Abstract: Consistent with the present disclosure, an encoder circuit is provided at a transmit side of an optical fiber link that maps an input sequence of bits of fixed length k a sequence of symbols of a codeword of length n, such that the symbols of the codeword define a predetermined transmission probability distribution. Preferably, each symbol of the codeword is generated during a corresponding clock cycle, such that after n clock cycles, a complete codeword corresponding to the input bit sequence is output. On a receive end of the link, a decoder is provided that outputs the k-bit sequence every n clock cycles. Accordingly, buffers need not be provided at the output of the encoder and the input of the decoder, such that processing of the input sequence, codewords, and output sequence may be achieved efficiently without large buffers and complicated circuitry. Moreover, the input sequence, with any binary alphabet may be matched to a desired output distribution with any arbitrary alphabet.

Abstract: Consistent with the present disclosure, an encoder circuit is provided at a transmit side of an optical fiber link that maps an input sequence of bits of fixed length k to a sequence of symbols of a codeword of length n, such that the symbols of the codeword define a predetermined transmission probability distribution. In one example, each subgroup of bits of the k input bit sequence is provided to a respective look-up table, whereby the sub-group of bits constitutes an address of a particular memory location in the corresponding look-up table. Based on the address, the contents at the particular memory location addressed by each subgroup of bits are output as a corresponding portion of a codeword. Each such codeword portion is provided to a further memory or buffer, such that the entire codeword is assembled in the buffer and output to forward error correction (FEC) circuitry.

Abstract: Systems and methods for improving the error floor performance in decoding generalized product codes (GPC) are described. The systems and methods can implement a two stage process to decode a GPC block code and break a stall error pattern for the decoding the block code. In the first stage, erroneuous bits in a codeword can be flagged. In the second stage, some of these bits and related bits in a codeword can be toggled to generate one or more test patterns. The test patterns can be decoded and one of them can be selected using a particular selection criteria to ultimately break the stall error pattern and improve the error floor performance.

Abstract: Optical transmitters and receivers for improving synchronization of data transmitted over an optical network are described. The receiver can perform non-linear filtering as part of framer index estimation operations to improve the synchronization. The receiver can determine estimated positions of framer indices in data frames received from the transmitter. Next, using a non-linear filter, the receiver can remove estimated positions that are likely erroneous or are greater than a threshold away from the median or mode estimated framer index position. By removing the likely erroneous estimated positions, the receiver can then determine the estimated position of a framer index position for multiple frames with greater confidence.

Abstract: Probabilistic constellation shaping (PCS) is applied to a desired probability distribution over the 2-D constellation points. Constellation points are partitioned into multiple disjoint sets in which all the constellation points within a subset have the same energy level (i.e., amplitude) or distance from the origin on the complex plane. Each of the sets may be further subdivided into smaller disjoint sets of constellation points to facilitate labeling of the constellation points. The sets may be indexed from 0 to the total number of disjoint sets to form an index set. The desired distribution may then be applied over the index set either using a distribution matcher (DM) or using a lookup table. The desired distribution may be generated before forward error correction (FEC) encoding that preserves the generated amplitude distribution through FEC encoding of data bits.

Abstract: Consistent with a further aspect of the present disclosure, previously encoded data is stored in a memory, and an encoder accesses both input data and previously encoded data to generate new encoded data or a new codeword. Each codeword is stored in a row of the memory, and with each newly generated codeword, each previously stored code word is shifted to an adjacent row of the memory. In one example, the memory is delineated as a plurality of blocks including rows and columns of bits. When generating a new code word, randomly selected columns of bits in the memory are read from randomly selected blocks of the memory and supplied to the encoder. In this manner the number of times the memory is access is reduced and power consumption is reduced.

Abstract: Methods, systems, and apparatus, including computer programs encoded on computer storage media, for performing asymmetric pulse-shaping filtering. In some implementations, a receiver comprises a detector circuit operable to receive optical signal data from an optical link. The receiver comprises a filter circuit, coupled to the detector circuit, operable to (i) filter the optical signal data according to an asymmetric filtering scheme and (ii) output the filtered optical signal data, wherein the asymmetric filtering scheme comprises utilizing a shaping filter with first criteria, the first criteria including one or more values greater than one or more values of second criteria utilized by a shaping filter at a transmitter, the transmitter communicating with the receiver.

Abstract: Joint estimation of the framer index and the frequency offset in an optical communication system are described among various other features. A transmitter can transmit data frames using pilot and framer symbols. A receiver can estimate the framer index and frequency offset using the pilot and framer symbols, and identify the beginning of a header portion of a data frame. By identifying the beginning of the header portion of a data frame, the receiver can synchronize, with less error, the data transmitted by the transmitter and the data it received. To further improve the framer index estimation, a lock indicator signal can be generated to signal to other receiver components that the estimated framer indices are reliable. The receiver can determine frequency offset and additional framer index estimations with increased reliability when performed after the lock indicator signal is generated.

Abstract: Joint estimation of the framer index and the frequency offset in an optical communication system are described among various other features. A transmitter can transmit data frames using pilot and framer symbols. A receiver can estimate the framer index and frequency offset using the pilot and framer symbols, and identify the beginning of a header portion of a data frame. By identifying the beginning of the header portion of a data frame, the receiver can then process data received from the transmitter in a manner synchronous to the manner in which the data was transmitted by the transmitter.

Abstract: Consistent with the present disclosure, an encoder circuit is provided at a transmit side of an optical fiber link that maps an input sequence of bits of fixed length k a sequence of symbols of a codeword of length n, such that the symbols of the codeword define a predetermined transmission probability distribution. Preferably, each symbol of the codeword is generated during a corresponding clock cycle, such that after n clock cycles, a complete codeword corresponding to the input bit sequence is output. On a receive end of the link, a decoder is provided that outputs the k-bit sequence every n clock cycles. Accordingly, buffers need not be provided at the output of the encoder and the input of the decoder, such that processing of the input sequence, codewords, and output sequence may be achieved efficiently without large buffers and complicated circuitry. Moreover, the input sequence, with any binary alphabet may be matched to a desired output distribution with any arbitrary alphabet.

Abstract: Joint estimation of the framer index and the frequency offset in an optical communication system are described among various other features. A transmitter can transmit data frames using pilot and framer symbols. A receiver can estimate the framer index and frequency offset using the pilot and framer symbols, and identify the beginning of a header portion of a data frame. By identifying the beginning of the header portion of a data frame, the receiver can then process data received from the transmitter in a manner synchronous to the manner in which the data was transmitted by the transmitter.

Abstract: Systems and methods for more efficiently decoding generalized product codes (GPC) are described. A receiving device equipped with a decoder is configured to receive GPC-encoded signals and implement an early termination method to avoid executing multiple operations of the decoding scheme typically used by the receiving device. The receiving device can identify whether a particular condition is satisfied when decoding a signal, and if the condition is satisfied, can omit certain operations of the decoding scheme and thereby reduce power consumption. The particular condition can be satisfied when the syndromes for sign bits in a codeword associated with the received signal are zero.

Abstract: Joint estimation of the framer index and the frequency offset in an optical communication system are described among various other features. A transmitter can transmit data frames using pilot and framer symbols. A receiver can estimate the framer index and frequency offset using the pilot and framer symbols, and identify the beginning of a header portion of a data frame. By identifying the beginning of the header portion of a data frame, the receiver can then process data received from the transmitter in a manner synchronous to the manner in which the data was transmitted by the transmitter.

Abstract: Joint estimation of the framer index and the frequency offset in an optical communication system are described among various other features. A transmitter can transmit data frames using pilot and framer symbols. A receiver can estimate the framer index and frequency offset using the pilot and framer symbols, and identify the beginning of a header portion of a data frame. By identifying the beginning of the header portion of a data frame, the receiver can then process data received from the transmitter in a manner synchronous to the manner in which the data was transmitted by the transmitter.

Abstract: Joint estimation of the framer index and the frequency offset in an optical communication system are described among various other features. A transmitter can transmit data frames using pilot and framer symbols. A receiver can estimate the framer index and frequency offset using the pilot and framer symbols, and identify the beginning of a header portion of a data frame. By identifying the beginning of the header portion of a data frame, the receiver can then process data received from the transmitter in a manner synchronous to the manner in which the data was transmitted by the transmitter.

Abstract: Optical transmitters and receivers for improving synchronization of data transmitted over an optical network are described. The receiver can perform non-linear filtering as part of framer index estimation operations to improve the synchronization. The receiver can determine estimated positions of framer indices in data frames received from the transmitter. Next, using a non-linear filter, the receiver can remove estimated positions that are likely erroneous or are greater than a threshold away from the median or mode estimated framer index position. By removing the likely erroneous estimated positions, the receiver can then determine the estimated position of a framer index position for multiple frames with greater confidence.

Abstract: Joint estimation of the framer index and the frequency offset in an optical communication system are described among various other features. A transmitter can transmit data frames using pilot and framer symbols. A receiver can estimate the framer index and frequency offset using the pilot and framer symbols, and identify the beginning of a header portion of a data frame. By identifying the beginning of the header portion of a data frame, the receiver can then process data received from the transmitter in a manner synchronous to the manner in which the data was transmitted by the transmitter.

Abstract: Consistent with the present disclosure, an encoder circuit is provided at a transmit side of an optical fiber link that maps an input sequence of bits of fixed length k a sequence of symbols of a codeword of length n, such that the symbols of the codeword define a predetermined transmission probability distribution. Preferably, each symbol of the codeword is generated during a corresponding clock cycle, such that after n clock cycles, a complete codeword corresponding to the input bit sequence is output. On a receive end of the link, a decoder is provided that outputs the k-bit sequence every n clock cycles. Accordingly, buffers need not be provided at the output of the encoder and the input of the decoder, such that processing of the input sequence, codewords, and output sequence may be achieved efficiently without large buffers and complicated circuitry. Moreover, the input sequence, with any binary alphabet may be matched to a desired output distribution with any arbitrary alphabet.

Abstract: Joint estimation of the framer index and the frequency offset in a optical communication system are described among various other features. A transmitter can transmit data frames using pilot and framer symbols. A receiver can estimate the framer index and frequency offset using the pilot and framer symbols, and identify the beginning of a header portion of a data frame. The estimation can be performed to compensate for delays such as half-symbol delays and differential group delays. By identifying the beginning of the header portion of a data frame while compensating for certain delays, the receiver can synchronize, with less error, the data transmitted by the transmitter and the data it received.

Abstract: Joint estimation of the framer index and the frequency offset in an optical communication system are described among various other features. A transmitter can transmit data frames using pilot and framer symbols. A receiver can estimate the framer index and frequency offset using the pilot and framer symbols, and identify the beginning of a header portion of a data frame. By identifying the beginning of the header portion of a data frame, the receiver can synchronize, with less error, the data transmitted by the transmitter and the data it received. To further improve the framer index estimation, a lock indicator signal can be generated to signal to other receiver components that the estimated framer indices are reliable. The receiver can determine frequency offset and additional framer index estimations with increased reliability when performed after the lock indicator signal is generated.