SPRUIM2H May 2020 – October 2023 AM2431 , AM2432 , AM2434 , AM6411 , AM6412 , AM6421 , AM6422 , AM6441 , AM6442
BCH encoding considers a block of data to protect as a polynomial message M(x). In a standard case, 512 bytes of data (that is, 212 bits = 4096 bits) are seen as a polynomial of degree 212 – 1 = 4095, with parameters ranging from M0 to M4095. For 512 bytes of data, 52 bits are required for 4-bit error correction, 104 bits are required for 8-bit error correction, and 207 bits are required for 16-bit error correction. The ECC is a remainder polynomial R(x) of degree 103 (or 51, depending on the selected mode). The complete codeword C(x) is the concatenation of M(x) and R(x), as described in Table 12-3230.
Message M(x) | ECC R(x) | |||||
---|---|---|---|---|---|---|
Bit Number | M4095 | ... | M0 | R103 | ... | R0 |
If the message is extended by the addition of spare bytes to be protected by the same ECC, the principle is still valid. For example, a 3-byte extension of the message gives a polynomial message M(x) of degree ((512 + 3) × 8) – 1 = 4119, for a total of 3 + 13 = 16 spare bytes of spare, all protected as part of the same codeword.
The message and the ECC bits are manipulated and mapped in the GPMC byte-oriented system. The ECC bits are stored in the following registers (where i = 0 to 3):