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Register a new userOn information rates over a binary input channel
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Added by
Michael Peleg
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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We study communication systems over band-limited Additive White Gaussian Noise (AWGN) channels in which the transmitter output is constrained to be symmetric binary (bi-polar). In this work we improve the original Ozarov-Wyner-Ziv (OWZ) lower bound on capacity by introducing a new achievability scheme with two advantages over the studied OWZ scheme which is based on peak-power constrained pulse-amplitude modulation. Our scheme achieves a moderately improved information rate and it does so with much less sign transitions of the binary signal. The gap between the known upper-bound based on spectral constrains of bi-polar signals and our achievable lower bound is reduced to 0.86 bits per Nyquist interval at high SNR.
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We propose a technique to design finite-length irregular low-density parity-check (LDPC) codes over the binary-input additive white Gaussian noise (AWGN) channel with good performance in both the waterfall and the error floor region. The design process starts from a protograph which embodies a desirable degree distribution. This protograph is then lifted cyclically to a certain block length of interest. The lift is designed carefully to satisfy a certain approximate cycle extrinsic message degree (ACE) spectrum. The target ACE spectrum is one with extremal properties, implying a good error floor performance for the designed code. The proposed construction results in quasi-cyclic codes which are attractive in practice due to simple encoder and decoder implementation. Simulation results are provided to demonstrate the effectiveness of the proposed construction in comparison with similar existing constructions.
A method is proposed, called channel polarization, to construct code sequences that achieve the symmetric capacity $I(W)$ of any given binary-input discrete memoryless channel (B-DMC) $W$. The symmetric capacity is the highest rate achievable subject to using the input letters of the channel with equal probability. Channel polarization refers to the fact that it is possible to synthesize, out of $N$ independent copies of a given B-DMC $W$, a second set of $N$ binary-input channels ${W_N^{(i)}:1le ile N}$ such that, as $N$ becomes large, the fraction of indices $i$ for which $I(W_N^{(i)})$ is near 1 approaches $I(W)$ and the fraction for which $I(W_N^{(i)})$ is near 0 approaches $1-I(W)$. The polarized channels ${W_N^{(i)}}$ are well-conditioned for channel coding: one need only send data at rate 1 through those with capacity near 1 and at rate 0 through the remaining. Codes constructed on the basis of this idea are called polar codes. The paper proves that, given any B-DMC $W$ with $I(W)>0$ and any target rate $R < I(W)$, there exists a sequence of polar codes ${{mathscr C}_n;nge 1}$ such that ${mathscr C}_n$ has block-length $N=2^n$, rate $ge R$, and probability of block error under successive cancellation decoding bounded as $P_{e}(N,R) le bigoh(N^{-frac14})$ independently of the code rate. This performance is achievable by encoders and decoders with complexity $O(Nlog N)$ for each.
In this paper, the problem of securely computing a function over the binary modulo-2 adder multiple-access wiretap channel is considered. The problem involves a legitimate receiver that wishes to reliably and efficiently compute a function of distributed binary sources while an eavesdropper has to be kept ignorant of them. In order to characterize the corresponding fundamental limit, the notion of secrecy computation-capacity is introduced. Although determining the secrecy computation-capacity is challenging for arbitrary functions, it surprisingly turns out that if the function perfectly matches the algebraic structure of the channel and the joint source distribution fulfills certain conditions, the secrecy computation-capacity equals the computation capacity, which is the supremum of all achievable computation rates without secrecy constraints. Unlike the case of securely transmitting messages, no additional randomness is needed at the encoders nor does the legitimate receiver need any advantage over the eavesdropper. The results therefore show that the problem of securely computing a function over a multiple-access wiretap channel may significantly differ from the one of securely communicating messages.
Information theory and the framework of information dynamics have been used to provide tools to characterise complex systems. In particular, we are interested in quantifying information storage, information modification and information transfer as characteristic elements of computation. Although these quantities are defined for autonomous dynamical systems, information dynamics can also help to get a wholistic understanding of input-driven systems such as neural networks. In this case, we do not distinguish between the system itself, and the effects the input has to the system. This may be desired in some cases, but it will change the questions we are able to answer, and is consequently an important consideration, for example, for biological systems which perform non-trivial computations and also retain a short-term memory of past inputs. Many other real world systems like cortical networks are also heavily input-driven, and application of tools designed for autonomous dynamic systems may not necessarily lead to intuitively interpretable results. The aim of our work is to extend the measurements used in the information dynamics framework for input-driven systems. Using the proposed input-corrected information storage we hope to better quantify system behaviour, which will be important for heavily input-driven systems like artificial neural networks to abstract from specific benchmarks, or for brain networks, where intervention is difficult, individual components cannot be tested in isolation or with arbitrary input data.
The problem of channel coding over the Gaussian multiple-input multiple-output (MIMO) broadcast channel (BC) with additive independent Gaussian states is considered. The states are known in a noncausal manner to the encoder, and it wishes to minimize the amount of information that the receivers can learn from the channel outputs about the state sequence. The state leakage rate is measured as a normalized blockwise mutual information between the state sequence and the channel outputs sequences. We employ a new version of a state-dependent extremal inequality and show that Gaussian input maximizes the state-dependent version of Martons outer bound. Further we show that our inner bound coincides with the outer bound. Our result generalizes previously studied scalar Gaussian BC with state and MIMO BC without state.
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