Codes for limited magnitude asymmetric errors in flash memories

A data device that stores data for retrieval, the data device comprising:

• a host interface that provides communications between the data device and a host device;
• a memory interface that provides communications between memory cells and the data device;
• a microcontroller that manages communications for data transfer between the host interface and the memory interface, comprising an information channel, wherein the microcontroller processes an encoded data value comprising a codeword and performs operations such that the microcontroller
• receives a channel output y comprising symbols defined over an alphabet Q of size q;
• performs symbol recovery of the channel output y to obtain a word of symbols ψ over an alphabet Q′ of size q′ wherein q>q′ for an error correcting code Σ defined over Q′ and adapted to correct for up to t asymmetric l-limited magnitude errors;
• decodes the word of symbols ψ with the error correcting code Σ and obtains a decoded estimate {circumflex over (χ)} and an error-word estimate comprising a word of symbols {circumflex over (∈)} over Q′ such that ψ={circumflex over (χ)}+{circumflex over (∈)} mod q′;
• and
• combines the channel output y with the error-word estimate {circumflex over (∈)} and thereby produces the estimated codeword of the data value over the alphabet Q.

A method for run time programming of a data device to reach a target level of a physical quantity in memory cells of the data device, the method comprising:

• establishing an initial level and the target level of the physical quantity, wherein the target level corresponds to a codeword of an error correcting code;
• providing a programming pulse sequence comprising at least one pulse, wherein a first pulse increases the physical quantity from the initial level to a next level which is closer to the target level than the initial level, and subsequent pulses adjust the physical quantity toward the target level;
• terminating the programming pulse sequence at a terminating level when pulse sequence parameters are satisfied;
• applying error correction and adjusting the physical quantity from the terminating level to the target level for the codeword;
• wherein providing a programming pulse sequence comprises applying a predetermined number of pulses at the conclusion of which the terminating level is reached;
• and
• wherein the predetermined number of pulses is selected in accordance with a desired number N, given by
• N
• =
• log
• ⁡
• (
• I
• F
• -
• I
• 0
• )
• -
• log
• ⁡
• (
• Δ
• )
• -
• log
• ⁡
• (
• 1
• -
• K
• ∈
• )
• ,
• where the initial physical quantity level is given by Ii and the target level is given by IF and Δ corresponds to a desired error margin and K∈Δ−1/ln(∈).

A computer implemented method for error correction code design, the method comprising:

• receiving input parameters at a computer from a computer user for the error correction code design, the input parameters including values t and l, wherein l specifies a maximum magnitude of asymmetric errors in a codeword to be corrected by the error correction code and t specifies a maximum number of the l-limited magnitude asymmetric errors in a codeword;
• accessing, at the computer, an error correction code database containing error correction codes, and determining error correction codes that satisfy the input parameters;
• and
• retrieving, at the computer, database information that identifies the determined error correction codes that satisfy the input parameters and providing the information to the user;
• wherein the designed error correction code is sufficient for processing an encoded data value comprising a codeword received over an information channel, the codeword processing with the code comprising:
• receiving a channel output y comprising symbols defined over an alphabet Q of size q;
• performing symbol recovery of the channel output y to obtain a word of symbols ψ over an alphabet Q′ of size q′ wherein q>q′ for an error correcting code Σ defined over Q′ and adapted to correct for up to t asymmetric l-limited magnitude errors;
• decoding the word of symbols ψ with the error correcting code Σ and obtaining a decoded estimate {circumflex over (χ)} and an error-word estimate comprising a word of symbols {circumflex over (∈)} over Q′ such that ψ={circumflex over (χ)}+{circumflex over (∈)} mod q′;
• and
• combining the channel output y with the error-word estimate {circumflex over (∈)} and thereby producing the estimated codeword of the data value over the alphabet Q.

A method of encoding a data value comprising user information for transmission over an information channel, the method comprising:

• providing the data value to an encoder utilizing an error correcting code defined over a code alphabet and producing an encoder output X value;
• combining the X value and the data value and producing the encoded data value comprising a codeword of a code C over an alphabet larger than the Σ alphabet;
• wherein the encoded data value further comprises a symbol defined over an alphabet Q of size q, such that the symbol can be recovered by performing symbol recovery of the channel output y to obtain a word of symbols ψ over an alphabet Q′ of size q′ wherein q>q′ for an error correcting code Σ defined over Q′ and adapted to correct for up to t asymmetric l-limited magnitude errors, followed by decoding the word of symbols ψ with the error correcting code Σ and obtaining a decoded estimate {circumflex over (χ)} and an error-word estimate comprising a word of symbols {circumflex over (∈)} over Q′ such that ψ={circumflex over (χ)}+{circumflex over (∈)} mod q′;
• and combining the channel output y with the error-word estimate {circumflex over (∈)} and thereby producing the estimated codeword of the data value over the alphabet Q.

An encoder for encoding a data value comprising user information for transmission over an information channel, the encoder comprising:

• a Σ encoder utilizing a code defined over a code alphabet, wherein the encoder produces an encoder output X value;
• a combiner that combines the X value and the data value and produces the encoded data value comprising a codeword of a code C over an alphabet larger than the Σ alphabet;
• wherein the encoded data value further comprises a symbol defined over an alphabet Q of size q, such that the symbol can be recovered by performing symbol recovery of the channel output y to obtain a word of symbols ψ over an alphabet Q′ of size q′ wherein q>q′ for an error correcting code Σ defined over Q′ and adapted to correct for up to t asymmetric l-limited magnitude errors, followed by decoding the word of symbols ψ with the error correcting code Σ and obtaining a decoded estimate {circumflex over (χ)} and an error-word estimate comprising a word of symbols {circumflex over (∈)} over Q′ such that ψ={circumflex over (χ)}+{circumflex over (∈)} mod q′;
• and combining the channel output y with the error-word estimate {circumflex over (∈)} and thereby producing the estimated codeword of the data value over the alphabet Q.