A memory device includes a memory array, a processor coupled to the memory array, and a decoding apparatus. The decoding apparatus is configured to perform coarse decoding and fine decoding. In coarse decoding, the decoder decodes in parallel two or more codewords, which share a common block of bits, to determine error information. Next, the decoder corrects errors in a first codeword based on the error information. Then, it is determined if the shared common block of data bits is corrected. If the shared common data block is updated, then error correction based on the error information is prohibited in codewords sharing the common block of data bits with the first codeword. In fine decoding, a single codeword is decoded at a time for error correction.

Systems and methods for performing real-time feedback communication in accordance with various embodiments of the invention are disclosed. In many embodiments, instantaneous encoding is utilized for transmitting symbols from a streaming source over a DMC with feedback. In certain embodiments, instantaneous encoding is performed during the arriving period of the symbols. At time t, the encoder and the decoder calculate the priors of possible symbol sequences using the source distribution and the posteriors at time t−1. In a number of embodiments, the encoder and decoder then partition the evolving message alphabet into groups, so that the group priors are close to the capacity-achieving distribution. In contrast to the SED rule for symmetric binary-input channels, partitioning processes in accordance with several embodiments of the invention utilize group priors instead of group posteriors for the partitioning. In many embodiments, once the groups are partitioned, the encoder determines the index of the group that contains the true symbol sequence it received so far and uses the group index to determine the appropriate channel input.

Embodiments herein describe a FEC codec for generating a check byte for a message. The FEC codec includes a port encoder having a storage unit, a Galois field multiplier, and a sum unit. The storage unit stores a first staged result, which is accumulated based on previous sets of input bytes of the message for all clock cycles from a first clock cycle to a clock cycle immediately prior to the current clock cycle. The Galois field multiplier performs a Galois field multiplication of the first staged result and a power of the alpha to generate a Galois field product. The sum unit performs a Galois field addition on an internal input based on a consolidated byte for the current clock cycle and the Galois field product to generate a second staged result for subsequent use to generate the check byte. Other embodiments may be described and/or claimed.

A Reed-Solomon decoder circuit includes: a syndrome calculator circuit to compute syndrome values for a first codeword and a second codeword sequentially supplied to the syndrome calculator circuit, where last symbols of the first codeword overlap with first symbols of the second codeword during an overlap clock cycle between: a first plurality of non-overlap clock cycles during which the first codeword is supplied to the syndrome calculator circuit; and a second plurality of non-overlap clock cycles during which the second codeword is supplied to the syndrome calculator circuit; an error locator and error evaluator polynomial calculator circuit; an error location and error value calculator circuit; an error counter; and an error corrector circuit to correct the errors in the first codeword and the second codeword based on error counts and the error magnitudes computed by an error evaluator circuit.

Embodiments herein describe a FEC codec for generating a check byte for a message. The FEC codec includes a port encoder having a storage unit, a Galois field multiplier, and a sum unit. The storage unit stores a first staged result, which is accumulated based on previous sets of input bytes of the message for all clock cycles from a first clock cycle to a clock cycle immediately prior to the current clock cycle. The Galois field multiplier performs a Galois field multiplication of the first staged result and a power of the alpha to generate a Galois field product. The sum unit performs a Galois field addition on an internal input based on a consolidated byte for the current clock cycle and the Galois field product to generate a second staged result for subsequent use to generate the check byte. Other embodiments may be described and/or claimed.

An apparatus (100) for providing an joint error correction code (140) for a combined data frame (254) comprising first data (112) of a first data channel and second data (122) of a second data channel comprises a first error code generator (110) configured to provide, based on a linear code, information on a first error correction code (114a, 114b) using the first data (112). The apparatus further comprises a second error code generator (120) configured to provide, based on the linear code, information on a second error correction code (124) using the second data (122). The apparatus is configured to provide the joint error correction code (140) using the information on the first error correction code (114a, 114b) and the information on the second error correction code (124).

A memory system, Reed Solomon (“RS”) Decoder, and method for decoding Reed-Solomon codewords includes: a Syndrome Computation engine configured as a first stage of a pipeline for receiving the RS codeword and computing one or more Syndromes; an initialization unit for providing initialization values for a key equation solver engine that generates the errata locator polynomial and the errata magnitude polynomial configured as a second stage; and as a third stage a Chien Search engine for receiving the error locator polynomial and determining the one or more locations of the one or more erasures and random errors in the received RS codeword and an error-value evaluation (“EE”) engine for receiving the errata magnitude polynomial and determining the one or more magnitudes of the one or more erasures and random errors in the RS received codeword.

An apparatus (100) for providing an joint error correction code (140) for a combined data frame (254) comprising first data (112) of a first data channel and second data (122) of a second data channel comprises a first error code generator (110) configured to provide, based on a linear code, information on a first error correction code (114a, 114b) using the first data (112). The apparatus further comprises a second error code generator (120) configured to provide, based on the linear code, information on a second error correction code (124) using the second data (122). The apparatus is configured to provide the joint error correction code (140) using the information on the first error correction code (114a, 114b) and the information on the second error correction code (124).

A memory system, Reed Solomon (“RS”) Decoder, and method for decoding Reed-Solomon codewords includes: a Syndrome Computation engine configured as a first stage of a pipeline for receiving the RS codeword and computing one or more Syndromes; an initialization unit for providing initialization values for a key equation solver engine that generates the errata locator polynomial and the errata magnitude polynomial configured as a second stage; and as a third stage a Chien Search engine for receiving the error locator polynomial and determining the one or more locations of the one or more erasures and random errors in the received RS codeword and an error-value evaluation (“EE”) engine for receiving the errata magnitude polynomial and determining the one or more magnitudes of the one or more erasures and random errors in the RS received codeword.

An encoder for encoding source information into an encoded codeword used in a communication channel includes a data input to receive source data, a processor, and a memory to store an encoder program. The encoder program makes the processor to encode the source data into a turbo product coding (TPC) structure, and the TPC structure comprises a data block corresponding to the source data, a first parity block including a first column part, a first corner part and a first bottom part, the first parity block being arranged so as to cover a right end column of the data block, a right bottom corner of the data block and a bottom row of the data block by the first column part, the first corner part and the first bottom part, and a second parity block having a row parity block, a joint parity block and a column parity block.