Error Detection and Correction Using the BCH Code

نویسندگان

  • Hank Wallace
  • Claude Shannon
چکیده

The information revolution is in full swing, having matured over the last thirty or so years. It is estimated that there are hundreds of millions to several billion web pages on computers connected to the Internet, depending on whom you ask and the time of day. As of this writing, the google.com search engine listed 1,346,966,000 web pages in its database. Add to that email, FTP transactions, virtual private networks and other traffic, and the data volume swells to many terabits per day. We have all learned new standard multiplier prefixes as a result of this explosion. These days, the prefix “mega,” or million, when used in advertising (“Mega Cola”) actually makes the product seem trite.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Fast Inversion of Hankel Systems and E cient BCH 1 Decoding

| BCH decoding usually involves the evaluation of the error-locator polynomial. This is often achieved with the Berlekamp-Massey algorithm. The evaluation of the error-locator polynomial may also be computed using fast inversion techniques for Hankel matrices. It can be shown that O(lt) steps are necessary, with l being the number of errors which occurred and t being the error-correction capabi...

متن کامل

Undetected error probabilities of binary primitive BCH codes for both error correction and detection

In this paper, we investigate the undetected error probabilities for bounded-distance decoding of binary primitive BCH codes when they are used for both error correction and detection on a binary symmetric channel. We show that the undetected error probability of binary linear codes can be quite simplified and quantified if weight distribution of the code is binomial-like. We obtain bounds on t...

متن کامل

Levinson-Durbin Algorithm Used for Fast BCH Decoding

BCH decoding usually involves the evaluation of the error-locator polynomial. This is often achieved with the Berlekamp-Massey algorithm, which requires about O(t) computational steps, where t is the error-correction capability of the BCH code. The evaluation of the errorlocator polynomial may also be computed using fast inversion techniques for Hankel matrices. It will be shown that only O(lt)...

متن کامل

Quantum Error Correction Codes

This report contains the comprehensive explanation of some most important quantum error correction codes. After the brief corroboration of the quantum mechanical principles that govern any quantum mechanical process, we introduce stabilizer formalism and stabilizer codes for quantum error correction (QEC). As an interesting derivative from classical counterpart we also present Quantum Reed Mull...

متن کامل

Reliable MLC NAND Flash Memoris Based on Nonlinear t-Error-Correcting Codes

Multi-level cell (MLC) NAND flash memories are very popular storage media because of their power efficiency and big storage capacity. This paper proposes to use nonlinear t-error-correcting codes to replace linear BCH codes for error detection and correction in MLC NAND flash memories. Compared to linear BCH codes with the same bit-error correcting capability t, the proposed codes have the adva...

متن کامل

Quantum Bch Codes

After a brief introduction to both quantum computation and quantum error correction, we show how to construct quantum error-correcting codes based on classical BCH codes. With these codes, decoding can exploit additional information about the position of errors. This error model—the quantum erasure channel—is discussed. Finally, parameters of quantum BCH codes are provided.

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2005