Hierarchical coding architectures and schemes based on multistage concatenated codes are described. For instance, multiple encoder and decoder hierarchies may be implemented along with use of corresponding stages of concatenated codes. The coding scheme generally includes an inner coding scheme (e.g., a polar coding scheme, such as a hybrid polar code or Bose Chaudhuri and Hocquenghem (BCH) code), an outer coding scheme (e.g., a Reed-Solomon (RS) coding scheme), and one or more middle coding schemes. The inner coding scheme is based on a polarization transformation (e.g., polar codes with cyclic redundancy check (CRC) codes, polar codes with dynamic freezing codes, polarization-adjusted convolutional (PAC) codes, etc.) which allows for embedding parity data from an outer code inside a codeword along with the user data. The outer coding scheme has a similar concatenated structure (e.g., of an inner RS code with an outer RS code).

Systems and methods of communicating using asymmetric polar codes are provided which overcome the codeword length constraints of systems and methods of communicating that use traditional polar codes. Used herein, asymmetric polar codes refers to a polarizing linear block code of any arbitrary length that is constructed by connecting together constituent polar codes of unequal length. Asymmetric polar codes may be known by other names. In comparison to conventional solutions for variable codeword length, asymmetric polar codes may provide more flexibility, improved performance, and/or reduced complexity of decoding, encoding, or code design. The system and method provide a flexible, universal, and well-defined coding scheme and to provide sound bit-error correction performance and low decoding latency (compared with current length-compatible methods which can be used with current hardware designs). For the most part, the provided embodiments can be implemented with nearly all available current encoding/decoding polar code techniques.

A bit interleaver, a bit-interleaved coded modulation (BICM) device and a bit interleaving method are disclosed herein. The bit interleaver includes a first memory, a processor, and a second memory. The first memory stores a low-density parity check (LDPC) codeword having a length of 16200 and a code rate of 3/15. The processor generates an interleaved codeword by interleaving the LDPC codeword on a bit group basis. The size of the bit group corresponds to a parallel factor of the LDPC codeword. The second memory provides the interleaved codeword to a modulator for quadrature phase shift keying (QPSK) modulation.

A method in a first wireless device (WD) supporting wireless communication with a second WD is described. A plurality of wireless packets is received from the second WD including at least a first wireless packet. At least another wireless packet of the plurality of wireless packets is one of a retry packet and a repeat packet of the first packet. Each wireless packet of the plurality of wireless packets includes a plurality of bits and a first group of bits. For each received wireless packet, the plurality of bits corresponding to the received wireless packet is de-spread, and the first group of bits is correlated with a predetermined group of bits. The method further includes performing a majority vote based on the correlation of the first group of bits of each received wireless packet and creating a corrected packet based in part on the majority vote.

Methods, systems, and apparatuses include receiving a codeword stored in a memory device. Energy function values are determined for bits of the codeword based on soft information for the bits of the codeword. A bit of the codeword is flipped when the energy function values for a bit of the codeword satisfies a bit flipping criterion. A corrected codeword that results from the flipping of the bits is returned.

An apparatus is provided which comprises at least one processor, at least one memory including computer program code, and the at least one processor, with the at least one memory and the computer program code, being arranged to cause the apparatus to at least perform generating a code block including information bits and parity bits, the parity bits being generated by performing a cyclic redundancy check on the information bits, determining the number of parity bits used in generating the code block based on an applied linear error correcting code base graph and/or based on the number of the information bits, and encoding the code block by using the applied linear error correcting code base graph.

An optimal detection voltage obtaining method, a reading control method and an apparatus are provided. The method includes: obtain a plurality of first difference values and a plurality of second difference values, the second difference value characterizes a difference value of two detection voltages which are adjacent in numerical value, the first difference value characterizes a difference between numbers of memory cells whose threshold voltages respectively equal to the two detection voltages used by the second difference value; dividing the first difference by the second difference to obtain a plurality of tangent approximations; selecting a first tangent approximation and a second tangent approximation from the plurality of tangent approximations, the first tangent approximation is a positive number and the second tangent approximation is a negative number; calculating an optimal detection voltage according to the first tangent approximation, the second tangent approximation, a first detection voltage and a second detection voltage.

Techniques for using erasure coding in a single region to reduce the likelihood of losing objects in a cloud object storage platform are provided. In one set of embodiments, a computer system can upload a plurality of data objects to a region of a cloud object storage platform, where the plurality of data objects including modifications to a data set. The computer system can further compute a parity object based on the plurality of data objects, where the parity object encodes parity information for the plurality of data objects. The computer system can then upload the parity object to the same region where the plurality of data objects was uploaded.

Methods and transceivers transmit communication frames that comprise a sequence of N symbols, ensuing payload header symbols, and ensuing payload message symbols. The sequence of N symbols encodes information according to signal-to-noise ratio associated with the communication frame.

An integrated circuit (IC) includes: a storage having a storage interface and addressable bytes, the storage interface coupled to first and second sets of peripheral terminals; control circuitry having control circuitry inputs and control circuitry outputs, the control circuitry inputs coupled to the storage interface and configured to receive configuration bits provided by the storage responsive to a control circuitry update trigger, and the control circuitry outputs coupled to first and second sets of peripheral outputs; and a cyclic-redundancy check (CRC) engine coupled to the storage interface, the CRC engine configured to distinguish between purposeful updates to the data in the storage and bit errors in the data in the storage.