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...

The BeiDou satellite-induced code biases have been confirmed to be orbit type-, frequency-, and elevation-dependent. Such code-phase divergences (code bias variations) severely affect absolute precise applications which use code measurements. To reduce their adverse effects, an improved correction model is proposed in this paper. Different from the model proposed by Wanninger and Beer (2015), m...

Compressed images transmitted over noisy channels are extremely sensitive to bit errors. This necessitates the application of error control channel coding to the compressed representation before transmission. This paper presents an image transmission system which takes advantage of the superior performance of Turbo codes, an important new class of parallel concatenated codes. Several aspects of...

A new method for computing the minimum distances of linear error correcting codes is proposed and justi ed Unlike classical techniques that rely on exhaustive or partial enu meration of codewords this new method is based on the ability of the Soft In decoder to overcome Error Impulse input patterns It is shown that the maximum magnitude of the Error Impulse that can be corrected by the decoder ...

In digital communication system error correction codes are used when channel is noisy. An error correction code removes errors induced in communication and make possible error free transmission. By use of such error correction code we can send signal at lower transmit power as compared to un-coded system. Convolutional code corrects both type of errors random and burst and used in deep space an...

A parallel concatenated convolutional coding scheme consists of two constituent systematic convolutional encoders linked by an interleaver. The information bits at the input of the rst encoder are scrambled by the interleaver before entering the second encoder. The codewords of the parallel concatenated code consist of the information bits followed by the parity check bits of both encoders. Par...

Error correction codes are used for long years to protect memories from the soft errors. For a single bit error correction, the SEC single bit error correction code that correct one bit error per word are used. Double bit error detection code are used to detect the double bit errors. In the increasing of the technology the single bit error correction codes are used in the various places such as...

The paper starts with a short overview of channel coding and the reader is reminded the concept of convolutional encoding. Bottlenecks of the traditional approach are described and the motivation behind turbo codes is explained. After examining the turbo codes design more in detail, reasons behind their efficiency are brought out. Finally, a real-world example of the turbo code used in the thir...

We give efficient constructions for error correcting unordered {ECU) codes, i.e., codes such that any pair of codewords are at a certain minimal distance apart and at the same time they are unordered. These codes are used for detecting a predetermined number of (symmetric) errors and for detecting all unidirectional errors. We also give an application in parallel asynchronous communications.