Abstract:
An extended symbol Galois field error correcting device is provided. The device includes a singly-extended Reed-Solomon encoder configured to generate an encoded codeword, {tilde over (c)}(x). The device also includes a channel medium that is signal coupled with the singly-extended Reed-Solomon encoder. The channel medium is configured to receive the encoded codeword, {tilde over (c)}(x), and output a received input codeword, {tilde over (r)}(x). The channel medium is capable of introducing error, {tilde over (e)}(x), to the encoded codeword, {tilde over (c)}(x). The device further includes a singly-extended Reed-Solomon decoder that is coupled with the channel medium. The singly-extended Reed-Solomon decoder is configured to receive the received input codeword, {tilde over (r)}(x). The singly-extended Reed-Solomon decoder has error detection circuitry and extended symbol correction circuitry. The error detection circuitry is configured to detect presence of error, {tilde over (e)}(x), within the received input codeword, {tilde over (r)}(x).