16 research outputs found
Minimum Energy to Send k Bits Through the Gaussian Channel With and Without Feedback
The minimum achievable energy per bit over memoryless Gaussian channels has been previously addressed in the limit when the number of information bits goes to infinity, in which case it is known that the availability of noiseless feedback does not lower the minimum energy per bit, which is -1.59 dB below the noise level. This paper analyzes the behavior of the minimum energy per bit for memoryless Gaussian channels as a function of k, the number of information bits. It is demonstrated that in this nonasymptotic regime, noiseless feedback leads to significantly better energy efficiency. In particular, without feedback achieving energy per bit of -1.57 dB requires coding over at least k=10[superscript 6] information bits, while we construct a feedback scheme that transmits a single information bit with energy -1.59 dB and zero error. We also show that unless k is very small, approaching the minimal energy per bit does not require using the feedback link except to signal that transmission should stop.National Science Foundation (U.S.) (Grant CCF-06-35154)National Science Foundation (U.S.) (grant CNS-09-05398
A Rate-Compatible Sphere-Packing Analysis of Feedback Coding with Limited Retransmissions
Recent work by Polyanskiy et al. and Chen et al. has excited new interest in
using feedback to approach capacity with low latency. Polyanskiy showed that
feedback identifying the first symbol at which decoding is successful allows
capacity to be approached with surprisingly low latency. This paper uses Chen's
rate-compatible sphere-packing (RCSP) analysis to study what happens when
symbols must be transmitted in packets, as with a traditional hybrid ARQ
system, and limited to relatively few (six or fewer) incremental transmissions.
Numerical optimizations find the series of progressively growing cumulative
block lengths that enable RCSP to approach capacity with the minimum possible
latency. RCSP analysis shows that five incremental transmissions are sufficient
to achieve 92% of capacity with an average block length of fewer than 101
symbols on the AWGN channel with SNR of 2.0 dB.
The RCSP analysis provides a decoding error trajectory that specifies the
decoding error rate for each cumulative block length. Though RCSP is an
idealization, an example tail-biting convolutional code matches the RCSP
decoding error trajectory and achieves 91% of capacity with an average block
length of 102 symbols on the AWGN channel with SNR of 2.0 dB. We also show how
RCSP analysis can be used in cases where packets have deadlines associated with
them (leading to an outage probability).Comment: To be published at the 2012 IEEE International Symposium on
Information Theory, Cambridge, MA, USA. Updated to incorporate reviewers'
comments and add new figure
A Beta-Beta Achievability Bound with Applications
A channel coding achievability bound expressed in terms of the ratio between
two Neyman-Pearson functions is proposed. This bound is the dual of a
converse bound established earlier by Polyanskiy and Verd\'{u} (2014). The new
bound turns out to simplify considerably the analysis in situations where the
channel output distribution is not a product distribution, for example due to a
cost constraint or a structural constraint (such as orthogonality or constant
composition) on the channel inputs. Connections to existing bounds in the
literature are discussed. The bound is then used to derive 1) an achievability
bound on the channel dispersion of additive non-Gaussian noise channels with
random Gaussian codebooks, 2) the channel dispersion of the exponential-noise
channel, 3) a second-order expansion for the minimum energy per bit of an AWGN
channel, and 4) a lower bound on the maximum coding rate of a multiple-input
multiple-output Rayleigh-fading channel with perfect channel state information
at the receiver, which is the tightest known achievability result.Comment: extended version of a paper submitted to ISIT 201
Joint source-channel coding with feedback
This paper quantifies the fundamental limits of variable-length transmission
of a general (possibly analog) source over a memoryless channel with noiseless
feedback, under a distortion constraint. We consider excess distortion, average
distortion and guaranteed distortion (-semifaithful codes). In contrast to
the asymptotic fundamental limit, a general conclusion is that allowing
variable-length codes and feedback leads to a sizable improvement in the
fundamental delay-distortion tradeoff. In addition, we investigate the minimum
energy required to reproduce source samples with a given fidelity after
transmission over a memoryless Gaussian channel, and we show that the required
minimum energy is reduced with feedback and an average (rather than maximal)
power constraint.Comment: To appear in IEEE Transactions on Information Theor
Communicating over Filter-and-Forward Relay Networks with Channel Output Feedback
Relay networks aid in increasing the rate of communication from source to
destination. However, the capacity of even a three-terminal relay channel is an
open problem. In this work, we propose a new lower bound for the capacity of
the three-terminal relay channel with destination-to-source feedback in the
presence of correlated noise. Our lower bound improves on the existing bounds
in the literature. We then extend our lower bound to general relay network
configurations using an arbitrary number of filter-and-forward relay nodes.
Such network configurations are common in many multi-hop communication systems
where the intermediate nodes can only perform minimal processing due to limited
computational power. Simulation results show that significant improvements in
the achievable rate can be obtained through our approach. We next derive a
coding strategy (optimized using post processed signal-to-noise ratio as a
criterion) for the three-terminal relay channel with noisy channel output
feedback for two transmissions. This coding scheme can be used in conjunction
with open-loop codes for applications like automatic repeat request (ARQ) or
hybrid-ARQ.Comment: 15 pages, 8 figures, to appear in IEEE Transactions on Signal
Processin
Beta-Beta Bounds: Finite-Blocklength Analog of the Golden Formula
It is well known that the mutual information between two random variables can
be expressed as the difference of two relative entropies that depend on an
auxiliary distribution, a relation sometimes referred to as the golden formula.
This paper is concerned with a finite-blocklength extension of this relation.
This extension consists of two elements: 1) a finite-blocklength channel-coding
converse bound by Polyanskiy and Verd\'{u} (2014), which involves the ratio of
two Neyman-Pearson functions (beta-beta converse bound); and 2) a novel
beta-beta channel-coding achievability bound, expressed again as the ratio of
two Neyman-Pearson functions.
To demonstrate the usefulness of this finite-blocklength extension of the
golden formula, the beta-beta achievability and converse bounds are used to
obtain a finite-blocklength extension of Verd\'{u}'s (2002) wideband-slope
approximation. The proof parallels the derivation of the latter, with the
beta-beta bounds used in place of the golden formula.
The beta-beta (achievability) bound is also shown to be useful in cases where
the capacity-achieving output distribution is not a product distribution due
to, e.g., a cost constraint or structural constraints on the codebook, such as
orthogonality or constant composition. As an example, the bound is used to
characterize the channel dispersion of the additive exponential-noise channel
and to obtain a finite-blocklength achievability bound (the tightest to date)
for multiple-input multiple-output Rayleigh-fading channels with perfect
channel state information at the receiver.Comment: to appear in IEEE Transactions on Information Theor
Fundamental limits of many-user MAC with finite payloads and fading
Consider a (multiple-access) wireless communication system where users are
connected to a unique base station over a shared-spectrum radio links. Each
user has a fixed number of bits to send to the base station, and his signal
gets attenuated by a random channel gain (quasi-static fading). In this paper
we consider the many-user asymptotics of Chen-Chen-Guo'2017, where the number
of users grows linearly with the blocklength. In addition, we adopt a per-user
probability of error criterion of Polyanskiy'2017 (as opposed to classical
joint-error probability criterion). Under these two settings we derive bounds
on the optimal required energy-per-bit for reliable multi-access communication.
We confirm the curious behaviour (previously observed for non-fading MAC) of
the possibility of perfect multi-user interference cancellation for user
densities below a critical threshold. Further we demonstrate the suboptimality
of standard solutions such as orthogonalization (i.e., TDMA/FDMA) and treating
interference as noise (i.e. pseudo-random CDMA without multi-user detection).Comment: 38 pages, conference version accepted to IEEE ISIT 201