An example device includes processing circuitry configured to determine a first state of a data structure, the first state representing a first quantizer applied to a previously quantized or inverse quantized value of a previous transform coefficient of residual data for a block of the video data and update the data structure to a second state according to the first state and a parity of a partial set of syntax elements representing a partial set of a plurality of coefficient levels for the previous transform coefficient. The processing circuitry is further configured to determine a second quantizer to be used to quantize or inverse quantize a current value of a current transform coefficient according to the second state of the data structure and quantize or inverse quantize the current value of the current transform coefficient using the second quantizer.

An optical module processes first FEC (Forward Error Correction) encoded data produced by a first FEC encoder. The optical module has a second FEC encoder for further coding a subset of the first FEC encoded data to produce second FEC encoded data. The optical module also has an optical modulator for modulating, based on a combination of the second FEC encoded data and a remaining portion of the first FEC encoded data that is not further coded, an optical signal for transmission over an optical channel. The second FEC encoder is an encoder for an FEC code that has a bit-level trellis representation with a number of states in any section of the bit-level trellis representation being less than or equal to 64 states. In this manner, the second FEC encoder has relatively low complexity (e.g. relatively low transistor count) that can reduce power consumption for the optical module.

A method for data retrieval includes receiving a set of probability metrics. A set of probability metrics is received for each one of a plurality of read values, and each probability metric of the set of probability metrics corresponds to a statistical likelihood that the read value is representative of one of a number of symbols. The symbols define a set of allowed transitions between a number of states, and a series of successive allowed transitions between states define allowed paths between the states. The method further includes determining a survival path between the states. The survival path is based on an accumulation of probability metrics corresponding to the statistical likelihood that successive ones of the plurality of read values are representative of successive ones of the symbols defining each transition in the survival path. The method further includes decoding a symbol stream based on the survival path.

A digital system, components and method are configured with nonvolatile memory for storing digital data using codewords. The data is stored in the memory using multiple bits per memory cell of the memory. A code efficiency, for purposes of write operations and read operations relating to the memory, can be changed on a codeword to codeword basis based on input parameters. The code efficiency can change based on changing any one of the input parameters including bit density that is stored by the memory. Storing and reading fractional bit densities is described.

This disclosure describes systems and methods for detecting multiple insertion and deletion errors in the presence of substitution errors in a signal (such as a sequenced DNA string). A convolutional code that includes two or more component convolutional codes is used for encoding. Each of the two or more component convolutional codes generates only a subset of all possible outputs of the convolutional code. The subsets of the two or more component convolutional codes are disjoint from each other. Only one of the two or more convolutional codes is active at any given time. The two or more convolutional codes together define a super code. The two or more convolutional codes are time interlaced within the super code, and the super code defines the convolutional code. A trellis that includes two or more component trellises designed based on the two or more component convolutional codes is used for decoding.

The present invention discloses a Trellis-Coded-Modulation (TCM) decoder applied in a receiver, wherein the TCM decoder includes a branch metric unit, a path metric unit, a trace-back length selection circuit and a survival path management circuit. In operations of the TCM decoder, the branch metric unit is configured to receive multiple input codes to generate multiple sets of branch information. The path metric unit is configured to calculate multiple survival paths according to the multiple sets of branch information. The trace-back length selection circuit is configured to select a trace-back length, wherein the trace-back length is determined according to a signal quality of the receiver. The survival path management circuit is configured to return the multiple survival paths for the trace-back length in order to generate an output code.

The present invention discloses a Trellis-Coded-Modulation (TCM) decoder applied in a receiver, wherein the TCM decoder includes a branch metric unit, a path metric unit, a trace-back length selection circuit and a survival path management circuit. In operations of the TCM decoder, the branch metric unit is configured to receive multiple input codes to generate multiple sets of branch information. The path metric unit is configured to calculate multiple survival paths according to the multiple sets of branch information. The trace-back length selection circuit is configured to select a trace-back length, wherein the trace-back length is determined according to a signal quality of the receiver. The survival path management circuit is configured to return the multiple survival paths for the trace-back length in order to generate an output code.

A wireless communication method for transmitting wireless signals from a transmitter includes dividing bits of the transport block into a number of code blocks, wherein each code block corresponds to a bit-level of a multi-level modulation scheme used for transmission, and wherein a size of each code block is inversely proportional to a corresponding coding rate used for coding the code block.

A system includes: a transmitter including: a coding unit generating a first bit sequence by convolutional coding on information bits based on a code rate; a bit erasing unit generating a second bit sequence by erasing one or more bits from the first bit sequence for every predetermined first number of bits; and a modulation unit generating a symbol by modulation using the second bit sequence; and a receiver including: a demodulation unit calculating first reliabilities that can be derived from the symbol; a likelihood extension unit generating extended bit sequences each composed of bits for the first number of bits, and generating a plurality of second reliabilities by assigning first reliabilities duplicated, as the reliabilities of the extended bit sequences; and a decoding unit creating a trellis diagram using the code rate and the extended bit sequences, and assigning the second reliabilities to branches of the trellis diagram.

The present disclosure relates to a pre-5.sup.th-Generation (5G) or 5G communication system to be provided for supporting higher data rates Beyond 4.sup.th-Generation (4G) communication system such as Long Term Evolution (LTE). A method of decoding a signal in a communication system includes receiving an encoded bit-stream corresponding to message bits and first Cyclic Redundancy Check (CRC) bits, obtaining a codeword through a traceback for at least part of the encoded bit-stream, generating second CRC bits by performing CRC encoding on the codeword, and performing decoding based on at least part of the second CRC bits.