Error detection and correction codes for channels and memories with incomplete error characteristics

A system including:

• at least one memory device including a plurality of memory cells, each memory cell having a plurality of storage states in a one-to-one correspondence with the members of a set of stored symbols, the memory device having an error mechanism having incomplete error introduction properties,
• a memory controller coupled to the at least one memory device to cause data derived from symbols selected from the set of stored symbols to be read out of a plurality of memory cells of the at least one memory device,
• a channel decoder coupled to the memory controller to correct errors in the data read out of the at least one memory device, the errors having been introduced at least in part by the error mechanism,
• wherein the channel decoder decodes a code comprising of a set of code words, the minimum modified Hamming separation among the elements of the set of code words in light of the incomplete error introduction properties of the at least one memory device is greater than the minimum Hamming distance among the elements of the set of code words.

A method of operating a channel having a first end, a second end, and an error injection mechanism with an incomplete error property, the method comprising the steps of:

• receiving a symbol stream from the channel, the received symbol stream comprising a plurality of symbol words each symbol word comprising one or more symbols selected from a symbol set;
• and
• decoding the received symbol words to produce either a corrected data stream, according to an error correcting and/or detecting code, the code comprising a set of code words with a minimum modified Hamming distance of the code, the minimum modified Hamming separation being computed according to the error injection properties of the error injection mechanism of the channel, the minimum modified Hamming distance being greater than the minimum of the Hamming distances of the code,
• wherein the decoding of a symbol word comprises determining which code word of the set of code words yields the smallest modified Hamming distance, and outputting the code word.