We develop a theoretical framework for achieving the maximum possible speed on constrained digital channels with a finite alphabet. A common inaccuracy that is made when computing the capacity of digital channels is to assume that the inputs and outputs of the channel are analog Gaussian random variables, and then based upon that assumption, invoke the Shannon capacity bound for an additive whi...

In this paper, we study the relation between the stable throughput regions and the capacity regions for a Gaussian multiple access channel. Our main focus is to study how the extent of side information about source arrival statistics and/or instantaneous queue states at each transmitter influence the achievable stable throughput region. Two notions of MAC capacity are studied. The first notion ...

An independent set with vertices in the strong product of four cycles C C C C is given This improves the best known lower bound for the Shannon capacity of the graph C which is the zero error capacity of the corresponding noisy channel The search was done by a computer program using the simulated annealing algorithm with a constant time temperature schedule

In the last lecture, we stated Shannon’s capacity theorem for the BSC, which we restate here: Theorem 0.1. Let 0 ≤ p < 1/2 be a real number. For every 0 < ε ≤ 1/2 − p, the following statements are true for large enough integer n: (i) There exists a real δ > 0, an encoding function E : {0, 1} → {0, 1}, and a decoding function D : {0, 1} → {0, 1}, where k ≤ b(1−H(p+ ε))nc such that the following ...

The articulation index (AI), denoted ¢ ¡ snr£ , first described by Fletcher in 1921 (Fletcher 1995), has served the speech and hearing community well, as a well known method for characterizing nonsense speech sound intelligibility. For example, the AI is a basic tool of hearing aid research, and has even been used to fit hearing aids. It is defined in terms of an average of a special function o...

Let $W$ be a binary-input memoryless symmetric (BMS) channel with Shannon capacity notation="LaTeX">$I(W)$ and fix any notation="LaTeX">$\alpha &gt; 0$ . We construct, for sufficiently small notation="LaTeX">$\delta , binary linear co...

The information rates achievable with a photon-gas model of electromagnetic radiation are studied. At any frequency, information rates over the photon-gas model essentially coincide with the Shannon capacity when the signal-to-noise ratio is below a threshold. Only above the threshold does the photon gas incur in a significant loss in information rates; the loss can amount to half of the capaci...

Let G be a t uniform s regular linear hypergraph with r vertices It is shown that the number of independent sets I G in G satis es log I G r t O log ts s This leads to an improvement of a previous bound by Alon obtained for t i e for regular ordinary graphs It is also shown that for the Hamming graph H n q with vertices consisting of all n tuples over an alphabet of size q and edges connecting ...