A coding and modulation apparatus and method are presented. The apparatus (10) comprises an encoder (11) that encodes input data into cell words, and a modulator (12) that modulates said cell words into constellation values of a non-uniform constellation. The modulator (12) is configured to use, based on the total number M of constellation points of the constellation, the signal-to-noise ratio SNR in dB and the channel characteristics, a non-uniform constellation from a group of constellations comprising one or more of predetermined constellations defined by the constellation position vector u1 . . . v, wherein v=sqrt(M)/2−1.

A transmitting apparatus and a receiving apparatus are provided. The transmitting apparatus includes: an encoder configured to generate a low density parity check (LDPC) codeword by LDPC encoding based on a parity check matrix; an interleaver configured to interleave the LDPC codeword; and a modulator configured to map the interleaved LDPC codeword onto a modulation symbol, wherein the modulator is further configured to map a bit included in a predetermined bit group from among a plurality of bit groups constituting the LDPC codeword onto a predetermined bit of the modulation symbol.

An apparatus and method for generating a broadcast signal frame corresponding to a time interleaver supporting a plurality of operation modes are disclosed. An apparatus for generating broadcast signal frame according to an embodiment of the present invention includes a combiner configured to generate a multiplexed signal by combining a core layer signal and an enhanced layer signal at different power levels; a power normalizer configured to reduce the power of the multiplexed signal to a power level corresponding to the core layer signal; a time interleaver configured to generate a time-interleaved signal by performing interleaving that is applied to both the core layer signal and the enhanced layer signal; and a frame builder configured to generate a broadcast signal frame including a preamble for signaling time interleaver information corresponding to the time interleaver, the time interleaver uses one of time interleaver groups, and the time interleaver performs the interleaving by using one of a plurality of operation modes.

Techniques are described for wireless communication. One method includes segmenting a payload into a plurality of code blocks; generating, for each code block, a cyclic redundancy check (CRC); encoding each code block and associated CRC in one or more codewords of a plurality of codewords; and transmitting the codewords. The encoding is based at least in part on a low density parity check code (LDPCC) encoding type. Another method includes receiving a plurality of codewords associated with a payload encoded using a LDPCC encoding type; decoding a set of the codewords associated with the first payload and a CRC; and transmitting one of an acknowledgement (ACK) or a non-acknowledgement (NAK) for the set of the codewords.

Techniques are described for wireless communication. One method includes segmenting a payload into a plurality of code blocks; generating, for each code block, a cyclic redundancy check (CRC); encoding each code block and associated CRC in one or more codewords of a plurality of codewords; and transmitting the codewords. The encoding is based at least in part on a low density parity check code (LDPCC) encoding type. Another method includes receiving a plurality of codewords associated with a payload encoded using a LDPCC encoding type; decoding a set of the codewords associated with the first payload and a CRC; and transmitting one of an acknowledgement (ACK) or a non-acknowledgement (NAK) for the set of the codewords.

This disclosure focuses on example embodiments of a classical approach to the problem of quantum error correction in the presence of faults. Linear codes equipped with faulty parity measurements are disclosed. Example definitions of fault tolerance are introduced and embodiments of a fault tolerant scheme are disclosed that reduce the number of parity measurements required compared with Shor method. Such schemes are well suited to be implemented in the classical control device of a quantum computer in order to ensure quantum fault tolerance.

Apparatuses for transmitting and receiving a signal in a communication system are provided. An apparatus of a receive device includes a receiver configured to receive, from a transmit device, a signal comprising remaining bits of parity bits after puncturing, wherein the parity bits are obtained by adding at least one shortened bit to information bits to obtain input bits for an encoding, if a number of the information bits is less than a number of the input bits for the encoding; and a hardware processor configured to determine a number of puncture bits for the parity bits, generate an output signal by adding at least one value corresponding to the number of the puncture bits to the signal, and decode the output signal.

Systems and methods are disclosed that are of retrieving, by a processing device, a codeword stored at a memory sub-system, determining parity data of the codeword, generating additional parity bits based on one or more bits of the parity data of the codeword, and generating host data by decoding the codeword using the additional parity bits.

A method for encoding may include receiving, at an encoder, a series of data bits, performing, at the encoder, first transition encoding on the data bits to generate an encoded series of data bits based on a key, performing, at the encoder, protection encoding on the key to generate key protection data, performing, at the encoder, second transition encoding on the key protection data to generate encoded key protection data, and transmitting an encoded series of transmission bits to a receiver, the encoded series of transmission bits including the encoded series of data bits and the encoded key protection data.

A method for adjustable error correction in a storage cluster is provided. The method includes determining health of a non-volatile memory of a non-volatile solid-state storage unit of each of a plurality of storage nodes in a storage cluster on a basis of per flash package, per flash die, per flash plane, per flash block, or per flash page. The determining is performed by the storage cluster. The plurality of storage nodes is housed within a chassis that couples the storage nodes as the storage cluster. The method includes adjusting erasure coding across the plurality of storage nodes based on the health of the non-volatile memory and distributing user data throughout the plurality of storage nodes through the erasure coding. The user data is accessible via the erasure coding from a remainder of the plurality of storage nodes if any of the plurality of storage nodes are unreachable.