |
20130315264 | Srinivasa et al. | Nov 2013 | A1 |
20130315501 | Atanassov et al. | Nov 2013 | A1 |
20130346830 | Ordentlich et al. | Dec 2013 | A1 |
20140068385 | Zhang et al. | Mar 2014 | A1 |
20140068391 | Goel et al. | Mar 2014 | A1 |
20140079394 | Xie et al. | Mar 2014 | A1 |
20150070201 | Dedic et al. | Mar 2015 | A1 |
20150092532 | Shokrollahi et al. | Apr 2015 | A1 |
20150381315 | Thomson et al. | Dec 2015 | A1 |
20160020796 | Hormati et al. | Jan 2016 | A1 |
20160134267 | Adachi | May 2016 | A1 |
20160380787 | Hormati et al. | Dec 2016 | A1 |
20170017604 | Chen et al. | Jan 2017 | A1 |
20170222752 | Hamada | Aug 2017 | A1 |
20170317855 | Shokrollahi et al. | Nov 2017 | A1 |
20190095380 | Das Sharma | Mar 2019 | A1 |
20200145341 | Das Sharma | May 2020 | A1 |
20200313841 | Ulrich et al. | Oct 2020 | A1 |
Number | Date | Country |
---|---|---|
1671092 | Sep 2005 | CN |
101820288 | Jan 2013 | CN |
1926267 | May 2008 | EP |
WO-2004042991 | May 2004 | WO |
2005002162 | Jan 2005 | WO |
Entry |
---|
International Search Report and Written Opinion for PCT/US2022/021179, dated Jul. 6, 2022, 1-11 (11 pages). |
Belogolovy, A. , et al., “Forward Error Correction for 10GBASE-KR PHY”, IEEE 802.3ap-00/0000r4, Nov. 2005, 1-13 (13 pagges. |
Ben-Neticha, Zouhair , et al., “The “Stretched”—Golay and Other Codes for High-SNR Finite-Delay Quantization of the Gaussian Source at 1/2 Bit Per Sample”, IEEE Transactions on Communications, New York, US, vol. 38, No. 12, XP000203339, Dec. 1990, 2089-2093 (5 pages). |
Burr, A.G. , “Spherical Codes for M-ARY Code Shift Keying”, Second IEE National Conference on Telecommunications, University of York, UK, Apr. 2, 1989, 67-72 (6 pages). |
Ericson, Thomas , et al., “Spherical Codes Generated by Binary Partitions of Symmetric Pointsets”, IEEE Transactions on Information Theory, vol. 41, No. 1, Jan. 1995, 107-129 (23 pages). |
Number | Date | Country | |
---|---|---|---|
20230299879 A1 | Sep 2023 | US |
Number | Date | Country | |
---|---|---|---|
Parent | 17834628 | Jun 2022 | US |
Child | 18322247 | US | |
Parent | 17207565 | Mar 2021 | US |
Child | 17834628 | US |