Method and apparatus for computing reed-solomon error magnitudes
AssigneeTexas Instruments Incorporated
InventorDarrell K. Cox
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Abstract
In a Reed-Solomon decoder, error magnitudes are determined from a root matrix and a syndrome vector. The root matrix is triangularized (60) using recursive calculations. The syndrome vector is adjusted to the triangulization (62) by recursive calculations. The error magnitudes are then determined through substitution (64).
Claims18
A method of determining error magnitudes in Reed-Solomon decoding, wherein a vector of v syndromes El and v error locations lj are determined from a received codeword, and error magnitudes elj at the v error locations can be determined from the equation
- 21 E l = ∑ j = 1 v ⅇ l j a i l j ,
- where a is a primitive of the codeword, comprising the steps of:
- triangularizing a v×v Vandermonde matrix of the elements ailj to generate elements of a matrix V;
- generating a syndrome vector W of syndromes Ei, adjusted for the triangularization of matrix V;
- generating a solution to an equation of a form Vx M=W, where M is a vector of the error magnitudes elj and Vx is a vector of matrix V, having a single unknown error magnitude;
- substituting to create other equations of the form Vx M=W having a single unknown that can be solved for a respective error magnitude.
A method of Reed-Solomon decoding, comprising the steps of:
- generating a vector of v syndromes Ei from a received codeword;
- generating v error locations lj from the received codeword,
- determining error magnitudes elj at the v error locations from the equation
- 23 E l = ∑ j = 1 v ⅇ l j a i l j ,
- where a is a primitive of the codeword by:
- triangularizing a v×v Vandermonde matrix of the elements ailj to generate elements of a matrix V;
- generating a syndrome vector W of syndromes Ei, adjusted for the triangularization of matrix V;
- generating a solution to an equation of a form Vx M=W, where M is a vector of the error magnitudes elj and Vx is a vector of matrix V, having a single unknown error magnitude,
- substituting to create other equations of the form Vx M=W having a single unknown that can be solved for a respective error magnitude..
A Reed-Solomon decoder comprising:
- circuitry for generating a vector of v syndromes Ei from a received codeword;
- circuitry for generating v error locations lj from the received codeword,
- circuitry for determining error magnitudes elj at the v error locations from the equation
- 24 E l = ∑ j = 1 v ⅇ l j a i l j ,
- where a is a primitive of the codeword by the operations of:
- triangularizing a v×v Vandermonde matrix of the elements ailj to generate elements of a matrix V;
- generating a syndrome vector W of syndromes Ei adjusted for the triangularization of matrix V;
- generating a solution to an equation of a form Vx M=W, where M is a vector of the error magnitudes elj and Vx is a vector of matrix V, having a single unknown error magnitude;
- substituting to create other equations of the form Vx M=W having a single unknown that can be solved for a respective error magnitude.
Dependencies are inferred from the claim text.