University of California

Paul Siegel

Jack K Wolf

Alexander Vardy

Eitan Yaakobi

Mats Oberg

Scott Kayser

Mats Öberg

Mats &Ouml;berg

The invention provides a family of 2-write WOM-codes, preferred embodiments of which provide improved WOM-rates. Embodiments of the invention provide constructs for linear codes C having a 2-write WOM-code. Embodiments of the invention provide 2-write WOM-codes that improve the best known WOM-rates known to the present inventors at the time of filing with two writes. Preferred WOM-codes are proved to be capacity achieving when the parity check matrix of the linear code C is chosen uniformly at random. Preferred embodiments of the invention provide an electronic device utilizing an efficient coding scheme of WOM-codes with two write capability. The coding method is based on linear binary codes and allows the electronic device to write information to the memory twice before erasing it. This method can be applied for any kind of memory systems, and in particular for flash memories. The method is shown to outperform all well-known codes.

Efficient two write WOM codes, coding methods and devices

The invention provides WOM coding methods and electronic devices with error correcting codes that provide single, double and triple error correction. In one coding, if the code corrects two/three errors, it has two/three parts of redundancy bits. For double error correction, if only one part of the redundancy bit has no errors then it is possible to correct one error. For triple error correction, if only one/two parts of the redundancy bits have no errors then it is possible to correct one/two errors. Codes that correct/detect a single, two and three cell-erasures are provided. A code that has three roots, &#x3b1;, &#x3b1;, &#x3b1;, each of which is a primitive element and where every pair of roots generates a double error correcting code, is provided. Codes and coding utilizing a triple error correcting WOM code that can correct an arbitrary number of errors are provided.

Strong single and multiple error correcting WOM codes, coding methods and devices

The invention provides a channel coding method for encoding systematic data for transmission in a communication channel. The systematic data has a runlength constraint. In the method, data words are permuted. Error codes are generated based upon the permuted data words. The error codes are appended to original data words to form channel input for serial transmission in the communication channel. The number of error code bits is limited to ensure the channel input meets the runlength constraint. The error code can be a parity check bit.

Parity check outer code and runlength constrained outer code usable with parity bits

A method uses an outer code that is a concatenation of code words generated by a parity check encoder. The outer code word is permuted by an interleaver. The high rate coding provides good performance with a simple structure. A parity check bit is generated for each data word of received systematic dates. Code words are formed by adding a generated parity bit to each data word. Groups of code words are permuted to form encoded input for transmission in a communication channel. The invention further includes encoding to maintain a runlength-limiting (RLL) constraint at the channel input. Interleaved runlength encoded system data is used to generate error code bits. Insertion of error code bits in the system data at the channel input is controlled. This guarantees that the channel input stream comprised of the runlength-limited system data and inserted error code bits meets the runlength constraints.

A method uses an outer code that is a concatenation of code words generated by a parity check encoder. The outer code word is permuted by an interleaver. The high rate coding provides good performance with a simple structure. An odd parity check bit is generated for each data word of received systematic dates. Code words are formed by adding a generated parity bit to each data word. Groups of code words are permuted to form encoded input for transmission in a communication channel. The invention further includes encoding to maintain a runlength-limiting (RLL) constraint at the channel input. Interleaved runlength encoded system data is used to generate error code bits. Insertion of error code bits in the system data at the channel input is controlled. This guarantees that the channel input stream comprised of the runlength-limited system data and inserted error code bits meets the runlength constraints.

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La Jolla, CA, United States of America

Paul Siegel