Coding sub-channel selection involves, in an embodiment, determining, from sub-channels that are defined by a code and that have associated reliabilities for input bits at input bit positions, a first number of the sub-channels to carry bits that are to be encoded. A second number of the sub-channels, greater than the first number, are selected. The second number of sub-channels are selected to provide exactly the first number sub-channels to be available to carry the bits that are to be encoded.

This disclosure provides methods, components, devices and systems for low-density parity check (LDPC) coding. Some aspects more specifically relate to extending LDPC codewords to produce longer codewords. In some examples, a first wireless device may generate a baseline LDPC code by performing a first lifting on a base matrix, which may produce an LDPC code used for a current Wi-Fi implementation. The first wireless device may then perform a second lifting or a re-lifting (such as a cyclic lifting, a product lifting, a swapping lifting, or a combination thereof) to generate an extended lifted code. This extended lifted code may be an extension of the first LDPC code such that the first LDPC code may be preserved as part of the extended code. Then first wireless device may then transmit the extended LDPC code as an extended or lifted codeword.

A data error correction method, apparatus, device, and readable storage medium are disclosed. The method includes: acquiring target data to be error-corrected; performing error correction on the target data using an error-correcting code to obtain first data; judging whether the performing of the error correction on the target data is successful; responsive to the performing of the error correction on the target data being not successful, correcting the target data using a target neural network to obtain second data, determining the second data as the target data, and continuing to perform the error correction on the target data again; and responsive to the performing of the error correction on the target data being successful, determining the first data as the error-corrected target data.

Disclosed herein are example embodiments of protocols to distill magic states for T-gates. Particular examples have low space overhead and use an asymptotically optimal number of input magic states to achieve a given target error. The space overhead, defined as the ratio between the physical qubits to the number of output magic states, is asymptotically constant, while both the number of input magic states used per output state and the T-gate depth of the circuit scale linearly in the logarithm of the target error. Unlike other distillation protocols, examples of the disclosed protocol achieve this performance without concatenation and the input magic states are injected at various steps in the circuit rather than all at the start of the circuit. Embodiments of the protocol can be modified to distill magic states for other gates at the third level of the Clifford hierarchy, with the same asymptotic performance. Embodiments of the protocol rely on the construction of weakly self-dual Calderbank-Shor-Steane codes (CSS codes) with many logical qubits and large distance, allowing one to implement control-Swaps on multiple qubits. This code is referred to herein as the inner code. The control-Swaps are then used to measure properties of the magic state and detect errors, using another code that is referred to as the outer code. Alternatively, one can use weakly-self dual CSS codes which implement controlled Hadamards for the inner code, reducing circuit depth. Several specific small examples of this protocol are disclosed herein.

A number K of N sub-channels that are defined by a code and that have associated reliabilities for input bits at N input bit positions, are to be selected to carry bits that are to be encoded. A localization area that includes multiple sub-channels and is located below fewer than K of the N sub-channels in a partial order of the N sub-channels is determined based on one or more coding parameters. The fewer than K sub-channels of the N sub-channels above the localization area in the partial order are selected, and a number of sub-channels from those in the localization area are also selected. The selected fewer than K sub-channels and the number of sub-channels selected from those in the localization area together include K sub-channels to carry the bits that are to be encoded.

An ordered number sequence may be determined based on an ordered sub-channel sequence specifying an order of N sub-channels that are defined by a code and that have associated reliabilities for input bits at N input bit positions. The ordered number sequence represents the ordered sub-channel sequence as a sequence of fewer than N numbers. The numbers in the ordered number sequence indicate the sub-channels, by representing numbers of the sub-channels for example, from different subsets of the N sub-channels, that appear in the order specified by the ordered sub-channel sequence. Using ordered number sequences, longer ordered sub-channel sequences could be constructed from smaller ordered sub-channel sequences, and/or sub-channels that to be selected from a longer ordered sub-channel sequence could be divided into two or more parts, with each part to be selected from shorter ordered sub-channel sequences.

A method for determining features of an error correcting code system, comprising independent error correcting codes and a polarization module, allowing transmitting a binary input vector on block fading sub-channels, the independent error correcting codes generating components of the binary input vector and a channel polarization being applied to the binary input vector by the polarization module. The method comprises: obtaining characteristics of the block fading sub-channels; and, determining features of said error correcting code system, comprising, for each error correcting code, a rate of said error correcting code, adapted to the obtained characteristics and minimizing a function of a probability that an instantaneous equivalent channel capacity of the block fading sub-channels is below a transmission rate transmitted on the block fading sub-channels.

Aspects of the disclosure relate to a channel coding and decoding algorithm that provides for generalized polar codes, including the concatenation of a plurality of component codes via one-step polarization. In a further aspect, selection of suitable component codes in this scheme can result in a generalized polar code having a cyclic shift property, such that information can be implicitly communicated according to the magnitude of the cyclic shift. In yet another aspect, a decoding algorithm provides for reliable decoding of such generalized polar codes, including exploitation of time diversity in sequential transmissions. Other aspects, embodiments, and features are also claimed and described.

Decoding and encoding methods, systems, and devices for wireless communication are described. One method may include receiving a codeword over a wireless channel, the codeword being encoded using a polar code, identifying a set of repeated bit locations in the received codeword, and identifying a set of bit locations of the polar code used for information bits for the encoding. The set of bit locations may be determined based at least in part on recursively partitioning bit-channels of the polar code for each stage of polarization and assigning portions of a number of the information bits to bit-channel partitions of each stage of polarization based on a mutual information transfer function of respective aggregate capacities of the bit-channel partitions. The method may also include decoding the received codeword according to the polar code to obtain an information bit vector at the set of bit locations, and other aspects and features.

A method, device and system disclosed used in storage technique, comprising: splitting a file of size M into k blocks, that is to say, each block is of size M/k; issuing the above k blocks across k different storage nodes in the distributed network storage system in a distributed manner; using the k blocks, constructing nk independent blocks via linear coding method, and satisfying the property that any k of the n encoded blocks can be used to reconstruct the original data in the file, which means the linear coding method is a kind of Maximum-Distance Separable (MDS) code; distribute the nk encoded blocks to the rest nk different storage codes in the distributed network storage systems.