TL;DR: In this paper all error detecting and error correcting mechanisms are studied and best mechanism on the basis of accuracy, complexity and power consumption is selected.
Abstract: In most communication system convolutional encoders are used and AWGN introduces errors during transmission. In this paper all error detecting and error correcting mechanisms are studied and best mechanism on the basis of accuracy, complexity and power consumption is selected. Error detection and correction mechanisms are vital and numerous techniques exist for reducing the effect of bit - errors and trying to ensure that the receiver eventually gets an error free version of the packet. In order to protect memories against MCUs as well as SEUs is to make use of advanced Error detecting and correcting codes that can correct more than one error per word. There should be tradeoff between complexity of hardware and power consumption in decoder. Index Term:- Error correcting codes, error detecting codes, hamming codes, block codes INTRODUCTION: Error detection and correction mechanisms are vital and numerous techniques exist for reducing the effect of bit -errors and trying to ensure that the receiver eventually gets an error free version of the packet. The major techniques used are error detection with Automatic Repeat Request, Forward Error Correction and hybrid forms. Forward Error Correction is the method of transmitting error correction information along with the message. To prevent soft errors from causing data corruption, memories are typically protected with error correction codes. Error correcting codes (ECCs) are commonly used to protect against soft errors and thereby enhance system reliability and data integrity. Single error detecting and single error correcting codes are used for this purpose, these codes are able to correct single bit errors and detect double bit errors in a codeword. The code is often designed first with the goal of minimizing the gap from Shannon capacity and attaining the target error probability. ECC protects against undetected data corruption, and is used in computers where such corruption is unacceptable, as with some scientific and financial computing applications and as file servers. ECC also reduces the number of crashes, particularly unacceptable in multi-user server applications and maximum-availability systems. Error detection is most commonly realized using a suitable hash function (or checksum algorithm). A hash function adds a fixed-length tag to a message, which enables receivers to verify the delivered message by recomputing the tag and comparing it with the one provided.
TL;DR: The basic goal in digital communications is to transport bits of information without losing too much information along the way, but the level of information loss that is tolerable/acceptable varies for different applications.
Abstract: The basic goal in digital communications is to transport bits of information without losing too much information along the way. The level of information loss that is tolerable/acceptable varies for different applications. The loss is measured in terms of the bit error rate, or BER. An interesting application that employs error control coding is a system with a storage medium such as a hard disk drive or a compact disc (CD). We can think of the channel as a block that causes errors to occur when a signal passes through it. Regardless of the error source, we can describe the problem as follows: when the transmitted signal arrives at the receiver after passing through the channel, the received data will have some bits that are in error. The system designer would like to incorporate ways to detect and correct these errors. The field that covers such digital processing techniques is known as error control coding.
TL;DR: The proposed analysis offers a simple and unifying approach to evaluating the performance of uncoded and (possibly space-time) coded transmissions over fading channels, and the method applies to almost all digital modulation schemes, including M-ary phaseshift keying, quadrature amplitude modulation, and frequency-shift keying with coherent or noncoherent detection.
Abstract: We quantify the performance of wireless transmissions over random fading channels at high signal-to-noise ratio (SNR). The performance criteria we consider are average probability of:error and outage probability. We show that as functions of the average SNR, they can both be characterized by two parameters: the diversity and coding gains. They both exhibit identical diversity orders, but their coding gains in decibels differ by a constant. The diversity and coding gains are found to depend on the behavior of-the random SNR's probability density function only at the origin, or equivalently, on the decaying order of the corresponding moment generating function (i.e., how fast the moment generating function goes to zero as its argument goes to infinity). Diversity and coding gains for diversity combining systems are expressed in terms of the diversity branches' individual diversity and coding gains, where the branches can come from any diversity technique such as space, time, frequency, or, multipath. The proposed analysis offers a simple and unifying approach to evaluating the performance of uncoded and (possibly space-time) coded transmissions over fading channels, and the method applies to almost all digital modulation schemes, including M-ary phaseshift keying, quadrature amplitude modulation, and frequency-shift keying with coherent or noncoherent detection.
TL;DR: A new multilevel coding method that uses several error-correcting codes that makes effective use of soft-decisions to improve the performance of decoding and is superior to other multileVEL coding systems.
Abstract: A new multilevel coding method that uses several error-correcting codes is proposed. The transmission symbols are constructed by combining symbols of codewords of these codes. Usually, these codes are binary error-correcting codes and have different error-correcting capabilities. For various channels, efficient systems can be obtained by choosing these codes appropriately. Encoding and decoding procedures for this method are relatively simple compared with those of other multilevel coding methods. In addition, this method makes effective use of soft-decisions to improve the performance of decoding. The decoding error probability is analyzed for multiphase modulation, and numerical comparisons to other multilevel coding systems are made. When equally complex systems are compared, the new system is superior to other multilevel coding systems.