Identifying uncorrectable codewords in a Reed-Solomon decoder for errors and erasures

A detector circuit arranged to identify an uncorrectable codeword, for use in a Reed-Solomon decoder handling errors and erasures, the circuit comprising:

• a logic unit arranged to identify each condition:
• (a) no solution to key equation σ(x)T(x)≡(x)modx2T;
• (b) deg σ(x)≠nerrors;
• (c) error and erasure locations coincide;
• (d) degω(x) ≧nerrors+nerasures;
• (e) nerasures+2*nerrors>2T;
• and
• (f) an error location has a zero correction magnitude;
• where nerrors and nerasures represents, respectively, a number of errors and erasures with reference to an error locator polynomial σ(x) and an erasure locator polynomial Λ(x), 2T is the strength of a Reed-Solomon code, ω(x) is an errata evaluator polynomial, and T(x) is a modified syndrome polynomial;
• and
• an indicator unit arranged to indicate an uncorrectable codeword, responsive to the logic unit.

A method of identifying uncorrectable Reed-Solomon codewords in a group Reed-Solomon codewords being passed to a Reed-Solomon decoder, the Reed-Solomon decoder including a polynomial generation unit, a polynomial evaluation unit, an uncorrectable error detector and an error correction block, the method comprising:

• generating polynomial data in the polynomial generation unit representing locations and magnitudes of errors and erasure in a Reed-Solomon codeword passed to the Reed-Solomon decoder,
• performing a Chien search on said polynomial data in the polynomial evaluation unit and solving Forney's equations to determine correction locations and magnitudes to be applied to the Reed-Solomon codeword passed to the Reed-Solomon decoder, and
• detecting, in the uncorrectable error detector, that the Reed-Solomon codeword passed to the Reed-Solomon decoder is an uncorrectable codeword when any one or more of the following conditions (a) to (f) is satisfied:
• (a) no solution to key equation σ(x)T(x)≡(x)modx2T is found by a first logic means;
• (b) deg σ(x)≠nerrors is determined by a second logic means;
• (c) error and erasure locations coincide is determined by a third logic means;
• (d) deg ω(x)≧nerrors+nerasures is determined by a forth logic means;
• (e) nerasures+2*nerrors>2T is determined by a fifth logic means and
• (f) an error location has a zero correction magnitude is determined by a sixth logic means;
• where nerrors and nerasures represent, respectively, a number of errors with reference to an error locator polynomial σ(x) and a number of erasures with reference to an erasure locator polynomial Λ(x), 2T is the strength of a Reed-Solomon code, ω(x) is an errata evaluator polynomial, and T(x) is a modified syndrome polynomial;
• and
• if the Reed-Solomon codeword passed to the Reed-Solomon decoder is not an uncorrectable codeword, then performing error correction on the Reed-Solomon codeword passed to the Reed-Solomon decoder using the correction locations and magnitudes determined by solving Forney's equations.