Hard-decision decoding scheme

Codeword length (n) : 31 symbols.

Message length (k) : 19 symbols.

Error correction capability (t) : 6 symbols

One symbol represents 5 bit.

Uses GF(2^5) with primitive polynomial p(x) = X^5 X^2 + 1

Generator polynomial, g(x) = a^15 a^21*X + a^6*X^2 + a^15*X^3 + a^25*X^4 + a^17*X^5 + a^18*X^6 + a^30*X^7 + a^20*X^8 + a^23*X^9 + a^27*X^10 + a^24*X^11 + X^12. Note: a = alpha, primitive element in GF(2^5) and a^i is root of g(x) for i = 19, 20, ..., 30.

Uses Verilog descr iption with synthesizable RTL modelling.

Consists of 5 main blocks: SC (Syndrome Computation), KES (Key Equation Solver), CSEE (Chien Search and Error Evaluator), Controller and FIFO Register.

-Hard-decision decoding scheme Codeword l KV (n) : 31 symbols. Message length (k) : 19 symbols. Error correction capability (t) : 6 symbols One symbol represents five bit. Uses GF (2 ^ 5) with primitive polynomial p (x) = x ^ x ^ 5 2 1 Ge nerator polynomial. g (x) = a ^ a ^ 15 * 21 ^ 6 a X * X ^ a ^ 15 2 * X ^ a ^ 3 25 * X ^ a ^ 4 17 5 * X ^ a ^ 18 ^ 6 X * a * X 30 ^ 7 ^ a ^ 20 * X ^ a ^ 23 8 * X ^ a ^ 9 * 27 X 10 ^ a ^ 24 * 11 ^ X ^ X 12. Note : a = alpha, primitive element in GF (2 ^ 5) and a ^ i is the root of g (x) for i = 19, 20, ..., 30. Uses Verilog descr iption with synthesizab le RTL modeling. Consists of five main blocks : SC (Syndrome Computation), KES (Key Equation Solver). CSEE (Chien Search and Error Evaluator) Controller and FIFO Register.