Binary Asymmetric Channel Research Articles

On capacity and performance of noncoherent OFDM-IM systems with binary codes

This paper studies the capacity and error performance of a noncoherent index-modulated orthogonal frequency division multiplexing (OFDM-IM) system with binary coded subcarrier activation patterns. To that end, soft-decision (i.e., unquantized) and hard-decision (i.e., quantized) channels are considered, where the latter is equivalent to a binary asymmetric channel (BAC). By using maximum likelihood and maximum a posteriori criteria, crossover probabilities of the quantized channel are derived in order to characterize its capacity and probability of error in detecting IM signals. Capacity expressions are then given for both channels. Using the Blahut-Arimoto algorithm, an iterative algorithm is developed to find the optimal input distribution for the unquantized channel, while for the quantized channel, it is found by solving a nonlinear equation for its zero. It is shown that using a uniform input distribution instead of the optimal (nonuniform) one results in a negligible capacity loss, therefore binary codes with a uniform distribution of 1s and 0s are nearly optimal. Compared to the unquantized channel, it is shown that an approximate loss less than 2dB is incurred when quantization is used and this loss diminishes rapidly as signal-to-noise ratio (SNR) increases. In addition, it is demonstrated that the gap (in dB) between uncoded noncoherent OFDM-IM system and the capacity limit is generally wide, and the gap narrows when subcarrier clustering is considered. The findings in this paper can have theoretical and practical significance for understanding capacity limits and can provide some guidance for coding design in noncoherent OFDM-IM systems.

Sequential Transmission Over Binary Asymmetric Channels With Feedback

In this paper, we consider variable-length coding over the memoryless binary asymmetric channel (BAC) with full noiseless feedback, including the binary symmetric channel (BSC) as a special case. In 2012, Naghshvar et al. introduced a coding scheme, which we refer to as the small-enough-difference (SED) coding scheme. For symmetric binary-input channels, the deterministic variable-length feedback (VLF) code constructed with the SED coding scheme asymptotically achieves both capacity and Burnashev’s optimal error exponent. Building on the work of Naghshvar et al., this paper extends the SED coding scheme to the BAC and develops a non-asymptotic VLF achievability bound that is shown to achieve both capacity and the optimal error exponent. For the specific case of the BSC, we develop an additional non-asymptotic VLF achievability bound using a two-phase analysis that leverages both a submartingale synthesis and a Markov chain time of first passage analysis. Numerical evaluations show that both new VLF achievability bounds outperform Polyanskiy’s achievability bound for variable-length stop-feedback codes.

Parameters of Codes for the Binary Asymmetric Channel

We introduce two notions of discrepancy between binary vectors, which are not metric functions in general but nonetheless capture the mathematical structure of the binary asymmetric channel. These lead to two new fundamental parameters of binary error-correcting codes, both of which measure the probability that the maximum likelihood decoder fails. We then derive various bounds for the cardinality and weight distribution of a binary code in terms of these new parameters, giving examples of codes meeting the bounds with equality.

Bayesian Learning of Occupancy Grids

Occupancy grids encode for hot spots on a map that is represented by a two dimensional grid of disjoint cells. The problem is to recursively update the probability that each cell in the grid is occupied, based on a sequence of sensor measurements from a moving platform. In this paper, we provide a new Bayesian framework for generating these probabilities that does not assume statistical independence between the occupancy state of grid cells. This approach is made analytically tractable through the use of binary asymmetric channel models that capture the errors associated with observing the occupancy state of a grid cell. Binary-valued measurement vectors are the thresholded output of a sensor in a radar, sonar, or other sensory system. We compare the performance of the proposed framework to that of the classical formulation for occupancy grids. The results show that the proposed framework identifies occupancy grids with lower false alarm and miss detection rates, and requires fewer observations of the surrounding area, to generate an accurate estimate of occupancy probabilities when compared to conventional formulations.

Design and Evaluation of the Efficiency of Channel Coding LDPC Codes for 5G Information Technology

This paper proposes a result of an investigation of a topical problem and the development of models for efficient coding in information networks based on codes with a low density of parity check. The main advantage of the technique is the presented recommendations for choosing a signal-code construction is carried out taking into account the code rate and the number of iterations decoding for envisaging the defined noise immunity indices. The noise immunity of signal-code constructions based on low-density codes has been increased by combining them with multi position digital modulation. This solution eventually allowed to develop a strategy for decoder designing of such codes and to optimize the code structure for a specific information network. To test the effectiveness of the proposed method, MATLAB simulations are carried out under for various Information channels binary symmetric channel (BSC), a channel with additive white Gaussian noise (AWGN), binary asymmetric channel (BAC), asymmetric channel Z type. In addition, different code rates were used during the experiment. The study of signal-code constructions with differential modulation is presented. The efficiency of different decoding algorithms is investigated. The advantage of the obtained results over the known ones consists in determining the maximum noise immunity for the proposed codes. The energy gain was on the order of 6 dB, and an increase in the number of decoding iterations from 3 to 10 leads to a gain in coding energy of 5 dB. Envisaged that the results obtained can be very useful in the development of practical coding schemes in 5G networks.

Bounds for the capacity error function for unidirectional channels with noiseless feedback

In digital systems such as fiber optical communications, the ratio between probability of errors of type 1→0 and 0→1 can be large. Practically, one can assume that only one type of error can occur. These errors are called asymmetric. Unidirectional errors differ from asymmetric type of errors; here both 1→0 and 0→1 type of errors are possible, but in any submitted codeword all the errors are of the same type. This can be generalized for the q-ary case.We consider q-ary unidirectional channels with feedback where the errors have magnitude one and give bounds for the capacity error function. It turns out that the bounds depend on the parity of the alphabet size q. Furthermore, we show that for feedback, the capacity error function for the binary asymmetric channel is different from the symmetric channel. This is in contrast to the behavior of the function without feedback.

Performance analysis optimization and experimental verification of a photon-counting communication system based on non-photon-number-resolution detectors

With the increase in free-space optical communication distance and link attenuation, photon-counting communication based on a single photon detector will be the development trend in the future. In this paper, we use a single-pixel single photon avalanche diode (SPAD) detector to study the bit error rate (BER) performance of photon counting communication. As the single-pixel SPAD cannot distinguish the number of photons in a single detection event, we theoretically derive the (BER) model of a pulse position modulation (PPM) communication system based on a single-pixel SPAD detector. Then, the binary asymmetric channel (BAC) model is adopted to modify the channel log-likelihood in Serially Concatenated Pulse Position Modulation (SCPPM) decoding. Research results show that, when the BER is 10−6 , the photon efficiency can reach 1.6 photon per bit (PPB) in the modified BAC scheme with 0.1 photon/slot noise intensity, which is 28.6% better than the photon efficiency of 2.24 PPB in the unmodified Poisson channel scheme.

Synaptic Information Transmission in a Two-State Model of Short-Term Facilitation

Action potentials (spikes) can trigger the release of a neurotransmitter at chemical synapses between neurons. Such release is uncertain, as it occurs only with a certain probability. Moreover, synaptic release can occur independently of an action potential (asynchronous release) and depends on the history of synaptic activity. We focus here on short-term synaptic facilitation, in which a sequence of action potentials can temporarily increase the release probability of the synapse. In contrast to the phenomenon of short-term depression, quantifying the information transmission in facilitating synapses remains to be done. We find rigorous lower and upper bounds for the rate of information transmission in a model of synaptic facilitation. We treat the synapse as a two-state binary asymmetric channel, in which the arrival of an action potential shifts the synapse to a facilitated state, while in the absence of a spike, the synapse returns to its baseline state. The information bounds are functions of both the asynchronous and synchronous release parameters. If synchronous release facilitates more than asynchronous release, the mutual information rate increases. In contrast, short-term facilitation degrades information transmission when the synchronous release probability is intrinsically high. As synaptic release is energetically expensive, we exploit the information bounds to determine the energy–information trade-off in facilitating synapses. We show that unlike information rate, the energy-normalized information rate is robust with respect to variations in the strength of facilitation.

Enhancement of reliability and security in a time-diversity FSO/CDMA wiretap channel

Due to atmospheric turbulence, the reliability and security of free space optical (FSO) communication is seriously affected. In this paper, we propose a new FSO wiretap channel model based on a time-diversity scheme and optical code division multiple access (OCDMA). At the receiving end, the legitimate user employs time-diversity reception by matched optical decoders, while an eavesdropper uses a random optical decoder for eavesdropping. Using an avalanche photodiode (APD) photon counting model, bit error rate (BER) performances of legitimate and eavesdropping users are theoretically analyzed under different turbulence and diversity. Based on the binary asymmetric channel model, the physical layer security performance of the time-diversity FSO/CDMA wiretap channel is evaluated by using security capacity. With the increase of time-diversity order, the reliability and security performances of FSO/CDMA wiretap channel are improved. Simulation results show that the performances of the time-diversity FSO/CDMA wiretap channel are better than those of a non-diversity FSO/CDMA system.

Method for Determining Broadcaster Advised Emergency Wake-up Signal for ISDB-T Digital Television Receivers

There is a way to automatically wake up television receivers when a broadcaster sends out an emergency alert. In the Integrated Services Digital Broadcasting-Terrestrial (ISDB-T) digital television standard, the emergency wake-up procedure is called an Emergency Warning System (EWS). In ISDB-T, the special signal is embedded in a control message known as transmission and modulation configuration control (TMCC). However, improper identification of the wake-up signal, often encountered in mobile reception, leads to unnecessary wake ups. In this paper, a method of reliably determining a wake-up signal is proposed by assuming that broadcasters will not change the TMCC message except for the wake-up signal when the broadcaster sends out an emergency alert. A change in the wake-up bit leads to variation parity, and the proposed method also relies on such variations. Mutual information to be obtained by the wake-up receiver is evaluated using the memoryless binary asymmetric channel model. Results showed that the proposed method provided mutual information even at a Eb/N₀ being lower than 10 dB. Mutual information of the proposed method with intermittent reception is also analyzed as a function of the duty ratio of the intermittent receiver.

Matched Metrics to the Binary Asymmetric Channels

In this paper, we establish some criteria to decide when a discrete memoryless channel admits a metric in such a way that the maximum likelihood decoding coincides with the nearest neighbor decoding. In particular, we prove a conjecture presented by M. Firer and J. L. Walker, establishing that every binary asymmetric channel admits a matched metric.

Large Degree Asymptotics and the Reconstruction Threshold of the Asymmetric Binary Channels

In this paper, we consider a broadcasting process in which information is propagated from a given root node on a noisy tree network, and answer the question that whether the symbols at the nth level of the tree contain non-vanishing information of the root as n goes to infinity. Although the reconstruction problem on the tree has been studied in numerous contexts including information theory, mathematical genetics and statistical physics, the existing literatures with rigorous reconstruction thresholds established are very limited. In the remarkable work of Borgs, Chayes, Mossel and Roch (The Kesten-Stigum reconstruction bound is tight for roughly symmetric binary channels), the exact threshold for the reconstruction problem for a binary asymmetric channel on the d-ary tree is establish, provided that the asymmetry is sufficiently small, which is the first exact reconstruction threshold obtained in roughly a decade. In this paper, by means of refined analyses of moment recursion on a weighted version of the magnetization, and concentration investigations, we rigorously give a complete answer to the question of how small it needs to be to establish the tightness of the reconstruction threshold and further determine its asymptotics of large degrees.

An Information-Theoretic Approach to the Chipless RFID Tag Identification

In this paper, we focus on the chipless radio-frequency identification (RFID), where the tag information bits are encoded by the peak/notch pattern appeared in the frequency spectrum of the radar cross section (RCS) of the tag. In particular, we restrict our attention to a simple yet prevalent “binary” coding method, where a bit 0 or bit 1 is encoded by the absence or presence of the peak/notch, respectively. We provide an information-theoretic framework for the tag identification based on such a binary coding method. Our aim is to accommodate more bits in the limited bandwidth without degrading the identification performance. To this end, we first formulate the detection of each bit as a binary asymmetric channel (where a signal processing approach is integrated into each interrogation to enhance the underlying channel quality). Moreover, it is proposed to perform multiple interrogations with majority rule-based detection (in correspondence to the signal processing approach in each interrogation). Furthermore, we introduce some error-detecting codes to further improve the performance of tag identification. For instance, motivated by the asymmetric property of the channel model, we propose to apply the constant weight code and the Berger–Freiman code (as two representatives of non-systematic and systematic codes, respectively) to the problem to be addressed in this paper. In addition, an investigation is also conducted into the cyclic redundancy check (CRC) codes (as a representative of those codes that are not dedicated to the binary asymmetric channel but could be potentially competitive for error detection). The system’s performance is analyzed through the key parameters, namely the successful transmission rate, the false identification rate (i.e., the probability of undetected errors), and the expected number of retransmissions/interrogations. The effectiveness of the proposed methods is demonstrated by the numerical results.

On Equivalence of Binary Asymmetric Channels Regarding the Maximum Likelihood Decoding

We study the problem of characterizing when two memoryless binary asymmetric channels, described by their transition probabilities $(p,q)$ and $(p^\prime,q^\prime)$ , are equivalent from the point of view of maximum likelihood decoding when restricted to $n$ -block binary codes. This equivalence of channels induces a partition (depending on $n$ ) on the space of parameters $(p,q)$ into regions associated with the equivalence classes. Explicit expressions for describing these regions, their number and areas are derived. Some perspectives of applications of our results to decoding problems are also presented.

A Source and Channel Coding Approach for Improving Flash Memory Endurance

The introduction of multiple-level cell (MLC) and triple-level cell (TLC) technologies reduced the reliability of flash memories significantly compared with single-level cell flash. With MLC and TLC flash cells, the error probability varies for the different states. Hence, asymmetric models are required to characterize the flash channel, e.g., the binary asymmetric channel (BAC). This contribution presents a combined channel and source coding approach improving the reliability of MLC and TLC flash memories. With flash memories data compression has to be performed on block level considering short-data blocks. We present a coding scheme suitable for blocks of 1 kB of data. The objective of the data compression algorithm is to reduce the amount of user data such that the redundancy of the error correction coding can be increased in order to improve the reliability of the data storage system. Moreover, data compression can be utilized to exploit the asymmetry of the channel to reduce the error probability. With redundant data, the proposed combined coding scheme results in a significant improvement of the program/erase cycling endurance and the data retention time of flash memories.

Eliminating Leakage in Reverse Fuzzy Extractors

In recent years, physically unclonable functions (PUFs) have been proposed as a promising building block for key storage and device authentication. PUFs are physical systems, and as such, their responses are inherently noisy, precluding a straightforward derivation of cryptographic key material from raw PUF measurements. To overcome this drawback, fuzzy extractors are used to eliminate the noise and guarantee robust outputs. A special type is reverse fuzzy extractors, shifting the computational load of error correction toward a computationally powerful verifier. However, the reverse fuzzy extractor reveals error patterns to any eavesdropper, which may cause privacy issues (due to a systematic drift of the PUF responses, the error pattern is linkable to the identity) and even security problems (if the noise is data-dependent). In this paper, we quantify the issue of leakage due to asymmetry of noise, leveraging the binary asymmetric channel (BAC) model. We further propose to concatenate two BACs to form a symmetric channel, as a solution that is able to eliminate such noise. Finally, we propose a modified reverse fuzzy extractor that does not leak via the error patterns even in the case of systematic drift of the PUF responses.

Achieving Secrecy Capacity of the Gaussian Wiretap Channel With Polar Lattices

In this paper, an explicit scheme of wiretap coding based on polar lattices is proposed to achieve the secrecy capacity of the additive white Gaussian noise (AWGN) wiretap channel. First, polar lattices are used to construct secrecy-good lattices for the mod- $\Lambda _{s}$ Gaussian wiretap channel (GWC). Then, we propose an explicit shaping scheme to remove this mod- $\Lambda _{s}$ front end and extend polar lattices to the genuine GWC. The shaping technique is based on the lattice Gaussian distribution, which leads to a binary asymmetric channel at each level for the multilevel lattice codes. By employing the asymmetric polar coding technique, we construct an AWGN-good lattice and a secrecy-good lattice with optimal shaping simultaneously. As a result, the encoding complexity for the sender and the decoding complexity for the legitimate receiver are both $O(N\log N\log (\log N))$ . The proposed scheme is proven to be semantically secure.

Constructive minimax classification of discrete observations with arbitrary loss function

This paper develops a multihypothesis testing framework for calculating numerically the optimal minimax test with discrete observations and an arbitrary loss function. Discrete observations are common in data processing and make tractable the calculation of the minimax test. Each hypothesis is both associated to a parameter defining the distribution of the observations and to an action which describes the decision to take when the hypothesis is true. The loss function measures the gap between the parameters and the actions. The minimax test minimizes the maximum classification risk. It is the solution of a finite linear programming problem which gives the worst case classification risk and the worst case prior distribution. The minimax test equalizes the classification risks whose prior probabilities are strictly positive. The minimax framework is applied to vector channel decoding which consists in classifying some codewords transmitted on a binary asymmetric channel. The Hamming metric is used to measure the number of differences between the emitted codeword and the decoded one.

Information Rate Analysis of a Synaptic Release Site Using a Two-State Model of Short-Term Depression.

Synapses are the communication channels for information transfer between neurons; these are the points at which pulse-like signals are converted into the stochastic release of quantized amounts of chemical neurotransmitter. At many synapses, prior neuronal activity depletes synaptic resources, depressing subsequent responses of both spontaneous and spike-evoked releases. We analytically compute the information transmission rate of a synaptic release site, which we model as a binary asymmetric channel. Short-term depression is incorporated by assigning the channel a memory of depth one. A successful release, whether spike evoked or spontaneous, decreases the probability of a subsequent release; if no release occurs on the following time step, the release probabilities recover back to their default values. We prove that synaptic depression can increase the release site's information rate if spontaneous release is more strongly depressed than spike-evoked release. When depression affects spontaneous and evoked release equally, the information rate must invariably decrease, even when the rate is normalized by the resources used for synaptic transmission. For identical depression levels, we analytically disprove the hypothesis, at least in this simplified model, that synaptic depression serves energy- and information-efficient encoding.

On the Rate-Distortion Function for Binary Source Coding With Side Information

We present an in-depth analysis of the problem of lossy compression of binary sources in the presence of correlated side information, where the correlation is given by a generic binary asymmetric channel and the Hamming distance is the distortion metric. Our analysis is motivated by systematic rate-distortion gains observed when applying asymmetric correlation models in Wyner-Ziv video coding. First, we derive for the first time the rate-distortion function for conventional predictive coding in the binary-asymmetric-correlation-channel scenario. Second, we propose a new bound for the case where the side information is only available at the decoder—Wyner-Ziv coding. We conjecture this bound to be tight. We show that the maximum rate needed to encode as well as the maximum rate-loss of Wyner-Ziv coding relative to predictive coding corresponds to uniform sources and symmetric correlations. Importantly, we show that the upper bound on the rate-loss established by Zamir is not tight and that the maximum value is actually significantly lower. Moreover, we prove that the only binary correlation channel that incurs no rate-loss for Wyner-Ziv coding compared with predictive coding is the Z-channel. Finally, we complement our analysis with new compression performance results obtained with our state-of-the-art Wyner-Ziv video coding system.