733 research outputs found
Superadditivity of Quantum Channel Coding Rate with Finite Blocklength Joint Measurements
The maximum rate at which classical information can be reliably transmitted
per use of a quantum channel strictly increases in general with , the number
of channel outputs that are detected jointly by the quantum joint-detection
receiver (JDR). This phenomenon is known as superadditivity of the maximum
achievable information rate over a quantum channel. We study this phenomenon
for a pure-state classical-quantum (cq) channel and provide a lower bound on
, the maximum information rate when the JDR is restricted to making
joint measurements over no more than quantum channel outputs, while
allowing arbitrary classical error correction. We also show the appearance of a
superadditivity phenomenon---of mathematical resemblance to the aforesaid
problem---in the channel capacity of a classical discrete memoryless channel
(DMC) when a concatenated coding scheme is employed, and the inner decoder is
forced to make hard decisions on -length inner codewords. Using this
correspondence, we develop a unifying framework for the above two notions of
superadditivity, and show that for our lower bound to to be equal to a
given fraction of the asymptotic capacity of the respective channel,
must be proportional to , where is the respective channel dispersion
quantity.Comment: To appear in IEEE Transactions on Information Theor
On capacity of optical communications over a lossy bosonic channel with a receiver employing the most general coherent electro-optic feedback control
We study the problem of designing optical receivers to discriminate between
multiple coherent states using coherent processing receivers---i.e., one that
uses arbitrary coherent feedback control and quantum-noise-limited direct
detection---which was shown by Dolinar to achieve the minimum error probability
in discriminating any two coherent states. We first derive and re-interpret
Dolinar's binary-hypothesis minimum-probability-of-error receiver as the one
that optimizes the information efficiency at each time instant, based on
recursive Bayesian updates within the receiver. Using this viewpoint, we
propose a natural generalization of Dolinar's receiver design to discriminate
coherent states each of which could now be a codeword, i.e., a sequence of
coherent states each drawn from a modulation alphabet. We analyze the
channel capacity of the pure-loss optical channel with a general
coherent-processing receiver in the low-photon number regime and compare it
with the capacity achievable with direct detection and the Holevo limit
(achieving the latter would require a quantum joint-detection receiver). We
show compelling evidence that despite the optimal performance of Dolinar's
receiver for the binary coherent-state hypothesis test (either in error
probability or mutual information), the asymptotic communication rate
achievable by such a coherent-processing receiver is only as good as direct
detection. This suggests that in the infinitely-long codeword limit, all
potential benefits of coherent processing at the receiver can be obtained by
designing a good code and direct detection, with no feedback within the
receiver.Comment: 17 pages, 5 figure
Fundamental Limits on Data Acquisition: Trade-offs between Sample Complexity and Query Difficulty
We consider query-based data acquisition and the corresponding information
recovery problem, where the goal is to recover binary variables
(information bits) from parity measurements of those variables. The queries and
the corresponding parity measurements are designed using the encoding rule of
Fountain codes. By using Fountain codes, we can design potentially limitless
number of queries, and corresponding parity measurements, and guarantee that
the original information bits can be recovered with high probability from
any sufficiently large set of measurements of size . In the query design,
the average number of information bits that is associated with one parity
measurement is called query difficulty () and the minimum number of
measurements required to recover the information bits for a fixed
is called sample complexity (). We analyze the fundamental trade-offs
between the query difficulty and the sample complexity, and show that the
sample complexity of for some constant
is necessary and sufficient to recover information bits with high
probability as
Graph Matching in Correlated Stochastic Block Models for Improved Graph Clustering
We consider community detection from multiple correlated graphs sharing the
same community structure. The correlated graphs are generated by independent
subsampling of a parent graph sampled from the stochastic block model. The
vertex correspondence between the correlated graphs is assumed to be unknown.
We consider the two-step procedure where the vertex correspondence between the
correlated graphs is first revealed, and the communities are recovered from the
union of the correlated graphs, which becomes denser than each single graph. We
derive the information-theoretic limits for exact graph matching in general
density regimes and the number of communities, and then analyze the regime of
graph parameters, where one can benefit from the matching of the correlated
graphs in recovering the latent community structure of the graphs.Comment: Allerton Conference 202
Understanding Self-Distillation and Partial Label Learning in Multi-Class Classification with Label Noise
Self-distillation (SD) is the process of training a student model using the
outputs of a teacher model, with both models sharing the same architecture. Our
study theoretically examines SD in multi-class classification with
cross-entropy loss, exploring both multi-round SD and SD with refined teacher
outputs, inspired by partial label learning (PLL). By deriving a closed-form
solution for the student model's outputs, we discover that SD essentially
functions as label averaging among instances with high feature correlations.
Initially beneficial, this averaging helps the model focus on feature clusters
correlated with a given instance for predicting the label. However, it leads to
diminishing performance with increasing distillation rounds. Additionally, we
demonstrate SD's effectiveness in label noise scenarios and identify the label
corruption condition and minimum number of distillation rounds needed to
achieve 100% classification accuracy. Our study also reveals that one-step
distillation with refined teacher outputs surpasses the efficacy of multi-step
SD using the teacher's direct output in high noise rate regimes
Unequal Error Protection Querying Policies for the Noisy 20 Questions Problem
In this paper, we propose an open-loop unequal-error-protection querying
policy based on superposition coding for the noisy 20 questions problem. In
this problem, a player wishes to successively refine an estimate of the value
of a continuous random variable by posing binary queries and receiving noisy
responses. When the queries are designed non-adaptively as a single block and
the noisy responses are modeled as the output of a binary symmetric channel the
20 questions problem can be mapped to an equivalent problem of channel coding
with unequal error protection (UEP). A new non-adaptive querying strategy based
on UEP superposition coding is introduced whose estimation error decreases with
an exponential rate of convergence that is significantly better than that of
the UEP repetition coding introduced by Variani et al. (2015). With the
proposed querying strategy, the rate of exponential decrease in the number of
queries matches the rate of a closed-loop adaptive scheme where queries are
sequentially designed with the benefit of feedback. Furthermore, the achievable
error exponent is significantly better than that of random block codes
employing equal error protection.Comment: To appear in IEEE Transactions on Information Theor
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