This disclosure describes systems, methods, and devices related to over-puncture mitigation. A device may generate a frame comprising a payload having a payload size associated with a number of bits. The device may determine a low-density parity-check (LDPC) codeword size based on the payload size. The device may calculate a number of codewords based on the payload size. The device may calculate a number of shortening bits and a number of LDPC padding bits based on the number of codewords. The device may calculate a number of orthogonal frequency division multiplexing (OFDM) symbols for containing the number of codewords. The device may cause to send the frame with the number of OFDM symbols to a station device.

A quantum error correction (QEC) decoding system includes an error correction chip. The error correction chip is configured to: obtain error syndrome information of a quantum circuit; and decode the error syndrome information by running neural network decoders, to obtain error result information, a core operation of the neural network decoders being a multiply accumulate (MA) operation of unsigned fixed-point numbers obtained through numerical quantization. According to the present disclosure, for the system that uses the neural network decoders for QEC decoding, the core operation of the neural network decoders is the MA operation of unsigned fixed-point numbers obtained through numerical quantization, thereby minimizing the data volume and the calculation amount desirable by the neural network decoders, so as to better meet the requirement of real-time error correction.

A method includes generating, by processing circuitry of a communications device, a partitioned complementary sequence based on information bits for transmission. The partitioned complementary sequence may include zero-valued elements. The method may include encoding a plurality of symbols on a plurality of orthogonal subcarriers using the partitioned complementary sequence. The encoding may include mapping additional information bits on subcarriers associated with the zero-valued elements of the partitioned complementary sequence. Additionally, the method may include controlling a radio of the communications device to transmit the plurality of symbols on the plurality of orthogonal subcarriers via an antenna of the communications device.

A hybrid quantum classical (HQC) computer system, which includes both a classical computer component and a quantum computer component, implements indirect benchmarking of a near term quantum device by directly benchmarking a virtual quantum machine that models the quantum computer device and that has a level of errors that corresponds to the level of errors associated with the quantum computer device. The direct benchmarking, conducted using quantum error correction tools, produces a probability distribution of error syndromes that may be used as a probability distribution of error syndromes for the quantum computer device.

A configuration for a device to interleave a codeword, where the codeword is based on an enhanced noncoherent error correction code. The apparatus encodes a set of bits based on a noncoherent error correction code to generate a first codeword. The apparatus interleaves the first codeword to permute coded bits of the first codeword into a second codeword. The apparatus transmits the second codeword to a second device.

An encoding for data in an audio data stream may be indicated in the data stream using a footer stored in low-order bits of data frames in the audio data stream. When the audio data stream may include either Pulse Code Modulation (PCM) or Direct Stream Digital (DSD) data, PCM data may be marked with a footer to indicate the encoding as PCM. The footer may be a fixed value, an alternating fixed value, a predetermined sequence of values, or a value computed based on the PCM data. Examples of computed values for the footer marker may include an error code, an error correction code (ECC), and a scrambled code.

An encoding for data in an audio data stream may be indicated in the data stream using a footer stored in low-order bits of data frames in the audio data stream. When the audio data stream may include either Pulse Code Modulation (PCM) or Direct Stream Digital (DSD) data, PCM data may be marked with a footer to indicate the encoding as PCM. The footer may be a fixed value, an alternating fixed value, a predetermined sequence of values, or a value computed based on the PCM data. Examples of computed values for the footer marker may include an error code, an error correction code (ECC), and a scrambled code.

A quantum device includes a syndrome measurement circuit that implements an correction code using a plurality of Majorana qubit islands. The syndrome measurement circuit is adapted to effect a syndrome measurement by performing a sequence of measurement-only operations, where each one of the measurement-only operations involves at most two of the Majorana qubit islands.

An encoding for data in an audio data stream may be indicated in the data stream using a footer stored in low-order bits of data frames in the audio data stream. When the audio data stream may include either Pulse Code Modulation (PCM) or Direct Stream Digital (DSD) data, PCM data may be marked with a footer to indicate the encoding as PCM. The footer may be a fixed value, an alternating fixed value, a predetermined sequence of values, or a value computed based on the PCM data. Examples of computed values for the footer marker may include an error code, an error correction code (ECC), and a scrambled code.

An encoding for data in an audio data stream may be indicated in the data stream using a footer stored in low-order bits of data frames in the audio data stream. When the audio data stream may include either Pulse Code Modulation (PCM) or Direct Stream Digital (DSD) data, PCM data may be marked with a footer to indicate the encoding as PCM. The footer may be a fixed value, an alternating fixed value, a predetermined sequence of values, or a value computed based on the PCM data. Examples of computed values for the footer marker may include an error code, an error correction code (ECC), and a scrambled code.