46,234 research outputs found
Exact Asymptotics for the Random Coding Error Probability
Error probabilities of random codes for memoryless channels are considered in
this paper. In the area of communication systems, admissible error probability
is very small and it is sometimes more important to discuss the relative gap
between the achievable error probability and its bound than to discuss the
absolute gap. Scarlett et al. derived a good upper bound of a random coding
union bound based on the technique of saddlepoint approximation but it is not
proved that the relative gap of their bound converges to zero. This paper
derives a new bound on the achievable error probability in this viewpoint for a
class of memoryless channels. The derived bound is strictly smaller than that
by Scarlett et al. and its relative gap with the random coding error
probability (not a union bound) vanishes as the block length increases for a
fixed coding rate.Comment: Full version of the paper in ISIT2015 with some corrections and
refinement
Refinement of the random coding bound
An improved pre-factor for the random coding bound is proved. Specifically,
for channels with critical rate not equal to capacity, if a regularity
condition is satisfied (resp. not satisfied), then for any a
pre-factor of (resp. ) is achievable for rates above the
critical rate, where and is the blocklength and rate, respectively. The
extra term is related to the slope of the random coding
exponent. Further, the relation of these bounds with the authors' recent
refinement of the sphere-packing bound, as well as the pre-factor for the
random coding bound below the critical rate, is discussed.Comment: Submitted to IEEE Trans. Inform. Theor
Hypergraph-based Source Codes for Function Computation Under Maximal Distortion
This work investigates functional source coding problems with maximal
distortion, motivated by approximate function computation in many modern
applications. The maximal distortion treats imprecise reconstruction of a
function value as good as perfect computation if it deviates less than a
tolerance level, while treating reconstruction that differs by more than that
level as a failure. Using a geometric understanding of the maximal distortion,
we propose a hypergraph-based source coding scheme for function computation
that is constructive in the sense that it gives an explicit procedure for
defining auxiliary random variables. Moreover, we find that the
hypergraph-based coding scheme achieves the optimal rate-distortion function in
the setting of coding for computing with side information and the Berger-Tung
sum-rate inner bound in the setting of distributed source coding for computing.
It also achieves the El Gamal-Cover inner bound for multiple description coding
for computing and is optimal for successive refinement and cascade multiple
description problems for computing. Lastly, the benefit of complexity reduction
of finding a forward test channel is shown for a class of Markov sources
Multiuser Successive Refinement and Multiple Description Coding
We consider the multiuser successive refinement (MSR) problem, where the
users are connected to a central server via links with different noiseless
capacities, and each user wishes to reconstruct in a successive-refinement
fashion. An achievable region is given for the two-user two-layer case and it
provides the complete rate-distortion region for the Gaussian source under the
MSE distortion measure. The key observation is that this problem includes the
multiple description (MD) problem (with two descriptions) as a subsystem, and
the techniques useful in the MD problem can be extended to this case. We show
that the coding scheme based on the universality of random binning is
sub-optimal, because multiple Gaussian side informations only at the decoders
do incur performance loss, in contrast to the case of single side information
at the decoder. We further show that unlike the single user case, when there
are multiple users, the loss of performance by a multistage coding approach can
be unbounded for the Gaussian source. The result suggests that in such a
setting, the benefit of using successive refinement is not likely to justify
the accompanying performance loss. The MSR problem is also related to the
source coding problem where each decoder has its individual side information,
while the encoder has the complete set of the side informations. The MSR
problem further includes several variations of the MD problem, for which the
specialization of the general result is investigated and the implication is
discussed.Comment: 10 pages, 5 figures. To appear in IEEE Transaction on Information
Theory. References updated and typos correcte
Improved bounds for the rate loss of multiresolution source codes
We present new bounds for the rate loss of multiresolution source codes (MRSCs). Considering an M-resolution code, the rate loss at the ith resolution with distortion D/sub i/ is defined as L/sub i/=R/sub i/-R(D/sub i/), where R/sub i/ is the rate achievable by the MRSC at stage i. This rate loss describes the performance degradation of the MRSC compared to the best single-resolution code with the same distortion. For two-resolution source codes, there are three scenarios of particular interest: (i) when both resolutions are equally important; (ii) when the rate loss at the first resolution is 0 (L/sub 1/=0); (iii) when the rate loss at the second resolution is 0 (L/sub 2/=0). The work of Lastras and Berger (see ibid., vol.47, p.918-26, Mar. 2001) gives constant upper bounds for the rate loss of an arbitrary memoryless source in scenarios (i) and (ii) and an asymptotic bound for scenario (iii) as D/sub 2/ approaches 0. We focus on the squared error distortion measure and (a) prove that for scenario (iii) L/sub 1/<1.1610 for all D/sub 2/<0.7250; (c) tighten the Lastras-Berger bound for scenario (i) from L/sub i//spl les/1/2 to L/sub i/<0.3802, i/spl isin/{1,2}; and (d) generalize the bounds for scenarios (ii) and (iii) to M-resolution codes with M/spl ges/2. We also present upper bounds for the rate losses of additive MRSCs (AMRSCs). An AMRSC is a special MRSC where each resolution describes an incremental reproduction and the kth-resolution reconstruction equals the sum of the first k incremental reproductions. We obtain two bounds on the rate loss of AMRSCs: one primarily good for low-rate coding and another which depends on the source entropy
MAC with Action-Dependent State Information at One Encoder
Problems dealing with the ability to take an action that affects the states
of state-dependent communication channels are of timely interest and
importance. Therefore, we extend the study of action-dependent channels, which
until now focused on point-to-point models, to multiple-access channels (MAC).
In this paper, we consider a two-user, state-dependent MAC, in which one of the
encoders, called the informed encoder, is allowed to take an action that
affects the formation of the channel states. Two independent messages are to be
sent through the channel: a common message known to both encoders and a private
message known only to the informed encoder. In addition, the informed encoder
has access to the sequence of channel states in a non-causal manner. Our
framework generalizes previously evaluated settings of state dependent
point-to-point channels with actions and MACs with common messages. We derive a
single letter characterization of the capacity region for this setting. Using
this general result, we obtain and compute the capacity region for the Gaussian
action-dependent MAC. The unique methods used in solving the Gaussian case are
then applied to obtain the capacity of the Gaussian action-dependent
point-to-point channel; a problem was left open until this work. Finally, we
establish some dualities between action-dependent channel coding and source
coding problems. Specifically, we obtain a duality between the considered MAC
setting and the rate distortion model known as "Successive Refinement with
Actions". This is done by developing a set of simple duality principles that
enable us to successfully evaluate the outcome of one problem given the other.Comment: 1. Parts of this paper appeared in the IEEE International Symposium
on Information Theory (ISIT 2012),Cambridge, MA, US, July 2012 and at the
IEEE 27th Convention of Electrical and Electronics Engineers in Israel (IEEEI
2012), Nov. 2012. 2. This work has been supported by the CORNET Consortium
Israel Ministry for Industry and Commerc
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