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 memory device can include a memory array, a processor coupled to the memory array, and a decoding apparatus. The decoding apparatus is configured to perform parallel decoding of codewords. Each of the codewords has a plurality of data blocks, each data block having a number of data bits. The decoding apparatus is configured to decode in parallel two or more codewords, which share a common data block, to determine error information associated with each codeword. For each error, the error information identifies a data block having the and associated error bit patterns. The decoding apparatus is configured to update the two or more codewords based on the identified data blocks having errors and the associated error bit patterns.

A method of operating a decoder, which has variable nodes and check nodes, includes receiving variable-to-check (V2C) messages from the variable nodes using a first check node among the check nodes. The number of messages having a specific magnitude among the V2C messages is counted. The magnitude of a check-to-variable (C2V) message to be transmitted to a first variable node, among the variable nodes, is determined based on the count value and the magnitude of a V2C message of the first variable node.

The present disclosure discloses a new coding scheme, which is constructed by superimposing together a pair of basic codes in a twisted manner. A SCL decoding algorithm is proposed for the TPST codes, which may be early terminated by a preset threshold on the empirical divergence functions (EDF) to trade off performance with decoding complexity. The SCL decoding of TPST is based on the efficient list decoding of the basic codes, where the correct candidate codeword in the decoding list is distinguished by employing a typicality-based statistical learning aided decoding algorithm. Lower bounds for the two layers of TPST are derived, which may be used to predict the decoding performance and to show the near-ML performance of the proposed SCL decoding algorithm. The construction of TPST codes may be generalised by allowing different basic codes for the two layers.

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 non-systematic convolutional decoder of a convolutionally encoded multi-level data stream includes a shift register and two or more paths of exclusive-OR (XOR) gates, arranged to reconstruct an original input information stream, each path having a quantiser arranged to quantise the signal to two levels, and a set of XOR gates arranged to match an encoding path in an associated convolutional encoder, and a selector arranged to feed an output from each path to a single input of the shift register. If the paths have differing values at their output, the selector may choose the value from the path based upon a function of the multi-level signals associated with each path, such as the path with the largest absolute signal level. The decoder provides a simple means for decoding signals while allowing the signal to also or instead be decoded using e.g. a Viterbi decoder if higher performance is required.

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.

The disclosed techniques allow for transmitting a signal stream from a sender to a receiver in an environment including multiple senders and receivers. The technique for the sender decomposes a data stream from the sender into multiple substreams, encodes a substream by a codeword, further superimposes multiple codewords to form a signal stream in an asynchronous manner, and transmits the signal stream to the receiver. A codeword can span over multiple blocks. The receiver receives a first codeword stream from a first sender, receives a second codeword stream from a second sender, the two codeword streams may be received at the same time as one signal, and decodes the first codeword stream and second codeword stream over a sliding window of multiple blocks.

The present invention discloses a decoding path selection device for decoding codewords generated by convolutional codes or turbo codes encoders in error correction codes, the decoding path selection device comprising: a branch metrics calculation unit for receiving incoming signals and calculating branch metrics values; a programmable generalized trellis router for generating a decoding path control signal according to the turbo code or convolutional code specification employed by one of communications standards; a multiplexer for receiving the branch metrics values from the branch metrics calculation unit and the decoding path control signal from the programmable generalized trellis router and selecting a corresponding branch metrics value; a recursive calculation unit, connected after the multiplexer and for receiving the corresponding branch metrics value from the multiplexer; and an a-posteriori probability calculation unit, connected after the recursive calculation unit and for calculating a final decoding result.

The invention relates to a method for decoding at least M.sub.0 symbols X.sup.0.sub.1, . . . , X.sup.0.sub.M0 received from a transmitter through a wireless communication medium, said received symbols representing symbols encoded by an encoder E of the transmitter, said method comprising: inputting in a decoder the M.sub.0 symbols X.sup.0.sub.1, . . . , X.sup.0.sub.M0, said decoder comprising an artificial neural network system, wherein at least an activation function of the artificial neural network system is a multiple level activation function.