Reed-Solomon Euclid algorithm decoder having a process configurable Euclid stack
AssigneeIdaho Research Foundation, Inc.
InventorsKelly Cameron, Patrick A. Owsley
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Abstract
A Reed-Solomon Galois Field Euclid algorithm error correction decoder solves Euclid's algorithm with a Euclid stack which can be configured to function as a Euclid divide or a Euclid multiply module. The decorder is able to resolve twice the erasure errors by selecting .GAMMA.(x) and T(x) as the initial conditions for .LAMBDA..sup.(0) (x) and .OMEGA..sup.(0) (x), respectively.
Claims10
A Reed-Solomon Galois Field Euclid Algorithm decoder having:
- a. means for receiving an encoded electrical message signal;
- b. means for calculating .OMEGA.(x), a magnitude polynomial representing a portion of a magnitude of an error in the received message signal, wherein the means for calculating .OMEGA.(x) is coupled to the means for receiving;
- c. means for calculating .LAMBDA.(x), a location polynomial representing a location of said error in said received message signal, wherein the means for calculating .LAMBDA.(x) is coupled to the means for receiving, said location polynomial having a first derivative polynomial;
- d. means for calculating .GAMMA.(x), an erasure polynomial, wherein the means for calculating .GAMMA.(x) is coupled to the means for receiving;
- e. means for calculating T(x), a modified syndrome polynomial, wherein the means for calculating T(x) is coupled to the means for receiving, and
- f. means for correcting the error,
- wherein the means for calculating .OMEGA.(x), the means for calculating .LAMBDA.(x), the means for calculating .GAMMA.(x) and the means for calculating T(x) all have identical architectures.
A Reed-Solomon Galois Field Euclid Algorithm decoder for correcting an error in a received electrical message signal comprising a single Euclid stack means for forming an erasure polynomial .GAMMA.(x), a magnitude polynomial .OMEGA.(x), a modified syndrome polynomial T(x) and a location polynomial .LAMBDA.(x) wherein a control sequence for forming .GAMMA.(x) is the same as a control sequence for forming T(x) and a control sequence for forming .OMEGA.(x) is the same as a control sequence for forming .LAMBDA.(x) and further wherein .GAMMA.(x) comprises a set of initial conditions for forming .LAMBDA.(x) and is automatically in a correct position in the stack for performing a .LAMBDA.(x) recursion and similarly wherein T(x) comprises one of the initial conditions for forming .LAMBDA.(x) and is automatically in the correct position in the stack for performing a .OMEGA.(x) recursion wherein the decoder further comprises:
- a. means for calculating a magnitude polynomial representing a portion of a magnitude of said error in said received electrical message signal;
- b. means for calculating a location polynomial representing a location of said error in said received electrical message signal said location polynomial having a first derivative polynomial having an identical architecture to the means for calculating a magnitude polynomial;
- c. means for calculating the first derivative polynomial of said location polynomial, said first derivative having a plurality of non-zero values, each of said non-zero values having an inverse;
- d. means for calculating said inverse values;
- e. means for multiplying each of said inverse values with a value of said magnitude polynomial for forming a correction polynomial;
- and
- f. means for correcting the received electrical message signal.
Dependencies are inferred from the claim text.