Methods and systems for analyzing data are disclosed. An example method can comprise receiving a first data signal, decoding the first data signal, determining a second data signal based on the decoded first data signal, and determining a modulation error ratio based on a difference between the first data signal and the second data signal.

A cyclo-stationary characteristic of a communications channel and/or storage media is determined. The cyclo-stationary characteristic has K-cycles, K > 1. Markov transition probabilities are determined that depend on a discrete phase ϕ=t mod K, wherein t is a discrete time value. An encoder to optimize the Markov transition probabilities for encoding data sent through the communications channel and/or stored on the storage media. The optimized Markov transition probabilities are used to decode the data from the communication channel and/or read from the storage media.

A cyclo-stationary characteristic of a communications channel and/or storage media is determined. The cyclo-stationary characteristic has K-cycles, K > 1. Markov transition probabilities are determined that depend on a discrete phase ϕ=t mod K, wherein t is a discrete time value. An encoder to optimize the Markov transition probabilities for encoding data sent through the communications channel and/or stored on the storage media. The optimized Markov transition probabilities are used to decode the data from the communication channel and/or read from the storage media.

Disclosed is a compensation circuit which includes a data analyzer that receives a first bit stream including first to N-th bits, counts a number of times of coincidence of each of first to 2.sup.M-th patterns each having an M-bit size from the first bit stream, and generates a first pattern stream including first to 2.sup.M-th count values each corresponding to the number of times of coincidence of each of the first to 2.sup.M-th patterns, and a compensation calculator that determines first to 2.sup.M-th compensation values based on the first pattern stream such that results of multiplying the first to 2.sup.M-th count values and the first to 2.sup.M-th compensation values one-to-one are even. “N” is a natural number, and “M” is a natural number smaller than “N”.

A device includes a data path, a first interface configured to receive a first memory access request from a first peripheral device, and a second interface configured to receive a second memory access request from a second peripheral device. The device further includes an arbiter circuit configured to, in a first clock cycle, a pre-arbitration winner between a first memory access request and a second memory access request based on a first number of credits allocated to a first destination device and a second number of credits allocated to a second destination device. The arbiter circuit is further configured to, in a second clock cycle select a final arbitration winner from among the pre-arbitration winner and a subsequent memory access request based on a comparison of a priority of the pre-arbitration winner and a priority of the subsequent memory access request.

A decoder circuit includes first and second decoders. The first decoder is a first type of decoder configured to receive data encoded with an error correction code and decode and eliminate errors from a first subset of codewords of the data. The second decoder is a second type of decoder configured receive the data encoded with the error correction code and decode and eliminate errors from a second subset of codewords of the data, different from the first subset of the codewords, without attempting to decode and eliminate errors from the first subset of the codewords.

A device includes an arbiter circuit configured to receive a first request for a resource. The first request is associated with a first credit cost. The arbiter circuit is further configured to receive a second request for the resource. The second request is associated with a second credit cost. The arbiter circuit is further configured to select the first request for the resource as an arbitration winner. The arbiter circuit is further configured to decrement a number of available credits associated with the resource by the first credit cost. The arbiter circuit is further configured to, in response to the number of available credits associated with the resource falling to a lower credit threshold, wait until the number of available credits associated with the resource reaches an upper credit threshold to select an additional arbitration winner for the resource.

An error rate measuring apparatus includes: an operation unit that sets a codeword length, an FEC symbol length, and an FEC symbol error threshold; error counting unit for counting FEC symbol error and an uncorrectable codeword; a display unit that performs display by setting one zone of a display area as one FEC symbol length, matching a zone length of a horizontal axis of the display area with one codeword length, and performing line feed in codeword length units according to presence or absence of the FEC symbol error in FEC symbol length units based on a counting result; search unit for searching for the uncorrectable codeword starting from the cursor on the identification display; and display control unit for performing display control of the cursor at a position of a head error of the searched uncorrectable codeword.

Embodiments relate to the emulation of the effect of Forward Error Correction (FEC) codes, e.g., GF.sup.10 Reed Solomon (RS) FEC codes, on the bit error ratio (BER) of received Pseudo-Random Binary Sequences (PRBS) patterns. In particular, embodiments group errors into RS-FEC symbols and codewords in order to determine if the errors are correctable. By emulating the error correction capabilities of FEC codes in order to determine which errors are correctable by the code, embodiments afford a more accurate representation of the post-FEC BER of RS FEC codes from links carrying PRBS patterns. This FEC code emulation provides error correction statistics, for stand-alone use or for error correction in connection with Bit Error Rate Testers (BERTs).

Methods and systems for analyzing data are disclosed. An example method can comprise receiving a first data signal, decoding the first data signal, determining a second data signal based on the decoded first data signal, and determining a modulation error ratio based on a difference between the first data signal and the second data signal.