搜索结果：mBio

This paper considers the achievable rates and decoding complexity of low-density parity-check (LDPC) codes over statistically independent parallel channels. The paper starts with the derivation of bounds on the conditional entropy of the transmitted codeword given the received sequence at the output of the parallel channels; the component channels are considered to be memoryless, binary-input, and output-symmetric (MBIOS). These results serve for the derivation of an upper bound on the achievable rates of ensembles of LDPC codes under optimal maximum-likelihood (ML) decoding when their transmission takes place over parallel MBIOS channels. The paper relies on the latter bound for obtaining upper bounds on the achievable rates of ensembles of randomly and intentionally punctured LDPC codes over MBIOS channels. The paper also provides a lower bound on the decoding complexity (per iteration) of ensembles of LDPC codes under message-passing iterative decoding over parallel MBIOS channels; the bound is given in terms of the gap between the rate of these codes for which reliable communication is achievable and the channel capacity. The paper presents a diagram which shows interconnection

We consider decoding of binary Tanner codes using message-passing iterative decoding and linear programming (LP) decoding in MBIOS channels. We present new certificates that are based on a combinatorial characterization for local-optimality of a codeword in irregular Tanner codes with respect to any MBIOS channel. This characterization is based on a conical combination of normalized weighted subtrees in the computation trees of the Tanner graph. These subtrees may have any finite height h (even equal or greater than half of the girth of the Tanner graph). In addition, the degrees of local-code nodes in these subtrees are not restricted to two. We prove that local optimality in this new characterization implies maximum-likelihood (ML) optimality and LP optimality, and show that a certificate can be computed efficiently. We also present a new message-passing iterative decoding algorithm, called normalized weighted min-sum (NWMS). NWMS decoding is a BP-type algorithm that applies to any irregular binary Tanner code with single parity-check local codes. We prove that if a locally-optimal codeword with respect to height parameter h exists (whereby notably h is not limited by the girth o

The asymptotic iterative decoding performances of low-density parity-check (LDPC) codes using min-sum (MS) and sum-product (SP) decoding algorithms on memoryless binary-input output-symmetric (MBIOS) channels are analyzed in this paper. For MS decoding, the analysis is done by upper bounding the bit error probability of the root bit of a tree code by the sequence error probability of a subcode of the tree code assuming the transmission of the all-zero codeword. The result is a recursive upper bound on the bit error probability after each iteration. For SP decoding, we derive a recursively determined lower bound on the bit error probability after each iteration. This recursive lower bound recovers the density evolution equation of LDPC codes on the binary erasure channel (BEC) with inequalities satisfied with equalities. A significant implication of this result is that the performance of LDPC codes under SP decoding on the BEC is an upper bound of the performance on all MBIOS channels with the same uncoded bit error probability. All results hold for the more general multi-edge type LDPC codes.

This paper is focused on the derivation of some universal properties of capacity-approaching low-density parity-check (LDPC) code ensembles whose transmission takes place over memoryless binary-input output-symmetric (MBIOS) channels. Properties of the degree distributions, graphical complexity and the number of fundamental cycles in the bipartite graphs are considered via the derivation of information-theoretic bounds. These bounds are expressed in terms of the target block/ bit error probability and the gap (in rate) to capacity. Most of the bounds are general for any decoding algorithm, and some others are proved under belief propagation (BP) decoding. Proving these bounds under a certain decoding algorithm, validates them automatically also under any sub-optimal decoding algorithm. A proper modification of these bounds makes them universal for the set of all MBIOS channels which exhibit a given capacity. Bounds on the degree distributions and graphical complexity apply to finite-length LDPC codes and to the asymptotic case of an infinite block length. The bounds are compared with capacity-approaching LDPC code ensembles under BP decoding, and they are shown to be informative an

The canonical view of the interactions between viruses and their microbial hosts presumes that changes in host and virus fate require the initiation of infection of a host by a virus. That is, first virus particles diffuse randomly outside of host cells, then the virus genome enters the target host cell, and only then do intracellular dynamics and regulation of virus and host cell fate unfold. Intracellular dynamics may lead to the death of the host cell and release of viruses, to the elimination of the virus genome through cellular defense mechanisms, or the integration of the virus genome with the host as a chromosomal or extra-chromosomal element. Here we revisit this canonical view, inspired by recent experimental findings of Bautista and colleagues (mBio, 2015) in which the majority of target host cells can be induced into a dormant state when exposed to either active or de-activated viruses, even when viruses are present at low relative titer. We propose that both the qualitative phenomena and the quantitative time-scales of dormancy induction can be reconciled given the hypothesis that cellular physiology can be altered by contact on the surface of host cells rather than str

We derive bounds on the asymptotic density of parity-check matrices and the achievable rates of binary linear block codes transmitted over memoryless binary-input output-symmetric (MBIOS) channels. The lower bounds on the density of arbitrary parity-check matrices are expressed in terms of the gap between the rate of these codes for which reliable communication is achievable and the channel capacity, and the bounds are valid for every sequence of binary linear block codes. These bounds address the question, previously considered by Sason and Urbanke, of how sparse can parity-check matrices of binary linear block codes be as a function of the gap to capacity. Similarly to a previously reported bound by Sason and Urbanke, the new lower bounds on the parity-check density scale like the log of the inverse of the gap to capacity, but their tightness is improved (except for a binary symmetric/erasure channel, where they coincide with the previous bound). The new upper bounds on the achievable rates of binary linear block codes tighten previously reported bounds by Burshtein et al., and therefore enable to obtain tighter upper bounds on the thresholds of sequences of binary linear block c

We study error bounds for linear programming decoding of regular LDPC codes. For memoryless binary-input output-symmetric channels, we prove bounds on the word error probability that are inverse doubly-exponential in the girth of the factor graph. For memoryless binary-input AWGN channel, we prove lower bounds on the threshold for regular LDPC codes whose factor graphs have logarithmic girth under LP-decoding. Specifically, we prove a lower bound of $σ=0.735$ (upper bound of $\frac{Eb}{N_0}=2.67$dB) on the threshold of $(3,6)$-regular LDPC codes whose factor graphs have logarithmic girth. Our proof is an extension of a recent paper of Arora, Daskalakis, and Steurer [STOC 2009] who presented a novel probabilistic analysis of LP decoding over a binary symmetric channel. Their analysis is based on the primal LP representation and has an explicit connection to message passing algorithms. We extend this analysis to any MBIOS channel.

We introduce a new family of concatenated codes with an outer low-density parity-check (LDPC) code and an inner low-density generator matrix (LDGM) code, and prove that these codes can achieve capacity under any memoryless binary-input output-symmetric (MBIOS) channel using maximum-likelihood (ML) decoding with bounded graphical complexity, i.e., the number of edges per information bit in their graphical representation is bounded. In particular, we also show that these codes can achieve capacity on the binary erasure channel (BEC) under belief propagation (BP) decoding with bounded decoding complexity per information bit per iteration for all erasure probabilities in (0, 1). By deriving and analyzing the average weight distribution (AWD) and the corresponding asymptotic growth rate of these codes with a rate-1 inner LDGM code, we also show that these codes achieve the Gilbert-Varshamov bound with asymptotically high probability. This result can be attributed to the presence of the inner rate-1 LDGM code, which is demonstrated to help eliminate high weight codewords in the LDPC code while maintaining a vanishingly small amount of low weight codewords.

NAACP lawsuit says xAI uses gas turbines without permits for Grok data center

The bigger battery is standard and there are now simulated "E-Shifts

A bold claim that the universe’s accelerating expansion was an illusion has been put to the test—and failed。 Researchers found that the study behind the controversy made key mistakes when analyzing supernova data。 After revisiting the evidence, astronomers concluded that cosmic acceleration remains as strong as ever

Pentagon also claims 1。5 million personnel are using generative AI tools

Transferring genes across species doesn't just happen in microbes

Separately, neither could compete。 Now they hope they can

Pixels will get their OTA in the coming weeks, but don't expect monumental changes

Scientists have uncovered a surprising force that may help explain how binary star systems form so quickly。 New supercomputer simulations show that magnetic fields surrounding newborn stars can act like a cosmic brake, stripping away angular momentum and allowing two still-forming protostars to spiral closer together instead of drifting apart

Scientists discovered that rice behaves in a highly unusual way: it weakens under rapid compression but stays stronger when pressure is applied slowly。 Using this effect, they engineered a new material that reacts differently to gentle movements and sudden impacts。 The material can adapt its stiffness automatically, opening the door to safer soft r

Isar Aerospace is not hurting for money, but it is sorely lacking in the currency of flight experience

Researchers have discovered how microscopic imperfections and atomic vibrations can be used to control a powerful quantum effect in an advanced material。 The effect can turn alternating electrical signals from the environment directly into the kind of current electronic devices need, without traditional components。 As temperature changes, the signa