A method for Bose-Chaudhuri-Hocquenghem (BCH) soft error decoding includes receiving a codeword x, wherein the received codeword x has τ=t+r errors for some r≥1; computing a minimal monotone basis {λ.sub.i(x)}.sub.1≤i≤r+1.Math.F[x] of an affine space V={λ(x)ϵF[x]: λ(x).Math.S(x)=λ′(x) (mod x.sup.2t), λ(0)=1, deg(λ(x)≤t+r}, wherein λ(x) is an error locator polynomial and S(x) is a syndrome; computing a matrix A≡(λ.sub.jβ.sub.i)).sub.iϵ[W],jϵ[r+1], wherein W={β.sub.i, . . . , β.sub.W} is a set of weak bits in x; constructing a submatrix of r+1 rows from sub matrices of r+1 rows of the subsets of A such that the last column is a linear combination of the other columns; forming a candidate error locating polynomial using coefficients of the minimal monotone basis that result from the constructed submatrix; performing a fast Chien search to verify the candidate error locating polynomial; and flipping channel hard decision at error locations found in the candidate error locating polynomial.

This disclosure provides systems, methods and apparatus, including computer storage media, for retransmission of sidelink transmissions using network coding with binned feedback. A transmitting device transmits a transport block and a request for a network coding (NC) encoding device to retransmit the transport block to a plurality of user equipment (UEs). The UEs decode the transport block and report an acknowledgment (ACK) or negative acknowledgment (NACK) on a physical sidelink feedback channel (PSFCH) resource associated with a bin for the UEs. The NC encoding device decodes the PSFCH resource for each bin to determine an ACK or NACK status for each bin, and determines whether to encode the transport block in a NC combination packet. The UEs receive the NC combination packet including an encoding of a subset of transport blocks. The receiving devices transmit an ACK or NACK on a PSFCH resource for a bin for each transport block.

This disclosure provides systems, methods and apparatus, including computer storage media, for retransmission of sidelink transmissions using network coding with binned feedback. A transmitting device transmits a transport block and a request for a network coding (NC) encoding device to retransmit the transport block to a plurality of user equipment (UEs). The UEs decode the transport block and report an acknowledgment (ACK) or negative acknowledgment (NACK) on a physical sidelink feedback channel (PSFCH) resource associated with a bin for the UEs. The NC encoding device decodes the PSFCH resource for each bin to determine an ACK or NACK status for each bin, and determines whether to encode the transport block in a NC combination packet. The UEs receive the NC combination packet including an encoding of a subset of transport blocks. The receiving devices transmit an ACK or NACK on a PSFCH resource for a bin for each transport block.

The present invention is directed to communication systems and methods. In a specific embodiment, the present invention provides a receiver that includes an error correction module. A syndrome value, calculated based on received signals, may be used to enable the error correction module. The error correction module includes an error generator, a Nyquist error estimator, and a decoder. The decoder uses error estimation generated by the Nyquist error estimator to correct the decoded data. There are other embodiments as well.

A one-shot state transition decoder receives a codeword having N-bits. The decoder reads a first D-bits of the codeword to determine a stitching location d within the codeword. The stitching location identifies a start bit of unencoded data in the codeword. The codeword is decoded into an output buffer for user data of L bits, where N>L. Parameters of the decoder are set before the decoding, including setting a length of the codeword to N−L+d and a number of expected decoded bits to d. The decoding including decoding the d bits based on a set of state transition probabilities and copying decoded bits into the output buffer, the unencoded data being copied to the end of the output buffer.

A non-systematic convolutional decoder of a convolutionally encoded multi-level data stream includes a shift register and two or more paths of exclusive-OR (XOR) gates, arranged to reconstruct an original input information stream, each path having a quantiser arranged to quantise the signal to two levels, and a set of XOR gates arranged to match an encoding path in an associated convolutional encoder, and a selector arranged to feed an output from each path to a single input of the shift register. If the paths have differing values at their output, the selector may choose the value from the path based upon a function of the multi-level signals associated with each path, such as the path with the largest absolute signal level. The decoder provides a simple means for decoding signals while allowing the signal to also or instead be decoded using e.g. a Viterbi decoder if higher performance is required.

A decoder includes one or more Variable-Node Processors (VNPs) that hold respective variables, and logic circuitry. The logic circuitry is configured to decode a code word of an Error Correction Code (ECC), which is representable by a set of check equations, by performing a sequence of iterations such that each iteration involves processing of at least some of the variables, to hold one or more auxiliary equations derived from the check equations, so that a number of the auxiliary equations is smaller than a number of the check equations, to evaluate the auxiliary equations, during the sequence of iterations, using the variables, and, in response to detecting that the variables satisfy the auxiliary equations, to terminate the sequence of iterations and output the variables as the decoded code word.

Systems and methods for correcting corrupted network packets are provided. An example method includes receiving a network packet via a communication channel. The network packet includes a payload and a Cyclic Redundancy Check (CRC) associated with the payload. The method continues with calculating a reference CRC based on the received payload and determining, based on the reference CRC and the received CRC, whether the network packet is corrupted. Based on the determination that the network packet is corrupted, the method continues with selecting a predetermined number of positions of bits in the payload of the network packet, precalculating a set of additional CRCs, and determining, based on the reference CRC and the set of additional CRCs, a combination of bit flips at the predetermined number of positions. The method also includes modifying the payload according to the combination of bit flips at the predetermined number of positions.

A method for storing input data in a flash memory. The method comprising generating a codeword by encoding the input data with an error correcting code and generating a shaped codeword by applying a shaping function to at least a part of the codeword. The shaping function comprising logically inverting every n-th occurrence of a bit associated with a high-charge storage state in the part of the codeword. The method further comprising writing the shaped codeword to the flash memory, generating an estimated shaped codeword by reading the flash memory, generating soft decision information for the estimated shaped codeword, and retrieving the input data by decoding the soft decision information using an error correcting code soft decoder.

A method for storing input data in a flash memory. The method comprising generating a codeword by encoding the input data with an error correcting code and generating a shaped codeword by applying a shaping function to at least a part of the codeword. The shaping function comprising logically inverting every n-th occurrence of a bit associated with a high-charge storage state in the part of the codeword. The method further comprising writing the shaped codeword to the flash memory, generating an estimated shaped codeword by reading the flash memory, generating soft decision information for the estimated shaped codeword, and retrieving the input data by decoding the soft decision information using an error correcting code soft decoder.