Error detection and correction

About: Error detection and correction is a research topic. Over the lifetime, 29440 publications have been published within this topic receiving 409341 citations. The topic is also known as: error detection & error correction.

Error control coding

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.

A multiple error LMS algorithm and its application to the active control of sound and vibration

Abstract: An algorithm is presented to adapt the coefficients of an array of FIR filters, whose outputs are linearly coupled to another array of error detection points, so that the sum of all the mean square error signals is minimized. The algorithm uses the instantaneous gradient of the total error, and for a single filter and error reduces to the "filtered x LMS" algorithm. The application of this algorithm to active sound and vibration control is discussed, by which suitably driven secondary sources are used to reduce the levels of acoustic or vibrational fields by minimizing the sum of the squares of a number of error sensor signals. A practical implementation of the algorithm is presented for the active control of sound at a single frequency. The algorithm converges on a timescale comparable to the response time of the system to be controlled, and is found to be very robust. If the pure tone reference signal is synchronously sampled, it is found that the behavior of the adaptive system can be completely described by a matrix of linear, time invariant, transfer functions. This is used to explain the behavior observed in simulations of a simplified single input, single output adaptive system, which retains many of the properties of the multichannel algorithm.

Extrinsic information transfer functions: model and erasure channel properties

Abstract: Extrinsic information transfer (EXIT) charts are a tool for predicting the convergence behavior of iterative processors for a variety of communication problems. A model is introduced that applies to decoding problems, including the iterative decoding of parallel concatenated (turbo) codes, serially concatenated codes, low-density parity-check (LDPC) codes, and repeat-accumulate (RA) codes. EXIT functions are defined using the model, and several properties of such functions are proved for erasure channels. One property expresses the area under an EXIT function in terms of a conditional entropy. A useful consequence of this result is that the design of capacity-approaching codes reduces to a curve-fitting problem for all the aforementioned codes. A second property relates the EXIT function of a code to its Helleseth-Klove-Levenshtein information functions, and thereby to the support weights of its subcodes. The relation is via a refinement of information functions called split information functions, and via a refinement of support weights called split support weights. Split information functions are used to prove a third property that relates the EXIT function of a linear code to the EXIT function of its dual.

Very low rate convolution codes for maximum theoretical performance of spread-spectrum multiple-access channels

Abstract: A spread-spectrum multiple-access (SSMA) communication system is treated for which both spreading and error control is provided by binary PSK modulation with orthogonal convolution codes. Performance of spread-spectrum multiple access by a large number of users employing this type of coded modulation is determined in the presence of background Gaussian noise. With this approach and coordinated processing at a common receiver, it is shown that the aggregate data rate of all simultaneous users can approach the Shannon capacity of the Gaussian noise channel. >