Entropy

Research

311 KiB

Open AccessFeature PaperArticle

Multilevel Coding for the Full-Duplex Decode-Compress-Forward Relay Channel

by Ahmed Attia Abotabl and Aria Nosratinia

Entropy 2017, 19(11), 611; https://doi.org/10.3390/e19110611 - 14 Nov 2017

Viewed by 4200

The Decode-Compress-Forward (DCF) is a generalization of Decode-Forward (DF) and Compress-Forward (CF). This paper investigates conditions under which DCF offers gains over DF and CF, addresses the problem of coded modulation for DCF, and evaluates the performance of DCF coded modulation implemented via [...] Read more.

The Decode-Compress-Forward (DCF) is a generalization of Decode-Forward (DF) and Compress-Forward (CF). This paper investigates conditions under which DCF offers gains over DF and CF, addresses the problem of coded modulation for DCF, and evaluates the performance of DCF coded modulation implemented via low-density parity-check (LDPC) codes and polar codes. We begin by revisiting the achievable rate of DCF in discrete memoryless channels under backward decoding. We then study coded modulation for the decode-compress-forward via multi-level coding. We show that the proposed multilevel coding approaches the known achievable rates of DCF. The proposed multilevel coding is implemented (and its performance verified) via a combination of standard DVB-S2 LDPC codes, and polar codes whose design follows the method of Blasco-Serrano. Full article

(This article belongs to the Special Issue Multiuser Information Theory)

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1699 KiB

Open AccessArticle

Sum Capacity for Single-Cell Multi-User Systems with M-Ary Inputs

by Pei Yang, Yue Wu, Liqiang Jin and Hongwen Yang

Entropy 2017, 19(9), 497; https://doi.org/10.3390/e19090497 - 15 Sep 2017

Cited by 5 | Viewed by 4659

Abstract

This paper investigates the sum capacity of a single-cell multi-user system under the constraint that the transmitted signal is adopted from M-ary two-dimensional constellation with equal probability for both uplink, i.e., multiple access channel (MAC), and downlink, i.e., broadcast channel (BC) scenarios. [...] Read more.

This paper investigates the sum capacity of a single-cell multi-user system under the constraint that the transmitted signal is adopted from M-ary two-dimensional constellation with equal probability for both uplink, i.e., multiple access channel (MAC), and downlink, i.e., broadcast channel (BC) scenarios. Based on the successive interference cancellation (SIC) and the entropy power Gaussian approximation, it is shown that both the multi-user MAC and BC can be approximated to a bank of parallel channels with the channel gains being modified by an extra attenuate factor that equals to the negative exponential of the capacity of interfering users. With this result, the capacity of MAC and BC with arbitrary number of users and arbitrary constellations can be easily calculated which in sharp contrast with using traditional Monte Carlo simulation that the calculating amount increases exponentially with the increase of the number of users. Further, the sum capacity of multi-user under different power allocation strategies including equal power allocation, equal capacity power allocation and maximum capacity power allocation is also investigated. For the equal capacity power allocation, a recursive relation for the solution of power allocation is derived. For the maximum capacity power allocation, the necessary condition for optimal power allocation is obtained and an optimal algorithm for the power allocation optimization problem is proposed based on the necessary condition. Full article

(This article belongs to the Special Issue Multiuser Information Theory)

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632 KiB

Open AccessArticle

On the Capacity and the Optimal Sum-Rate of a Class of Dual-Band Interference Channels

by Subhajit Majhi and Patrick Mitran

Entropy 2017, 19(9), 495; https://doi.org/10.3390/e19090495 - 14 Sep 2017

Cited by 2 | Viewed by 3627

Abstract

We study a class of two-transmitter two-receiver dual-band Gaussian interference channels (GIC) which operates over the conventional microwave and the unconventional millimeter-wave (mm-wave) bands. This study is motivated by future 5G networks where additional spectrum in the mm-wave band complements transmission in the [...] Read more.

We study a class of two-transmitter two-receiver dual-band Gaussian interference channels (GIC) which operates over the conventional microwave and the unconventional millimeter-wave (mm-wave) bands. This study is motivated by future 5G networks where additional spectrum in the mm-wave band complements transmission in the incumbent microwave band. The mm-wave band has a key modeling feature: due to severe path loss and relatively small wavelength, a transmitter must employ highly directional antenna arrays to reach its desired receiver. This feature causes the mm-wave channels to become highly directional, and thus can be used by a transmitter to transmit to its designated receiver or the other receiver. We consider two classes of such channels, where the underlying GIC in the microwave band has weak and strong interference, and obtain sufficient channel conditions under which the capacity is characterized. Moreover, we assess the impact of the additional mm-wave band spectrum on the performance, by characterizing the transmit power allocation for the direct and cross channels that maximizes the sum-rate of this dual-band channel. The solution reveals conditions under which different power allocations, such as allocating the power budget only to direct or only to cross channels, or sharing it among them, becomes optimal. Full article

(This article belongs to the Special Issue Multiuser Information Theory)

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1092 KiB

Open AccessFeature PaperArticle

Channel Coding and Source Coding With Increased Partial Side Information

by Avihay Sadeh-Shirazi, Uria Basher and Haim Permuter

Entropy 2017, 19(9), 467; https://doi.org/10.3390/e19090467 - 2 Sep 2017

Viewed by 4292

Abstract

Let

(S_{1, i}, S_{2, i}) \sim i . i . d p (s_{1}, s_{2})

,

i = 1, 2, \dots

be a memoryless, correlated partial side information sequence. In [...] Read more.

Let

(S_{1, i}, S_{2, i}) \sim i . i . d p (s_{1}, s_{2})

,

i = 1, 2, \dots

be a memoryless, correlated partial side information sequence. In this work, we study channel coding and source coding problems where the partial side information

(S_{1}, S_{2})

is available at the encoder and the decoder, respectively, and, additionally, either the encoder’s or the decoder’s side information is increased by a limited-rate description of the other’s partial side information. We derive six special cases of channel coding and source coding problems and we characterize the capacity and the rate-distortion functions for the different cases. We present a duality between the channel capacity and the rate-distortion cases we study. In order to find numerical solutions for our channel capacity and rate-distortion problems, we use the Blahut-Arimoto algorithm and convex optimization tools. Finally, we provide several examples corresponding to the channel capacity and the rate-distortion cases we presented. Full article

(This article belongs to the Special Issue Multiuser Information Theory)

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934 KiB

Open AccessArticle

On the Reliability Function of Variable-Rate Slepian-Wolf Coding

by Jun Chen, Da-ke He, Ashish Jagmohan and Luis A. Lastras-Montaño

Entropy 2017, 19(8), 389; https://doi.org/10.3390/e19080389 - 28 Jul 2017

Cited by 17 | Viewed by 3701

Abstract

The reliability function of variable-rate Slepian-Wolf coding is linked to the reliability function of channel coding with constant composition codes, through which computable lower and upper bounds are derived. The bounds coincide at rates close to the Slepian-Wolf limit, yielding a complete characterization [...] Read more.

The reliability function of variable-rate Slepian-Wolf coding is linked to the reliability function of channel coding with constant composition codes, through which computable lower and upper bounds are derived. The bounds coincide at rates close to the Slepian-Wolf limit, yielding a complete characterization of the reliability function in that rate region. It is shown that variable-rate Slepian-Wolf codes can significantly outperform fixed-rate Slepian-Wolf codes in terms of rate-error tradeoff. Variable-rate Slepian-Wolf coding with rate below the Slepian-Wolf limit is also analyzed. In sharp contrast with fixed-rate Slepian-Wolf codes for which the correct decoding probability decays to zero exponentially fast if the rate is below the Slepian-Wolf limit, the correct decoding probability of variable-rate Slepian-Wolf codes can be bounded away from zero. Full article

(This article belongs to the Special Issue Multiuser Information Theory)

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846 KiB

Open AccessArticle

Scaling Exponent and Moderate Deviations Asymptotics of Polar Codes for the AWGN Channel

by Silas L. Fong and Vincent Y. F. Tan

Entropy 2017, 19(7), 364; https://doi.org/10.3390/e19070364 - 15 Jul 2017

Cited by 6 | Viewed by 3908

Abstract

This paper investigates polar codes for the additive white Gaussian noise (AWGN) channel. The scaling exponent

μ

of polar codes for a memoryless channel

q_{Y | X}

with capacity

I (q_{Y | X})

characterizes the closest gap between the [...] Read more.

This paper investigates polar codes for the additive white Gaussian noise (AWGN) channel. The scaling exponent

μ

of polar codes for a memoryless channel

q_{Y | X}

with capacity

I (q_{Y | X})

characterizes the closest gap between the capacity and non-asymptotic achievable rates as follows: For a fixed

ε \in (0, 1)

, the gap between the capacity

I (q_{Y | X})

and the maximum non-asymptotic rate

R_{n}^{*}

achieved by a length-n polar code with average error probability

ε

scales as

n^{- 1 / μ}

, i.e.,

I (q_{Y | X}) - R_{n}^{*} = Θ (n^{- 1 / μ})

. It is well known that the scaling exponent

μ

for any binary-input memoryless channel (BMC) with

I (q_{Y | X}) \in (0, 1)

is bounded above by

4.714

. Our main result shows that

4.714

remains a valid upper bound on the scaling exponent for the AWGN channel. Our proof technique involves the following two ideas: (i) The capacity of the AWGN channel can be achieved within a gap of

O (n^{- 1 / μ} \sqrt{log n})

by using an input alphabet consisting of n constellations and restricting the input distribution to be uniform; (ii) The capacity of a multiple access channel (MAC) with an input alphabet consisting of n constellations can be achieved within a gap of

O (n^{- 1 / μ} log n)

by using a superposition of

log n

binary-input polar codes. In addition, we investigate the performance of polar codes in the moderate deviations regime where both the gap to capacity and the error probability vanish as n grows. An explicit construction of polar codes is proposed to obey a certain tradeoff between the gap to capacity and the decay rate of the error probability for the AWGN channel. Full article

(This article belongs to the Special Issue Multiuser Information Theory)

1623 KiB

Open AccessArticle

Multi-User Detection for Sporadic IDMA Transmission Based on Compressed Sensing

by Bo Li, Rui Du, Wenjing Kang and Gongliang Liu

Entropy 2017, 19(7), 334; https://doi.org/10.3390/e19070334 - 5 Jul 2017

Cited by 7 | Viewed by 4159

Abstract

The Internet of Things (IoT) is placing new demands on existing communication systems. The limited orthogonal resources do not meet the demands of massive connectivity of future IoT systems that require efficient multiple access. Interleave-division multiple access (IDMA) is a promising method of [...] Read more.

The Internet of Things (IoT) is placing new demands on existing communication systems. The limited orthogonal resources do not meet the demands of massive connectivity of future IoT systems that require efficient multiple access. Interleave-division multiple access (IDMA) is a promising method of improving spectral efficiency and supporting massive connectivity for IoT networks. In a given time, not all sensors signal information to an aggregation node, but each node transmits a short frame on occasion, e.g., time-controlled or event-driven. The sporadic nature of the uplink transmission, low data rates, and massive connectivity in IoT scenarios necessitates minimal control overhead communication schemes. Therefore, sensor activity and data detection should be implemented on the receiver side. However, the current chip-by-chip (CBC) iterative multi-user detection (MUD) assumes that sensor activity is precisely known at the receiver. In this paper, we propose three schemes to solve the MUD problem in a sporadic IDMA uplink transmission system. Firstly, inspired by the observation of sensor sparsity, we incorporate compressed sensing (CS) to MUD in order to jointly perform activity and data detection. Secondly, as CS detection could provide reliable activity detection, we combine CS and CBC and propose a CS-CBC detector. In addition, a CBC-based MUD named CBC-AD is proposed to provide a comparable baseline scheme. Full article

(This article belongs to the Special Issue Multiuser Information Theory)

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607 KiB

Open AccessArticle

An Information-Spectrum Approach to the Capacity Region of the Interference Channel

by Lei Lin, Xiao Ma, Chulong Liang, Xiujie Huang and Baoming Bai

Entropy 2017, 19(6), 270; https://doi.org/10.3390/e19060270 - 13 Jun 2017

Cited by 4 | Viewed by 4065

Abstract

In this paper, a general formula for the capacity region of a general interference channel with two pairs of users is derived, which reveals that the capacity region is the union of a family of rectangles. In the region, each rectangle is determined [...] Read more.

In this paper, a general formula for the capacity region of a general interference channel with two pairs of users is derived, which reveals that the capacity region is the union of a family of rectangles. In the region, each rectangle is determined by a pair of spectral inf-mutual information rates. The presented formula provides us with useful insights into the interference channels in spite of the difficulty of computing it. Specially, when the inputs are discrete, ergodic Markov processes and the channel is stationary memoryless, the formula can be evaluated by the BCJR (Bahl-Cocke-Jelinek-Raviv) algorithm. Also the formula suggests that considering the structure of the interference processes contributes to obtaining tighter inner bounds than the simplest one (obtained by treating the interference as noise). This is verified numerically by calculating the mutual information rates for Gaussian interference channels with embedded convolutional codes. Moreover, we present a coding scheme to approach the theoretical achievable rate pairs. Numerical results show that the decoding gains can be achieved by considering the structure of the interference. Full article

(This article belongs to the Special Issue Multiuser Information Theory)

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