In a NAND flash memory, optimal read levels for minimizing bit error rate (BER) can be determined as offsets from a default read level. In general, memory would be allocated to store all the offset values for each of the 128 word-lines in a block using three or more different read levels per word-line. Fluctuations occur in optimal read levels from word-line to word- line but nevertheless demonstrate a behavior that allows a compression of the number of read level offsets to be stored. It is desirable to reduce the memory required to store the offsets and to smooth the noisy estimates. We present three read level profiling algorithms with two optimization criteria to reduce the number of read level offsets that needs to be stored while minimizing the degradation in BER. The read level profiling algorithms cluster the word-lines into groups in which the word-lines belonging to the same group have the same read level offset value. These algorithms are tested on lab data and it has been shown that with a moderate number of groups, no significant BER degradation occurs that would increase decoding errors.

This paper presents a new method of characterizing error events that cause bit errors for a truncated Viterbi algorithm detector. The truncated Viterbi algorithm is a practical approximation of maximum likelihood sequence estimation. The approach is applicable to convolutional codes or partial response channels and results in tighter error bounds than previous approaches. The technique is applied to several partial response channels that are commonly used as equalization targets for digital storage channels.