34 research outputs found
Achievable Rates for K-user Gaussian Interference Channels
The aim of this paper is to study the achievable rates for a user
Gaussian interference channels for any SNR using a combination of lattice and
algebraic codes. Lattice codes are first used to transform the Gaussian
interference channel (G-IFC) into a discrete input-output noiseless channel,
and subsequently algebraic codes are developed to achieve good rates over this
new alphabet. In this context, a quantity called efficiency is introduced which
reflects the effectiveness of the algebraic coding strategy. The paper first
addresses the problem of finding high efficiency algebraic codes. A combination
of these codes with Construction-A lattices is then used to achieve non trivial
rates for the original Gaussian interference channel.Comment: IEEE Transactions on Information Theory, 201
Uniquely Decodable Ternary Codes for Synchronous CDMA Systems
In this paper, we consider the problem of recursively designing uniquely
decodable ternary code sets for highly overloaded synchronous code-division
multiple-access (CDMA) systems. The proposed code set achieves larger number of
users than any other known state-of-the-art ternary codes that
offer low-complexity decoders in the noisy transmission. Moreover, we propose a
simple decoder that uses only a few comparisons and can allow the user to
uniquely recover the information bits. Compared to maximum likelihood (ML)
decoder, which has a high computational complexity for even moderate code
length, the proposed decoder has much lower computational complexity. We also
derived the computational complexity of the proposed recursive decoder
analytically. Simulation results show that the performance of the proposed
decoder is almost as good as the ML decoder.Comment: arXiv admin note: text overlap with arXiv:1806.0395
Fast Decoder for Overloaded Uniquely Decodable Synchronous CDMA
We consider the problem of designing a fast decoder for antipodal uniquely
decodable (errorless) code sets for overloaded synchronous code-division
multiple access (CDMA) systems where the number of signals K_{max}^a is the
largest known for the given code length L. The proposed decoder is designed in
a such a way that the users can uniquely recover the information bits with a
very simple decoder, which uses only a few comparisons. Compared to
maximum-likelihood (ML) decoder, which has a high computational complexity for
even moderate code length, the proposed decoder has a much lower computational
complexity. Simulation results in terms of bit error rate (BER) demonstrate
that the performance of the proposed decoder only has a 1-2 dB degradation at
BER of 10^{-3} when compared to ML
Fast Decoder for Overloaded Uniquely Decodable Synchronous Optical CDMA
In this paper, we propose a fast decoder algorithm for uniquely decodable
(errorless) code sets for overloaded synchronous optical code-division
multiple-access (O-CDMA) systems. The proposed decoder is designed in a such a
way that the users can uniquely recover the information bits with a very simple
decoder, which uses only a few comparisons. Compared to maximum-likelihood (ML)
decoder, which has a high computational complexity for even moderate code
lengths, the proposed decoder has much lower computational complexity.
Simulation results in terms of bit error rate (BER) demonstrate that the
performance of the proposed decoder for a given BER requires only 1-2 dB higher
signal-to-noise ratio (SNR) than the ML decoder.Comment: arXiv admin note: substantial text overlap with arXiv:1806.0395
Smoothing of binary codes, uniform distributions, and applications
The action of a noise operator on a code transforms it into a distribution on
the respective space. Some common examples from information theory include
Bernoulli noise acting on a code in the Hamming space and Gaussian noise acting
on a lattice in the Euclidean space. We aim to characterize the cases when the
output distribution is close to the uniform distribution on the space, as
measured by R{\'e}nyi divergence of order . A version of
this question is known as the channel resolvability problem in information
theory, and it has implications for security guarantees in wiretap channels,
error correction, discrepancy, worst-to-average case complexity reductions, and
many other problems.
Our work quantifies the requirements for asymptotic uniformity (perfect
smoothing) and identifies explicit code families that achieve it under the
action of the Bernoulli and ball noise operators on the code. We derive
expressions for the minimum rate of codes required to attain asymptotically
perfect smoothing. In proving our results, we leverage recent results from
harmonic analysis of functions on the Hamming space. Another result pertains to
the use of code families in Wyner's transmission scheme on the binary wiretap
channel. We identify explicit families that guarantee strong secrecy when
applied in this scheme, showing that nested Reed-Muller codes can transmit
messages reliably and securely over a binary symmetric wiretap channel with a
positive rate. Finally, we establish a connection between smoothing and error
correction in the binary symmetric channel
Successive Refinement with Decoder Cooperation and its Channel Coding Duals
We study cooperation in multi terminal source coding models involving
successive refinement. Specifically, we study the case of a single encoder and
two decoders, where the encoder provides a common description to both the
decoders and a private description to only one of the decoders. The decoders
cooperate via cribbing, i.e., the decoder with access only to the common
description is allowed to observe, in addition, a deterministic function of the
reconstruction symbols produced by the other. We characterize the fundamental
performance limits in the respective settings of non-causal, strictly-causal
and causal cribbing. We use a new coding scheme, referred to as Forward
Encoding and Block Markov Decoding, which is a variant of one recently used by
Cuff and Zhao for coordination via implicit communication. Finally, we use the
insight gained to introduce and solve some dual channel coding scenarios
involving Multiple Access Channels with cribbing.Comment: 55 pages, 15 figures, 8 tables, submitted to IEEE Transactions on
Information Theory. A shorter version submitted to ISIT 201