Systems and methods are disclosed for optically communicating data by, at a transmitter side, encoding a block of input bits by one or more outer encoders, and after interleaving the encoded bits, permuting the encoded bits according to a predetermined sequence or order, and further encoding the encoded bits by an inner encoder, and at a receiver side, decoding received bits with an inner decoder, and after the encoded bits are permuted, subsequently decoding by and outer decoder, and returning information bits at an outer decoder as an output. The soft-decision and hard-decision outputs from the outer BCH code help the inner LDPC decoder to have better estimation of the received bits and gain performance. The performance in higher-order modulation formats could be as large as 0.5 dB in one embodiment.

Systems for performing turbo product code decoding includes an error intersection identifier determining a set of one or more error intersections using a set of error-containing codewords, and updating, based at least in part on Chase decoding performed on the set of error-containing codewords, the set of error intersections to obtain an updated set of one or more error intersections, a bit location selector suitable for selecting, from the set of error intersections, a set of one or more least reliable bit locations using soft information associated with the set of error-containing codewords, and a Chase decoder performing Chase decoding on the set of error-containing codewords based on a first value being a number of least reliable bit locations and a second value being a maximum number of allowable flips allowed out of the number of least reliable bit locations.

Techniques for reducing the latency for decoding product codewords with minimal hardware architecture changes are described. In an example, a system accesses and decodes a generalized product code (GPC) codeword by using at least one of a plurality of Chase decoding procedures available on the system. A first Chase decoding procedure is configured according to first values for a set of decoding parameters. A second Chase decoding procedure is configured according to second values for the set of decoding parameters. The second values are different from the first values. The first Chase decoding procedure has a smaller latency and a higher bit error rate (BER) relative to the second Chase decoding procedure based on the first values and the second values for the set of decoding parameters.

Embodiments of the present disclosure provide a high speed low latency rate configurable soft decision and hard decision based pipelined Reed-Solomon (RS) decoder architecture suitable for optical communication and storage. The proposed RS decoder is a configurable RS decoder that is configured to monitor the channel and adjust code parameters based on channel capacity. The proposed RS decoder includes interpolation and factorization free Low-Complexity-Chase (LCC) decoding to implement soft-decision decoder (SDD). The proposed RS decoder generates test vectors and feeds these to a pipelined 2-stage hard decision decoder (HDD). The proposed RS decoder architecture computes error locator polynomial in exactly 2t clock cycles without parallelism and supports high throughput, and further computes error evaluator polynomial in exactly t cycles. The present disclosure provides a 2-stage pipelined decoder to operate at least latency possible and reduced size of delay buffer.

According to the embodiments, a memory system includes a non-volatile memory, a control unit that reads a received word from the non-volatile memory, and a decoder that performs soft-decision decode to the received word. The decoder includes a test pattern generating unit that generates test patterns, a hard decision decoder that performs hard-decision decode by using the test pattern and the received word and outputs a decoded word, and a distance calculating unit that calculates Euclidean distance between the decoded word and the received word based on the decoded words of which the number is less than that of the test patterns of all the combinations in a case where the number of flips is of one to a predetermined value and selects a decoded word which is the decoding result from among the decoded words output from the hard decision decoder based on the Euclidean distance.

Systems and methods for decoding block and concatenated codes are provided, including channel state information estimation such as by using optimum filter lengths based on channel selectivity and adaptive decision-directed channel estimation. These improvements enhance the performance of various communication systems and consumer electronics, including HD Radio receivers and systems.

Examples are given for techniques associated with error correction for encoded data. In some examples, error correction code (ECC) information for the ECC encoded data may be received that indicates the ECC encoded data has bit errors that are not able to be corrected by the ECC used to encode the ECC encoded data. A soft decision decoding may be implemented that includes flipping a given number of bits of a selected portion of the ECC encoded data based on a combinatorial operation or method. One or more successful decodes may result from this selective flipping to enable the ECC to successfully decode the ECC encoded data.

An operation method of a flash memory system includes a hard decision decoding on a codeword and a soft decision decoding on an error message block. The hard decision decoding on a codeword and the codeword comprises message blocks encoded with row constituent codes and column constituent codes according to a block-wise concatenated BCH (BC-BCH) method. When the hard decision decoding fails, the error message block to which the hard decision decoding fails among a plurality of the message blocks is identified. Soft decision information corresponding to the row constituent codes and the column constituent codes of the error message block is generated and the soft decision decoding on the error message block based on the soft decision information is performed.

Systems and methods for decoding block and concatenated codes are provided. These include advanced iterative decoding techniques based on belief propagation algorithms, with particular advantages when applied to codes having higher density parity check matrices such as iterative soft-input soft-output and list decoding of convolutional codes, Reed-Solomon codes and BCH codes. Improvements are also provided for performing channel state information estimation including the use of optimum filter lengths based on channel selectivity and adaptive decision-directed channel estimation. These improvements enhance the performance of various communication systems and consumer electronics. Particular improvements are also provided for decoding HD radio signals, satellite radio signals, digital audio broadcasting (DAB) signals, digital audio broadcasting plus (DAB+) signals, digital video broadcasting-handheld (DVB-H) signals, digital video broadcasting-terrestrial (DVB-T) signals, world space system signals, terrestrial-digital multimedia broadcasting (T-DMB) signals, and China mobile multimedia broadcasting (CMMB) signals. These and other improvements enhance the decoding of different digital signals.

An operation method of a flash memory system includes reading data stored in a memory device, wherein the data is encoded by units of message blocks each including a row constituent code and a column constituent code by using a block-wise concatenated Bose-Chadhuri-Hocquenghem (BC-BCH) method; performing a hard decision decoding on the read data; determining, when the hard decision decoding fails, a reference voltage for a message block having an error among the message blocks of the read data; and performing a soft decision decoding by using the determined reference voltage.