BM-BASED FAST CHASE DECODING OF BINARY BCH CODES THROUGH DEGENERATE LIST DECODING

    公开(公告)号:US20180205398A1

    公开(公告)日:2018-07-19

    申请号:US15409724

    申请日:2017-01-19

    Abstract: An application specific integrated circuit (ASIC) tangibly encodes a method for fast polynomial updates in fast Chase decoding of binary Bose-Chaudhuri-Hocquenghem (BCH) codes. The method includes the steps of using outputs of a syndrome-based hard-decision (HD) algorithm to find a Groebner basis for a solution module of a modified key equation, upon failure of HD decoding of a BCH codeword received by the ASIC from a communication channel; evaluating polynomials obtained from said Groebner basis at inverses of specified weak-bit locations; and transforming a Groebner basis for a set of flipped weak-bit locations (α1, . . . , αr−1) to a Groebner basis for (α1, . . . , αr), wherein αr is a next weak-bit location, wherein r is a difference between a number of errors and a HD correction radius of the BCH codeword.

    ONE-SUB-SYMBOL LINEAR REPAIR SCHEMES
    3.
    发明申请

    公开(公告)号:US20190158119A1

    公开(公告)日:2019-05-23

    申请号:US15821480

    申请日:2017-11-22

    Abstract: A method for repairing a single erasure in a Reed Solomon code in a system of a plurality of n storage nodes and a controller, wherein a content of each storage node is a codeword and each node stores a vector v. The method includes identifying a failed storage node; transmitting an index of the failed storage node to each surviving storage node; multiplying the content of each node i by a j-th component of a vector that is a permutation of elements of vector v that correspond to the surviving storage nodes; determining a trace map of the result and converting the result from an m×r bit representation into a reduced representation of r bits; reconstructing the content of the failed storage node from the reduced representation of each surviving node's content; and outputting the reconstructed content of the failed storage node.

    GROEBNER-BASES APPROACH TO FAST CHASE DECODING OF GENERALIZED REED-SOLOMON CODES

    公开(公告)号:US20190068319A1

    公开(公告)日:2019-02-28

    申请号:US15683456

    申请日:2017-08-22

    Abstract: An application specific integrated circuit (ASIC) tangibly encodes a program of instructions executable by the integrated circuit to perform a method for fast Chase decoding of generalized Reed-Solomon (GRS) codes. The method includes using outputs of a syndrome-based hard-decision (HD) algorithm to find an initial Groebner basis G for a solution module of a key equation, upon failure of HD decoding of a GRS codeword received by the ASIC from a communication channel; traversing a tree of error patterns on a plurality of unreliable coordinates to adjoin a next weak coordinate, where vertices of the tree of error patterns correspond to error patterns, and edges connect a parent error pattern to a child error pattern having exactly one additional non-zero value, to find a Groebner basis for each adjoining error location; and outputting an estimated transmitted codeword when a correct error vector has been found.

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