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.

The present disclosure includes apparatus, systems, and techniques relating to noise-predictive detector adaptation. A described technique includes operating a decoder system to decode codewords that are based on a received encoded signal by processing the codewords and exchanging information between path and code decoders, operating the path decoder to use estimation parameters to produce first and second paths based on a codeword of the codewords, operating the code decoder to produce a decoded path based on the codeword; determining a winning path of first and second paths based on whether the decoded path matches the first path or the second path; and updating, based on one or more error terms and the winning path, the estimation parameters to favor selection of the winning path by the path decoder and to disfavor selection of a losing path of the first and second paths by the path decoder.

A one-shot state transition decoder receives a codeword having N-bits. The decoder reads a first D-bits of the codeword to determine a stitching location d within the codeword. The stitching location identifies a start bit of unencoded data in the codeword. The codeword is decoded into an output buffer for user data of L bits, where N>L. Parameters of the decoder are set before the decoding, including setting a length of the codeword to N−L+d and a number of expected decoded bits to d. The decoding including decoding the d bits based on a set of state transition probabilities and copying decoded bits into the output buffer, the unencoded data being copied to the end of the output buffer.

In a one-shot state transition encoder, L-bits of user data are received and encoded into a codeword of N-bits, wherein N>L. The encoding of the user data involves repeatedly performing: a) encoding a portion of user bits from the user data to a portion of encoded bits of the codeword based on a set of state transition probabilities, thereby reducing a size of a remaining buffer of the codeword and reducing a number of unencoded bits of the user data; and b) based on the number of unencoded bits of the user data being greater than or equal to the remaining buffer size of the codeword, terminating further encoding and storing the unencoded bits of the user data into the remaining buffer of the codeword.

A decoding circuit and a decoding method based on the Viterbi algorithm are provided. The decoding method includes the following steps: decoding an encoded data based on the Viterbi algorithm to generate a decoded data; performing error correction on the decoded data to obtain a data content of the encoded data; comparing the decoded data and the data content to generate bit correction information; using the encoded data to calculate multiple first branch metrics based on the Viterbi algorithm, the first branch metrics corresponding to a target bit of the data content; adjusting at least one of the first branch metrics based on the data content and the bit correction information to generate multiple second branch metrics; and selecting the first branch metrics or the second branch metrics based on the bit correction information.

Methods and apparatus are provided for calculating branch metrics, associated with possible transitions between states of a trellis, in a sequence detector for detecting symbol values corresponding to samples of an analog signal transmitted over a channel. For each sample and each transition, the method calculates a plurality of distance values indicative of distance between that sample and respective hypothesized sample values for that transition. In parallel with calculation of the distance values, the sample is compared with a set of thresholds, each defined between a pair of successive hypothesized symbol values arranged in value order, to produce a comparison result. An optimum distance value is selected as a branch metric for the transition in dependence on the comparison result.

A decoding circuit and a decoding method based on the Viterbi algorithm are provided. The decoding method includes the following steps: decoding an encoded data based on the Viterbi algorithm to generate a decoded data; performing error correction on the decoded data to obtain a data content of the encoded data; comparing the decoded data and the data content to generate bit correction information; using the encoded data to calculate multiple first branch metrics based on the Viterbi algorithm, the first branch metrics corresponding to a target bit of the data content; adjusting at least one of the first branch metrics based on the data content and the bit correction information to generate multiple second branch metrics; and selecting the first branch metrics or the second branch metrics based on the bit correction information.

In a one-shot state transition encoder, L-bits of user data are received and encoded into a codeword of N-bits, wherein N>L. The encoding of the user data involves repeatedly performing: a) encoding a portion of user bits from the user data to a portion of encoded bits of the codeword based on a set of state transition probabilities, thereby reducing a size of a remaining buffer of the codeword and reducing a number of unencoded bits of the user data; and b) based on the number of unencoded bits of the user data being greater than or equal to the remaining buffer size of the codeword, terminating further encoding and storing the unencoded bits of the user data into the remaining buffer of the codeword.

A system and method for applying noise to data is described. The system accesses a metric value of a metric of each user from a group of users of an application. The metric indicates a measure of an operation of the application by a corresponding user. The system generates noise values and defines a distribution of the noise values to the group of users. The system modifies the metric value of the metric of each user with a corresponding noise value from the noise values based on the distribution.

A decoding apparatus includes a multi-input branch metric calculation unit configured to calculate, by using a branch label corresponding to a path extending toward a state S at a time point N in a trellis diagram and a plurality of reception signal sequences, a branch metric in the state S, a path metric calculation unit configured to calculate a path metric in the state S at the time point N, and a surviving path list memory configured to store path labels corresponding to L path metrics among a plurality of calculated path metrics. The path metric calculation unit generates a path label in the state S at the time point N by combining the branch label with a path label in each of the states at the time point N−1 and the surviving path list memory outputs path labels corresponding to L path metrics.