16.18 PMECC Controller Functional Description
The Programmable Multibit Error Correcting Code (PMECC) controller is a programmable binary BCH (Bose, Chaudhuri and Hocquenghem) encoder/decoder. This controller can be used to generate redundancy information for both SLC and MLC NAND devices. It supports redundancy for correction of 2, 4, 8, 12, 24 or 32 errors per sector of data. The sector size is programmable and can be set to 512 bytes or 1024 bytes. The PMECC module generates redundancy at encoding time, when a NAND write page operation is performed. The redundancy is appended to the page and written in the spare area. This operation is performed by the processor. It moves the content of the PMECCX registers into the NAND Flash memory. The number of registers depends on the selected error correction capability (see the table Relevant Redundancy Registers). This operation is executed for each sector. At decoding time, the PMECC module generates the remainders of the received codeword by the minimal polynomials. When all remainders for a given sector are set to zero, no error occurred. When the remainders are different from zero, the codeword is corrupted and further processing is required.
The PMECC module generates an interrupt indicating that an error occurred. The processor must read the PMECC Interrupt Status register (HSMC_PMECCISR). This register indicates which sector is corrupted.
The processor must execute the following decoding steps to find the error location within a sector:
- Compute syndrome
- Find the error location polynomial
- Find the roots of the error location polynomial
All decoding steps involve finite field computation. It means that a library of finite field arithmetic must be available to perform addition, multiplication and inversion. These arithmetic operations can be performed through the use of a memory mapped lookup table, or direct software implementation. The software implementation presented is based on lookup tables. Two tables named gf_log and gf_antilog are used. If alpha is the primitive element of the field, then a power of alpha is in the field. Assuming that beta = alpha ^ index, then beta belongs to the field, and gf_log(beta) = gf_log(alpha ^ index) = index. The gf_antilog table provides exponent inverse of the element; if beta = alpha ^ index, then gf_antilog(index) = beta.
The first step consists in the syndrome computation. The PMECC module computes the remainders and the software must substitute the power of the primitive element. The procedure implementation is given in the section Remainder Substitution Procedure.
The second step is the most software intensive. It is the Berlekamp’s iterative algorithm for finding the error-location polynomial. The procedure implementation is given in the section Finding the Error Location Polynomial Sigma(x).
The Last step is finding the root of the error location polynomial. This step can be very software intensive. Indeed there is no straightforward method of finding the roots, except evaluating each element of the field in the error location polynomial. However, a hardware accelerator can be used to find the roots of the polynomial. The PMERRLOC module provides this kind of hardware acceleration.
