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Register a new userFinite-Blocklength Performance of Sequential Transmission over BSC with Noiseless Feedback
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Added by
Hengjie Yang
Publication date
2019
fields
Informatics Engineering
and research's language is
English
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In this paper, we consider the problem of sequential transmission over the binary symmetric channel (BSC) with full, noiseless feedback. Naghshvar et al. proposed a one-phase encoding scheme, for which we refer to as the small-enough difference (SED) encoder, which can achieve capacity and Burnashevs optimal error exponent for symmetric binary-input channels. They also provided a non-asymptotic upper bound on the average blocklength, which implies an achievability bound on rates. However, their achievability bound is loose compared to the simulated performance of SED encoder, and even lies beneath Polyanskiys achievability bound of a system limited to stop feedback. This paper significantly tightens the achievability bound by using a Markovian analysis that leverages both the submartingale and Markov properties of the transmitted message. Our new non-asymptotic lower bound on achievable rate lies above Polyanskiys bound and is close to the actual performance of the SED encoder over the BSC.
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Building on the work of Horstein, Shayevitz and Feder, and Naghshvar emph{et al.}, this paper presents algorithms for low-complexity sequential transmission of a $k$-bit message over the binary symmetric channel (BSC) with full, noiseless feedback. To lower complexity, this paper shows that the initial $k$ binary transmissions can be sent before any feedback is required and groups messages with equal posteriors to reduce the number of posterior updates from exponential in $k$ to linear in $k$. Simulation results demonstrate that achievable rates for this full, noiseless feedback system approach capacity rapidly as a function of average blocklength, faster than known finite-blocklength lower bounds on achievable rate with noiseless active feedback and significantly faster than finite-blocklength lower bounds for a stop feedback system.
In this paper, we present a finite-block-length comparison between the orthogonal multiple access (OMA) scheme and the non-orthogonal multiple access (NOMA) for the uplink channel. First, we consider the Gaussian channel, and derive the closed form expressions for the rate and outage probability. Then, we extend our results to the quasi-static Rayleigh fading channel. Our analysis is based on the recent results on the characterization of the maximum coding rate at finite block-length and finite block-error probability. The overall system throughput is evaluated as a function of the number of information bits, channel uses and power. We find what would be the respective values of these different parameters that would enable throughput maximization. Furthermore, we analyze the system performance in terms of reliability and throughput when applying the type-I ARQ protocol with limited number of retransmissions. The throughput and outage probability are evaluated for different blocklengths and number of information bits. Our analysis reveals that there is a trade-off between reliability and throughput in the ARQ. While increasing the number of retransmissions boosts reliability by minimizing the probability of reception error, it results in more delay which decreases the throughput. Nevertheless, the results show that NOMA always outperforms OMA in terms of throughput, reliability and latency regardless of the users priority or the number of retransmissions in both Gaussian and fading channels.
This paper investigates an energy-efficient non-orthogonal transmission design problem for two downlink receivers that have strict reliability and finite blocklength (latency) constraints. The Shannon capacity formula widely used in traditional designs needs the assumption of infinite blocklength and thus is no longer appropriate. We adopt the newly finite blocklength coding capacity formula for explicitly specifying the trade-off between reliability and code blocklength. However, conventional successive interference cancellation (SIC) may become infeasible due to heterogeneous blocklengths. We thus consider several scenarios with different channel conditions and with/without SIC. By carefully examining the problem structure, we present in closed-form the optimal power and code blocklength for energy-efficient transmissions. Simulation results provide interesting insights into conditions for which non-orthogonal transmission is more energy efficient than the orthogonal transmission such as TDMA.
We provide a practical implementation of the rubber method of Ahlswede et al. for binary alphabets. The idea is to create the skeleton sequence therein via an arithmetic decoder designed for a particular $k$-th order Markov chain. For the stochastic binary symmetric channel, we show that the scheme is nearly optimal in a strong sense for certain parameters.
We analyze a wireless communication system with finite block length and finite battery energy, under quasi-static Nakagami-m fading. Wireless energy transfer is carried out in the downlink while information transfer occurs in the uplink. Transmission strategies for scenarios with/without energy accumulation between transmission rounds are characterized in terms of error probability and energy consumption. A power control protocol for the energy accumulation scenario is proposed and results show the enormous impact on improving the system performance, in terms of error probability and energy consumption. The numerical results corroborate the existence and uniqueness of an optimum target error probability, while showing that a relatively small battery could be a limiting factor for some setups, specially when using the energy accumulation strategy.
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