Publication

Universal a posteriori metrics game

Graph Chatbot

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.

Viterbi decoder

A Viterbi decoder uses the Viterbi algorithm for decoding a bitstream that has been encoded using a convolutional code or trellis code. There are other algorithms for decoding a convolutionally encoded stream (for example, the Fano algorithm). The Viterbi algorithm is the most resource-consuming, but it does the maximum likelihood decoding. It is most often used for decoding convolutional codes with constraint lengths k≤3, but values up to k=15 are used in practice. Viterbi decoding was developed by Andrew J.

Decoding methods

In coding theory, decoding is the process of translating received messages into codewords of a given code. There have been many common methods of mapping messages to codewords. These are often used to recover messages sent over a noisy channel, such as a binary symmetric channel. is considered a binary code with the length ; shall be elements of ; and is the distance between those elements. One may be given the message , then ideal observer decoding generates the codeword .

Binary symmetric channel

A binary symmetric channel (or BSCp) is a common communications channel model used in coding theory and information theory. In this model, a transmitter wishes to send a bit (a zero or a one), and the receiver will receive a bit. The bit will be "flipped" with a "crossover probability" of p, and otherwise is received correctly. This model can be applied to varied communication channels such as telephone lines or disk drive storage.

Communication channel

A communication channel refers either to a physical transmission medium such as a wire, or to a logical connection over a multiplexed medium such as a radio channel in telecommunications and computer networking. A channel is used for information transfer of, for example, a digital bit stream, from one or several senders to one or several receivers. A channel has a certain capacity for transmitting information, often measured by its bandwidth in Hz or its data rate in bits per second.

Binary erasure channel

In coding theory and information theory, a binary erasure channel (BEC) is a communications channel model. A transmitter sends a bit (a zero or a one), and the receiver either receives the bit correctly, or with some probability receives a message that the bit was not received ("erased") . A binary erasure channel with erasure probability is a channel with binary input, ternary output, and probability of erasure . That is, let be the transmitted random variable with alphabet .

Error correction code

In computing, telecommunication, information theory, and coding theory, forward error correction (FEC) or channel coding is a technique used for controlling errors in data transmission over unreliable or noisy communication channels. The central idea is that the sender encodes the message in a redundant way, most often by using an error correction code or error correcting code (ECC). The redundancy allows the receiver not only to detect errors that may occur anywhere in the message, but often to correct a limited number of errors.

Continuous uniform distribution

In probability theory and statistics, the continuous uniform distributions or rectangular distributions are a family of symmetric probability distributions. Such a distribution describes an experiment where there is an arbitrary outcome that lies between certain bounds. The bounds are defined by the parameters, and which are the minimum and maximum values. The interval can either be closed (i.e. ) or open (i.e. ). Therefore, the distribution is often abbreviated where stands for uniform distribution.

Discrete uniform distribution

In probability theory and statistics, the discrete uniform distribution is a symmetric probability distribution wherein a finite number of values are equally likely to be observed; every one of n values has equal probability 1/n. Another way of saying "discrete uniform distribution" would be "a known, finite number of outcomes equally likely to happen". A simple example of the discrete uniform distribution is throwing a fair die. The possible values are 1, 2, 3, 4, 5, 6, and each time the die is thrown the probability of a given score is 1/6.

Erasure code

In coding theory, an erasure code is a forward error correction (FEC) code under the assumption of bit erasures (rather than bit errors), which transforms a message of k symbols into a longer message (code word) with n symbols such that the original message can be recovered from a subset of the n symbols. The fraction r = k/n is called the code rate. The fraction k’/k, where k’ denotes the number of symbols required for recovery, is called reception efficiency.

Maximum likelihood estimation

In statistics, maximum likelihood estimation (MLE) is a method of estimating the parameters of an assumed probability distribution, given some observed data. This is achieved by maximizing a likelihood function so that, under the assumed statistical model, the observed data is most probable. The point in the parameter space that maximizes the likelihood function is called the maximum likelihood estimate. The logic of maximum likelihood is both intuitive and flexible, and as such the method has become a dominant means of statistical inference.