Abstract: Methods, systems, and apparatus, including computer programs encoded on a computer storage medium, for scalable matrix factorization. A method includes obtaining a Structured Query Language (SQL) query to create a matrix factorization model based on a set of training data, generating SQL sub-queries that don't include non-scalable functions, obtaining the set of training data, and generating a matrix factorization model based on the set of training data and the SQL sub-queries that don't include non-scalable functions.

Abstract: Interleaved Forward Error Correction (FEC) encoded data from multiple FEC encoders for transport over a multi-channel physical transport medium, with cyclical rotation of the FEC encoded data bytes across transport channels in a given transmission interval as well as across time within each transport channel. A plurality of parallel FEC encoders are used to generate respective parallel FEC-encoded data streams, the outputs of which are then interleaved across a plurality of transport channels in a given transmission time interval, and, within each transport channel, the interleaved order varies over the time intervals.

Abstract: Transmission of baseband and carrier-modulated vector codewords, using a plurality of encoders, each encoder configured to receive information bits and to generate a set of baseband-encoded symbols representing a vector codeword; one or more modulation circuits, each modulation circuit configured to operate on a corresponding set of baseband-encoded symbols, and using a respective unique carrier frequency, to generate a set of carrier-modulated encoded symbols; and, a summation circuit configured to generate a set of wire-specific outputs, each wire-specific output representing a sum of respective symbols of the carrier-modulated encoded symbols and at least one set of baseband-encoded symbols.

Abstract: Methods and systems are described for generating a time-varying information signal at an output of a continuous time linear equalizer (CTLE), asynchronously sampling a data signal according to a sampling clock having a frequency less than a data rate of the data signal; generating corresponding pattern-verified samples for at least two data patterns, each of the at least two data patterns having a respective frequency content; determining corresponding frequency-specific voltage measurements associated with each of the at least two data patterns based on the corresponding pattern-verified samples of the at least two data patterns; and adjusting an equalization of the data signal based on a comparison of the corresponding frequency-specific voltage measurements.

Abstract: Multi-mode non-return-to-zero (NRZ) and orthogonal differential vector signaling (ODVS) clock and data recovery circuits having configurable sub-channel multi-input comparator (MIC) circuits for forming a composite phase-error signal from a plurality of data-driven phase-error signals generated using phase detectors in a plurality of receivers configured as ODVS sub-channel MICs generating orthogonal sub-channel outputs in a first mode and a separate first and second data driven phase-error signal from two receivers of a plurality of receivers configured as NRZ receivers in a second mode.

Abstract: An efficient communications apparatus is described for a vector signaling code to transport data and optionally a clocking signal between integrated circuit devices. Methods of designing such apparatus and their associated codes based on a new metric herein called the “ISI Ratio” are described which permit higher communications speed, lower system power consumption, and reduced implementation complexity.

Abstract: Generating, during a first and second signaling interval, an aggregated data signal by forming a linear combination of wire signals received in parallel from wires of a multi-wire bus, wherein at least some of the wire signals undergo a signal level transition during the first and second signaling interval; measuring a signal skew characteristic of the aggregated data signal; and, generating wire-specific skew offset metrics, each wire-specific skew offset metric based on the signal skew characteristic.

Abstract: Methods and systems are described for generating two comparator outputs by comparing a received signal to a first threshold and a second threshold according to a sampling clock, the first and second thresholds determined by an estimated amount of inter-symbol interference on a multi-wire bus, selecting one of the two comparator outputs as a data decision, the selection based on at least one prior data decision, and selecting one of the two comparator outputs as a phase-error decision, the phase error decision selected in response to identification of a predetermined data decision pattern.

Abstract: Methods and systems are described for generating early and late votes for a clock recovery system, each early or late vote associated with a detected transitional data pattern in a data stream, generating a first early-late vote measurement reflective of an imbalance between the early and late votes that are generated during a first time interval, generating a second early-late vote measurement reflective of an imbalance between the early and late votes that are generated during a second time interval, comparing the first and the second early-late vote measurements, and outputting a CDR-lock signal at least in part responsive to determining that the first and the second early-late vote measurements are within a predetermined threshold.

Abstract: Methods and systems are described for measuring a vertical opening of a signal eye of a pulse amplitude modulated (PAM) signal received over a channel to determine a vertically-centered voltage decision threshold of a sampler receiving a sampling clock, determining channel-characteristic parameters indicative of a frequency response of the channel, determining a correctional vernier value from the channel-characteristic parameters, and generating a horizontally-centered voltage decision threshold that introduces a horizontal sampling offset in the sampling clock in a direction closer to a horizontal center of the signal eye by combining the vertically-centered voltage decision threshold and the correctional vernier value.

Abstract: Methods and systems are described for asynchronously measuring an equalized information signal to obtain amplitude information, modifying frequency dependent parameters of a continuous-time linear equalization (CTLE) component of the signal path, determining a correlation between CTLE parameters and signal amplitude, and adjusting, responsive to the correlation, a continuous-time linear equalization (CTLE) code of a CTLE to adjust equalization of the equalized information signal.

Abstract: Methods and systems are described for receiving a plurality of signals corresponding to symbols of a codeword on a plurality of wires of a multi-wire bus, and responsively generating a plurality of sub-channel outputs using a plurality of multi-input comparators (MICs) connected to the plurality of wires of the multi-wire bus, generating a plurality of wire-specific skew control signals, each wire-specific skew control signal of the plurality of wire-specific skew control signals generated by combining (i) one or more sub-channel specific skew measurement signals associated with corresponding sub-channel outputs undergoing a transition and (ii) a corresponding wire-specific transition delta, and providing the plurality of wire-specific skew control signals to respective wire-skew control elements to adjust wire-specific skew.

Abstract: An efficient communications apparatus is described for a vector signaling code to transport data and optionally a clocking signal between integrated circuit devices. Methods of designing such apparatus and their associated codes based on a new metric herein called the “ISI Ratio” are described which permit higher communications speed, lower system power consumption, and reduced implementation complexity.

Abstract: Methods and systems are described for generating a time-varying information signal at an output of a continuous time linear equalizer (CTLE), asynchronously sampling a data signal according to a sampling clock having a frequency less than a data rate of the data signal; generating corresponding pattern-verified samples for at least two data patterns, each of the at least two data patterns having a respective frequency content; determining corresponding frequency-specific voltage measurements associated with each of the at least two data patterns based on the corresponding pattern-verified samples of the at least two data patterns; and adjusting an equalization of the data signal based on a comparison of the corresponding frequency-specific voltage measurements.

Abstract: Methods and systems are described for generating two comparator outputs by comparing a received signal to a first threshold and a second threshold according to a sampling clock, the first and second thresholds determined by an estimated amount of inter-symbol interference on a multi-wire bus, selecting one of the two comparator outputs as a data decision, the selection based on at least one prior data decision, and selecting one of the two comparator outputs as a phase-error decision, the phase error decision selected in response to identification of a predetermined data decision pattern.

Abstract: Methods and systems are described for generating a time-varying information signal at an output of a variable gain amplifier (VGA), sampling, using a sampler having a vertical decision threshold associated with a target signal amplitude, the time-varying information signal asynchronously to generate a sequence of decisions from varying sampling instants in sequential signaling intervals, the sequence of decisions comprising (i) positive decisions indicating the time-varying information signal is above the target signal amplitude and (ii) negative decisions indicating the time-varying information signal is below the target signal amplitude, accumulating a ratio of positive decisions to negative decisions, and generating a gain feedback control signal to adjust a gain setting of the VGA responsive to a mismatch of the accumulated ratio with respect to a target ratio.

Abstract: Methods and systems are described for measuring a vertical opening of a signal eye of a pulse amplitude modulated (PAM) signal received over a channel to determine a vertically-centered voltage decision threshold of a sampler receiving a sampling clock, determining channel-characteristic parameters indicative of a frequency response of the channel, determining a correctional vernier value from the channel-characteristic parameters, and generating a horizontally-centered voltage decision threshold that introduces a horizontal sampling offset in the sampling clock in a direction closer to a horizontal center of the signal eye by combining the vertically-centered voltage decision threshold and the correctional vernier value.

Abstract: Methods and systems are described for receiving symbols of a codeword via wires of a multi-wire bus, the codeword representing an aggregate sum of a plurality of sub-channel constituent codewords, each sub-channel constituent codeword representing a weight applied to an associated sub-channel vector of a plurality of sub-channel vectors of an orthogonal matrix, generating a plurality of comparator outputs using a plurality of common-mode resistant multi-input comparators (MICs), each common-mode resistant MIC having a set of input coefficients representing a corresponding sub-channel vector of the plurality of sub-channel vectors, each sub-channel vector (i) mutually orthogonal and (ii) orthogonal to a common-mode sub-channel vector, outputting a set of forward-channel output bits formed based on the plurality of comparator outputs, obtaining a sequence of reverse-channel bits, and transmitting the sequence of reverse-channel bits by sequentially transmitting common-mode codewords over the wires of the multi-

Abstract: Transmission of baseband and carrier-modulated vector codewords, using a plurality of encoders, each encoder configured to receive information bits and to generate a set of baseband-encoded symbols representing a vector codeword; one or more modulation circuits, each modulation circuit configured to operate on a corresponding set of baseband-encoded symbols, and using a respective unique carrier frequency, to generate a set of carrier-modulated encoded symbols; and, a summation circuit configured to generate a set of wire-specific outputs, each wire-specific output representing a sum of respective symbols of the carrier-modulated encoded symbols and at least one set of baseband-encoded symbols.

Abstract: Methods and systems are described for generating a time-varying information signal at an output of a continuous time linear equalizer (CTLE), asynchronously sampling a data signal according to a sampling clock having a frequency less than a data rate of the data signal; generating corresponding pattern-verified samples for at least two data patterns, each of the at least two data patterns having a respective frequency content; determining corresponding frequency-specific voltage measurements associated with each of the at least two data patterns based on the corresponding pattern-verified samples of the at least two data patterns; and adjusting an equalization of the data signal based on a comparison of the corresponding frequency-specific voltage measurements.