A method includes generating an extended result from a first operation circuitry having a result register bit width greater than a bus width associated with a residue check path of a second operation circuitry associated with a floating point unit. An extended result residue less a first portion residue of the extended result received from the residue check path is stored as a first partial result residue. The first partial result residue is compared with a first result residue of the second operation circuitry. The extended result residue less both the first partial result residue and a second portion residue of the extended result received from the residue check path as a second partial result residue is compared with a second result residue of the second operation circuitry.

This application discloses a polar code encoding method and apparatus, which can improve encoding performance through codeword construction. The method includes: obtaining K information bits to be encoded, where K is a positive integer; determining a first bit sequence based on the K information bits to be encoded, where a length of the first bit sequence is N, the first bit sequence includes fixed bits and the K information bits to be encoded, and the K information bits to be encoded may further include a check bit; determining a second bit sequence based on the first bit sequence and an upper triangular matrix, where the upper triangular matrix is a matrix having N rows and N columns, and the upper triangular matrix may be an upper triangular Toeplitz matrix; and performing polar code encoding on the second bit sequence to obtain and output an encoded sequence.

This application discloses a polar code encoding method and apparatus, which can improve encoding performance through codeword construction. The method includes: obtaining K information bits to be encoded, where K is a positive integer; determining a first bit sequence based on the K information bits to be encoded, where a length of the first bit sequence is N, the first bit sequence includes fixed bits and the K information bits to be encoded, and the K information bits to be encoded may further include a check bit; determining a second bit sequence based on the first bit sequence and an upper triangular matrix, where the upper triangular matrix is a matrix having N rows and N columns, and the upper triangular matrix may be an upper triangular Toeplitz matrix; and performing polar code encoding on the second bit sequence to obtain and output an encoded sequence.

A device encodes data using Mojette Transform to a block device configuration, in order to generate encoded data. The device transmits the data to other devices. The other devices store the received information. The data stored in the other devices can be efficiently updated using partial update.

A processing system and method are provided for reconstituting a block of pixels from bins generated by a Mojette Transform, using a processing and calculation unit (UTC), a bin memory (MB), and a pixel memory (MP). The unit is configured to carry out the operations of reconstructing the pixels, which are performed by reading the bins in the bin memory, reading the reconstructed pixels in the pixel memory, and writing the reconstructed pixels in the pixel memory, such that the steps of reconstructing the pixels do not include an operation of writing bins in the bin memory.

A processing system and method are provided for reconstituting a block of pixels from bins generated by a Mojette Transform, using a processing and calculation unit (UTC), a bin memory (MB), and a pixel memory (MP). The unit is configured to carry out the operations of reconstructing the pixels, which are performed by reading the bins in the bin memory, reading the reconstructed pixels in the pixel memory, and writing the reconstructed pixels in the pixel memory, such that the steps of reconstructing the pixels do not include an operation of writing bins in the bin memory.

A method and apparatus for detecting and correcting digit errors of arithmetic results and signed data represented in a redundant residue number system (RRNS) and further represented using a non-systematic method of complements suitable for processing by a complement based digital arithmetic of the full redundant range

A processive enzyme molecular sensor for use in a DNA data storage system is disclosed that can extract digital information suitably encoded into a synthetic DNA molecule. In various aspects, such sensors are provided in a high-density chip-based format that can provide the high throughput, low-cost and fast data extraction capability required for large scale DNA data storage systems. The sensor for reading the digital data stored in DNA molecules processes individual encoded DNA molecules directly, eliminating the need for complicated sample preparation such as making copies of DNA or clonal populations of such molecules.

A channel encoder for encoding a frame includes a multi-mode redundancy encoder for redundancy encoding the frame in accordance with a certain coding mode from a set of different coding modes, wherein the coding modes are different from each other with respect to an amount of redundancy added to the frame, wherein the multi-mode redundancy encoder is configured to output a coded frame including at least one code word; and a colorator for applying a coloration sequence to the at least one code word; wherein the coloration sequence is such that at least one bit of the code word is changed by the application of the at least one of coloration sequence, wherein the specific coloration sequence is selected in accordance with the certain coding mode.

A channel encoder for encoding a frame includes a multi-mode redundancy encoder for redundancy encoding the frame in accordance with a certain coding mode from a set of different coding modes, wherein the coding modes are different from each other with respect to an amount of redundancy added to the frame, wherein the multi-mode redundancy encoder is configured to output a coded frame including at least one code word; and a colorator for applying a coloration sequence to the at least one code word; wherein the coloration sequence is such that at least one bit of the code word is changed by the application of the at least one of coloration sequence, wherein the specific coloration sequence is selected in accordance with the certain coding mode.