Computationally efficient message encoding and decoding schemes for NCMA-based multiple access networks are enabled. Belief propagation decoding of fountain codes designed for NCMA-based multiple access networks may be enhanced using Gaussian elimination. Networks utilizing a network-coded slotted ALOHA protocol can benefit in particular. In such cases, Gaussian elimination may be applied locally to solve the linear system associated with each timeslot, and belief propagation decoding may be applied between the linear systems obtained over different timeslots. The computational complexity of such an approach may be of the same order as a conventional belief propagation decoding algorithm. The fountain code degree distribution may be tuned to optimize for different numbers of expected channel users.

A communication system is configured to use coded modulation architecture using sparse regression codes. A transmitter includes a plurality of antenna and processing circuitry configured to: divide a data signal into a plurality of layers, allocate power individually to each of the plurality layers, encode a subset of the plurality of layers, the subset comprising a number of layers less than the whole, and interleave the subset of the plurality of layers. A receiver includes a plurality of antenna and processing circuitry configured to divide a received data signal into a plurality of layers and perform layer-by-layer decoding on the received data and control signals.

A memory system includes a non-volatile memory. A coding unit generates a codeword by performing coding of a graph code using a graph. A side of the graph is associated with a block that is a part of user data and that has one or more symbols at which component codes intersect one another. A control unit stores the codeword in the non-volatile memory. Error correction is performed on the user data in accordance with the codeword.

An accelerated erasure coding system includes a processing core for executing computer instructions and accessing data from a main memory, and a non-volatile storage medium for storing the computer instructions. The processing core, storage medium, and computer instructions are configured to implement an erasure coding system, which includes: a data matrix for holding original data in the main memory; a check matrix for holding check data in the main memory; an encoding matrix for holding first factors in the main memory, the first factors being for encoding the original data into the check data; and a thread for executing on the processing core. The thread includes: a parallel multiplier for concurrently multiplying multiple entries of the data matrix by a single entry of the encoding matrix; and a first sequencer for ordering operations through the data matrix and the encoding matrix using the parallel multiplier to generate the check data.

Systems and methods for decoding block and concatenated codes are provided, including channel state information estimation such as by using optimum filter lengths based on channel selectivity and adaptive decision-directed channel estimation. These improvements enhance the performance of various communication systems and consumer electronics, including HD Radio receivers and systems.

A system for software error-correcting code (ECC) protection or compression of original data using ECC data in a first memory is provided. The system includes a processing core for executing computer instructions and accessing data from a main memory, and a non-volatile storage medium for storing the computer instructions. The software ECC protection or compression includes: a data matrix for holding the original data in the first memory; a check matrix for holding the ECC data in the first memory; an encoding matrix for holding first factors in the main memory, the first factors being for encoding the original data into the ECC data; and a thread for executing on the processing core. The thread includes a Galois Field multiplier for multiplying entries of the data matrix by an entry of the encoding matrix, and a sequencer for ordering operations using the Galois Field multiplier to generate the ECC data.

A method and an apparatus for encoding and decoding packets using a polar code is provided. The method includes acquiring a plurality of blocks constituting the packet, extracting a plurality of codeword candidates corresponding to the blocks, selecting some of the codeword candidates in a descending order of posterior probability among the codeword candidates corresponding to the blocks, combining the selected codeword candidates into a plurality of codeword combinations, selecting a codeword combination having the highest posterior probability and passed Cyclic Redundancy Check (CRC) test without error among the plurality of codeword combinations, and decoding the selected codeword combination. The packet encoding and decoding apparatus and method of the present disclosure is capable of encoding and decoding packets in a unit of blocks efficiently.

Methods, systems, and devices are described for wireless communications at a wireless device. A wireless device may adaptively select a parity check matrix to increase the reliability of signal transmission by adapting to different channel statistics and channel types (e.g., erasure channels, channels with additive white Gaussian noise, and channels with discrete or continuous alphabets). For example, polarization codes (i.e., codes based on rows of a polarization matrix) may be used to construct parity check matrices on-the-fly given an estimation of dynamic channel conditions or diverse channel structures. The channel may be decomposed into polarized sub-channels corresponding to the polarization codes, and mutual information profiles may be determined for each of the polarized sub-channels. The parity check matrix corresponding to the polarization codes may be constructed based on the mutual information profile of all polarized sub-channels. The wireless device may encode or decode data based on the constructed parity check matrix.

In an advanced adaptive modulation and coding (AMC) scheme, the code rate and the parity-check matrix (PCM) for low-density parity-check (LDPC) codes are adapted according to modulation formats and variable-iteration receivers. The degree distribution for the PCM adaptation is designed by heuristic optimization to minimize the required SNR via an extrinsic information transfer (EXIT) trajectory analysis for finite-iteration decoding. The method uses dynamic window decoding by generating spatially coupled PCM for quasi-cyclic LDPC convolutional coding. The method also provides a way to jointly optimize labeling and decoding complexity for high-order and high-dimensional modulations.

Systems and methods for decoding block and concatenated codes are provided. These include advanced iterative decoding techniques based on belief propagation algorithms, with particular advantages when applied to codes having higher density parity check matrices such as iterative soft-input soft-output and list decoding of convolutional codes, Reed-Solomon codes and BCH codes. Improvements are also provided for performing channel state information estimation including the use of optimum filter lengths based on channel selectivity and adaptive decision-directed channel estimation. These improvements enhance the performance of various communication systems and consumer electronics. Particular improvements are also provided for decoding HD radio signals, satellite radio signals, digital audio broadcasting (DAB) signals, digital audio broadcasting plus (DAB+) signals, digital video broadcasting-handheld (DVB-H) signals, digital video broadcasting-terrestrial (DVB-T) signals, world space system signals, terrestrial-digital multimedia broadcasting (T-DMB) signals, and China mobile multimedia broadcasting (CMMB) signals. These and other improvements enhance the decoding of different digital signals.