Channel capacity

The answer to the first question is very simple, although the proof is somewhat involved. Each discrete memoryless source has a number, JR, called the transmission rate, associated with it, and each discrete memoryless channel has a number, C, called the channel capacity, associated with it. If B < C, one can receive the source output at the... 

The significance of channel capacity, as will be shown later, is that the output from any given discrete memoryless source with an entropy per channel digit less than C can be transmitted over the channel with an arbitrarily small probability of decoding error t>y sufficiently... 

If the channel inputs are statistically independent, and if the individual letter probabilities are such as to give channel capacity, then the average mutual information transmitted by N letters is NO. 

Converse to Coding Theorem.—We shall show in this Section that reliable communication at rates greater than channel capacity is impossible. Although only discrete memoryless sources and channels will be considered here, it will be obvious that the results are virtually independent of the type of channel. It was shown in the last section that the average mutual information between source and destination can be no greater than channel capacity then if the source rate is greater than capacity, some information is lost. The problem is to relate this lost information, or equivocation, to the probability of error between the source and destination. 

Also consider a discrete memoryless channel with an input alphabet, xK, an output alphabet yu , yf, a set of transition probabilities, Pr(yj k), and a capacity C. Let Te be the time interval between channel uses, and define the channel capacity per unit time, CT, as... 

Equation (4-66) yields an implicit lower bound to Pe that is greater than 0 when BT > CT. Observe that the bound is independent of N and depends only on the source entropy, the channel capacity per source digit (CTTt), and the source alphabet size. It would be satisfying if the dependence of Eq. (4-66) on the source alphabet size could be removed. Unfortunately the dependence of Pe on M as well as (RT — Ct)Ts is necessary, as the next theorem shows. 

E could be increased somewhat for small R by optimizing F(x) for each p, but the simplicity of Eqs. (4-198) to (4r-201) make them useful despite the possibility of slight improvement. We see from setting p equal to 0 in Eq. (4-198) that channel capacity for this channel is given by... 

Channel capacity here is JBT(0), which is the well-known Shannon formula... 

A remarkable properties of very noisy channel with Gaussian noise distribution is that the channel capacity can be increased by discarding samples in... 

Figure 4. Channel capacity of noisy channel with discarded samples (SjN = 0.01)...

Information capacity (channel capacity) C = Mpot/1 bit/s Dynamic detectors, e.g., photomultiplier t time... 

With suitable scan-line delay circuits, the filter may be applied in real time to live video images. In data communications, bandwidth extrapolation offers the opportunity to make far better use of channel capacity than is now possible. The bounded methods produce their most impressive restorations when o(x) spends a lot of time at or near the bounds. The present method was designed for use with both upper and lower bounds, which makes it ideal for the bilevel signals used in digital transmission. 

Figure 2.12 shows an example (for Layer 3) of the succession of frames with different amounts of bits actually used. A pointer called main-data-begin is used to transmit the information about the actual accumulated deviation from the mean bit-rate to the decoder. The side information is still transmitted with the frame rate as derived from the channel capacity (mean rate). The main-data-begin pointer is used to find the main information in the input buffer of the decoder. 

Processing and transporting information needs time. An information channel may be characterized by its channel capacity / o, measured in bit/s. An ideal channel transfers information which can be recognized with a probability of almost 1. Noise introduced into the channel reduces the probability of recognizing the information to p. ... 

The definition of encoding and decoding schemes, rate, average decoding error probability and channel capacity for a SIC can be found in [GP80], These definitions are essentially similar to the definitions given in Section 2.1, except for the fact that the channel transition probabilities are dependent on the state r.v. S and the absence of a distortion constraint at the encoder. 

C Deriving Upper and Lower Bounds for BMS Channel Capacity... 

Fig. 9.3.15 Probability of false positives and ROC output vs. orthogonal channel capacity (OCC).

But comparing Pj f to the n = OCC or 1 /Pfp values in Table 9.3.1 shows the values to be about lOOx higher. The NRC committee assigned a Pj f of 1000 to IMS, based on an information theory method by Yost and Fetterolf [18], which includes resolvable amplitude levels. Without such levels, channel capacities of IMS and DMS (differential mobility spectroscopy) analyzers were determined to be in the range 14-20 [20], which would be a factor of 50-70 lower than 1000 and would bring P ml much closer to the n values in Table 9.3.1 for the GC/MS analyzer. One may conclude that the idea of relating OCC to FAR may not be so far fetched after all. 

The extent to which the orthogonal channel capacity (OCC) is available for each analysis, as the full capacity cannot always be harnessed, e.g., with an array of polymer film sensors where some polymers may not have any interaction with an analyte, or with some mass values of an analyte mixture not being represented in a mass spectrum. Appropriate OCC discounts may need to be derived. 

R.Upper extremity neuromotor channel capacity (bits/sec)... 

Channel capacity The maximum rate of information flow through a specific pathway from source to receiver. In the context of the human, a sensorimotor pathway (e.g., afferent sensory nerves, processors, descending cerebrospinal nerve and a-motoneuron) is an example of a channel through which motor control information flows from sensors to actuators (muscle). 

Speed-accuracy trade-off A fundamental limit of human information-processing systems at any level of abstraction that is most likely due to a more basic limit in channel capacity that is, channel capacity can be used to achieve more accuracy at the expense of speed or to achieve more speed at the expense of accuracy. 

General central nervous system effects (of drug) Selected activity of daily hving execution speed Postural stability Upper extremity neuromotor channel capacity Manual manipulation speed Visual-upper extremity information processing speed Visual attention span Visual-spatial memory capacity Visual-numerical memory capacity... 

The standard transinformation R is not necessarily the maximum amount of information that can be obtained by a given classifier. The maximum amount R is called channel capacity C417, 4273. R would be obtained for a random sample of patterns with optimally adjusted a priori probabilities. Because the optimal a priori probabilities depend on the classifier, the channel capacity is not suitable for the evaluation of classifiers. The only useful starting point for the classification of unknown chemical patterns is to assume equal probabilities for all classes. 

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