Devices and methods described herein decode a sequence of coded symbols by guessing noise. In various embodiments, noise sequences are ordered, either during system initialization or on a periodic basis. Then, determining a codeword includes iteratively guessing a new noise sequence, removing its effect from received data symbols (e.g. by subtracting or using some other method of operational inversion), and checking whether the resulting data are a codeword using a codebook membership function. This process is deterministic, has bounded complexity, asymptotically achieves channel capacity as in convolutional codes, but has the decoding speed of a block code. In some embodiments, the decoder tests a bounded number of noise sequences, abandoning the search and declaring an erasure after these sequences are exhausted. Abandonment decoding nevertheless approximates maximum likelihood decoding within a tolerable bound and achieves channel capacity when the abandonment threshold is chosen appropriately.

Devices and methods described herein decode a sequence of coded symbols by guessing noise. In various embodiments, noise sequences are ordered, either during system initialization or on a periodic basis. Then, determining a codeword includes iteratively guessing a new noise sequence, removing its effect from received data symbols (e.g. by subtracting or using some other method of operational inversion), and checking whether the resulting data are a codeword using a codebook membership function. This process is deterministic, has bounded complexity, asymptotically achieves channel capacity as in convolutional codes, but has the decoding speed of a block code. In some embodiments, the decoder tests a bounded number of noise sequences, abandoning the search and declaring an erasure after these sequences are exhausted. Abandonment decoding nevertheless approximates maximum likelihood decoding within a tolerable bound and achieves channel capacity when the abandonment threshold is chosen appropriately.

Devices and methods described herein decode a sequence of coded symbols by guessing noise. In various embodiments, noise sequences are ordered, either during system initialization or on a periodic basis. Then, determining a codeword includes iteratively guessing a new noise sequence, removing its effect from received data symbols (e.g. by subtracting or using some other method of operational inversion), and checking whether the resulting data are a codeword using a codebook membership function. This process is deterministic, has bounded complexity, asymptotically achieves channel capacity as in convolutional codes, but has the decoding speed of a block code. In some embodiments, the decoder tests a bounded number of noise sequences, abandoning the search and declaring an erasure after these sequences are exhausted. Abandonment decoding nevertheless approximates maximum likelihood decoding within a tolerable bound and achieves channel capacity when the abandonment threshold is chosen appropriately.

Hard errors are determined for an unsuccessful decoding of codeword bits read from NAND memory cells via a read channel and input to a low-density parity check (LDPC) decoder. A bit error rate (BER) for the hard errors is estimated and BER for the read channel is estimated. Hard error regions are found using a single level cell (SLC) reading of the NAND memory cells. A log likelihood ratio (LLR) mapping of the codeword bits input to the LDPC decoder is changed based on the hard error regions, the hard error BER, and/or the read channel BER.

Devices and methods described herein decode a sequence of coded symbols by guessing noise. In various embodiments, noise sequences are ordered, either during system initialization or on a periodic basis. Then, determining a codeword includes iteratively guessing a new noise sequence, removing its effect from received data symbols (e.g. by subtracting or using some other method of operational inversion), and checking whether the resulting data are a codeword using a codebook membership function. This process is deterministic, has bounded complexity, asymptotically achieves channel capacity as in convolutional codes, but has the decoding speed of a block code. In some embodiments, the decoder tests a bounded number of noise sequences, abandoning the search and declaring an erasure after these sequences are exhausted. Abandonment decoding nevertheless approximates maximum likelihood decoding within a tolerable bound and achieves channel capacity when the abandonment threshold is chosen appropriately.

Disclosed are devices, systems and methods for polar coding and decoding for correcting deletion and insertion errors caused by a communication channel. One exemplary method for error correction includes receiving a portion of a block of polar-coded symbols that includes d≥2 insertion or deletion symbol errors, the block comprising N symbols, the received portion of the block comprising M symbols; estimating, based on one or more recursive calculations in a successive cancellation decoder (SCD), a location or a value corresponding to each of the d errors; and decoding, based on estimated locations or values, the portion of the block of polar-coded symbols to generate an estimate of information bits that correspond to the block of polar-coded symbols, wherein the SCD comprises at least log.sub.2(N)+1 layers, each comprising up to d.sup.2N processing nodes arranged as N groups, each of the N groups comprising up to d.sup.2 processing nodes.

The present application provides a data transmission method which includes: obtaining statistical characteristics of interferences; determining a total number of coding layers of multi-layer coding and a code rate and transmitting power of each coding layer according to the statistical characteristics of the interferences; processing to-be-transmitted information bits through data re-organization according to the determined total number of coding layers of the multi-layer coding to obtain information bits of each coding layer; coding the information bits of each coding layer respectively according to the determined code rate of each coding layer to obtain a coded data stream of each coding layer; processing the coded data stream of each coding layer through layer mapping and modulation according to the determined transmitting power of each coding layer to obtain a symbol stream to be transmitted; and transmitting the symbol stream to be transmitted.

Channel state information (CSI) scaling modules for use in a demodulator configured to demodulate a signal received over a transmission channel, the demodulator comprising a soft decision error corrector (e.g. LDPC decoder) configured to decode data carried on data symbols of the received signal based on CSI values. The CSI scaling module is configured to monitor the performance of the soft decision error corrector and in response to determining the performance of the soft decision error corrector is below a predetermined level, dynamically select a new CSI scaling factor based on the performance of the soft decision error corrector.

According to one embodiment, a decoding device comprises a converter configured to convert read data to first likelihood information by using a first conversion table, a decoder which decodes the first likelihood information, a controller which outputs a decoding result of the decoder when the decoder succeeds decoding, and a creator module which creates a second conversion table based on the decoding result when the decoder fails decoding. When the second conversion table is created, at least a part of the decoding result is converted to second likelihood information by using the second conversion table the second likelihood information is decoded.

Channel state information (CSI) scaling modules for use in a demodulator configured to demodulate a signal received over a transmission channel, the demodulator comprising a soft decision error corrector (e.g. LDPC decoder) configured to decode data carried on data symbols of the received signal based on CSI values. The CSI scaling module is configured to monitor the performance of the soft decision error corrector and in response to determining the performance of the soft decision error corrector is below a predetermined level, dynamically select a new CSI scaling factor based on the performance of the soft decision error corrector.