This paper addresses the design of practical short-length coding schemes for Distributed Hypothesis Testing (DHT). While most prior work on DHT has focused on information-theoretic analyses—deriving bounds on Type-II error exponents via achievability schemes based on quantization and quantize-binning—the practical implementation of DHT coding schemes has remained largely unexplored. Moreover, existing practical coding solutions for quantization and quantize-binning approaches were developed for source reconstruction tasks considering very long code lengths, and they are not directly applicable to DHT. In this context, this paper introduces efficient short-length implementations of quantization and quantize-binning schemes for DHT, constructed from short binary linear block codes. Numerical results show the efficiency of the proposed coding schemes compared to uncoded cases and to existing schemes initially developed for data reconstruction. In addition to practical code design, the paper derives exact analytical expressions for the Type-I and Type-II error probabilities associated with each proposed scheme. The provided analytical expressions are shown to predict accurately the practical performance measured from Monte Carlo simulations of the proposed schemes. These theoretical results are novel and offer a useful framework for optimizing and comparing practical DHT schemes across a wide range of source and code parameters.

This paper investigates practical coding schemes for Distributed Hypothesis Testing (DHT). While the literature has extensively analyzed the information-theoretic performance of DHT and established bounds on Type-II error exponents through quantize and quantize-binning achievability schemes, the practical implementation of DHT coding schemes has not yet been investigated. Therefore, this paper introduces practical implementations of quantizers and quantize-binning schemes for DHT, leveraging short-length binary linear block codes. Furthermore, it provides exact analytical expressions for Type-I and Type-II error probabilities associated with each proposed coding scheme. Numerical results show the accuracy of the proposed analytical error probability expressions, and enable to compare the performance of the proposed schemes.

We explore the problem of distributed Hypothesis Testing (DHT) against independence, focusing specifically on Binary Symmetric Sources (BSS). Our investigation aims to characterize the optimal quantizer among binary linear codes, with the objective of identifying optimal error probabilities under the Neyman-Pearson (NP) criterion for short code-length regime. We define optimality as the direct minimization of analytical expressions of error probabilities using an alternating optimization (AO) algorithm. Additionally, we provide lower and upper bounds on error probabilities, leading to the derivation of error exponents applicable to large code-length regime. Numerical results are presented to demonstrate that, with the proposed algorithm, binary linear codes with an optimal covering radius perform near-optimally for the independence test in DHT.

We consider reliable and secure communication over intersymbol interference wiretap channels (ISI-WTCs). In particular, we first derive an achievable secure rate for ISI-WTCs without imposing any constraints on the input distribution. Afterwards, we focus on the setup where the input distribution of the ISI-WTC is constrained to be a time-invariant finite-order Markov chain. Optimizing the parameters of this Markov chain toward maximizing the achievable secure rates is a computationally intractable problem in general, and so, toward finding a local maximum, we propose an iterative algorithm that at every iteration replaces the secure rate function with a suitable surrogate function whose maximum can be found efficiently. Although the secure rates achieved in the unconstrained setup are potentially larger than the secure rates achieved in the constrained setup, the latter setup has the advantage of leading to efficient algorithms for estimating and optimizing the achievable secure rates, and also has the benefit of being the basis of efficient coding schemes.

A two-stage coding scheme is proposed for reliable and secure transmission over intersymbol interference wiretap channels (ISI-WTCs). It is shown that the ultimate bound on the secure rate of linear block codes over ISI-WTCs is achieved by an independent and uniformly distributed (i.u.d.) input process. Aiming to exceed the i.u.d. secure rate, the proposed scheme comprises the concatenation of an inner trellis code and an outer coset code. The inner stage emulates a Markov process for achieving the constrained secrecy capacity of the ISI-WTC. In contrast, the outer stage vanishes an obtained upper bound on the rate of information leakage toward satisfying the so-called weak secrecy criterion. A carefully modified density evolution confirms the secrecy and the reliability efficiency of the proposed coding scheme at secure rates close to the constrained secrecy capacity.

We consider reliable and secure communication over intersymbol interference wiretap channels (ISI-WTCs). In particular, we first examine the setup where the source at the input of an ISI-WTC is unconstrained and then, based on a general achievability result for arbitrary wiretap channels, we derive an achievable secure rate for this ISI-WTC. Afterwards, we examine the setup where the source at the input of an ISI-WTC is constrained to be a finite-state machine source (FSMS) of a certain order and structure. optimizing the parameters of this FSMS toward maximizing the secure rate is a computationally intractable problem in general, and so, toward finding a local maximum, we propose an iterative algorithm that at every iteration replaces the secure rate function by a suitable surrogate function whose maximum can be found efficiently.

The$L$-link binary Chief Executive Officer (CEO) problem under logarithmic loss is investigated in this paper. A quantization splitting technique is applied to convert the problem under consideration to a$(2L-1)$-step successive Wyner-Ziv (WZ) problem, for which a practical coding scheme is proposed. In the proposed scheme, Low-Density Generator-Matrix (LDGM) codes are used for binary quantization while Low-Density Parity-Check (LDPC) codes are used for syndrome generation; the decoder performs successive decoding based on the received syndromes and produces a soft reconstruction of the remote source. The simulation results indicate that the rate-distortion performance of the proposed scheme can approach the theoretical inner bound based on binary-symmetric test-channel models.

This study is concerned with the design of ensembles of systematic low‐density parity‐check (LDPC) codes to increase the lifetime of wireless sensors by taking advantage of the inherent correlation between the transmitted data of the sensors. The authors consider two correlated sensors where the data is encoded independently at each sensor through a systematic LDPC encoder and sent over two independent channels. At the receiver, a joint source‐channel decoder consisting of two component LDPC decoders is considered where the encoded bits at the output of each component decoder are used as the a priori information at the other decoder. The authors first perform asymptotic performance analysis using the concept of extrinsic information transfer (EXIT) charts. Then, the developed modified EXIT charts are used to design ensembles for different values of correlation. Our results show that as the average check node degree of the designed ensembles grow, the decoding thresholds corresponding to the designed ensembles approach the theoretical limit. Finite block‐length performance evaluation indicates that for larger values of correlation, deploying the designed ensembles through the joint decoder can almost double the sensor's lifetime without increasing the complexity of the encoder.

In this study, a practical coding scheme is designed for the binary Wyner–Ziv (WZ) problem by using nested low‐density generator‐matrix (LDGM) and low‐density parity‐check (LDPC) codes. This scheme contains two steps in the encoding procedure. The first step involves applying the binary quantisation by employing LDGM codes and the second one is using the syndrome‐coding technique by utilising LDPC codes. The decoding algorithm of the proposed scheme is based on the sum‐product algorithm with the help of a side information available at the decoder side. It is theoretically shown that the compound structure has the capability of achieving the WZ bound. The proposed method approaches this bound by utilising the iterative message‐passing algorithms in both encoding and decoding, although theoretical results show that it is asymptotically achievable.

The authors study the problem of two‐user Gaussian multiple access channel (GMAC) in the presence of an external eavesdropper, where all transmitted messages should be kept confidential against the eavesdropper. For this purpose, they propose a secure coding scheme on this channel which utilises low‐density parity‐check (LDPC) codes by employing random bit insertion and puncturing techniques. At each encoder, the confidential message with some random bits as a random message are systematically encoded, and then the associated bits to the confidential message are punctured. Next, the encoders send their unpunctured bits over a Gaussian multiple access wiretap channel (GMAC‐WT). The puncturing distribution applied to the LDPC code is considered in random and optimised cases. They utilise a modified extrinsic information transfer chart analysis to optimise the puncturing distributions. The security gap is used as a measure of secrecy. They compared the achieved secure rate pair with an achievable secrecy rate region of GMAC‐WT to show the effective performance of the proposed scheme. In this study, equal and unequal power conditions at the transmitters are investigated. For both cases, they attain a fairly small security gap which is equivalent to achieve the points near the secrecy rate region of GMAC‐WT.

In this paper, we propose an efficient coding scheme for the binary Chief Executive Officer (CEO) problem under logarithmic loss criterion. Courtade and Weissman obtained the exact rate-distortion bound for a two-link binary CEO problem under this criterion. We find optimal parameters of the binary symmetric test-channel model for the encoder of each link by using the given bound. Furthermore, an efficient coding scheme based on compound low-density generator matrix (LDGM)-low-density parity-check (LDPC) codes is presented to achieve the theoretical rates. In the proposed encoding scheme, a binary quantizer using LDGM codes and a syndrome generator using LDPC codes are applied. The proposed decoder employs a sum-product algorithm and a soft estimator to produce an approximate a posteriori distribution of the source bits given the data received through both links. Our numerical examples verify a close performance of the proposed coding scheme to the theoretical bound in several cases.

This paper is concerned with the design of capacity approaching ensembles of Low-Density Parity-Check (LDPC) codes for correlated sources. We consider correlated binary sources where the data is encoded independently at each source through a systematic LDPC encoder and sent over two independent Gaussian channels. At the receiver, a joint iterative decoder consisting of two component LDPC decoders is considered where the encoded bits at the output of each component decoder are used at the other decoder as the a priori information. We first provide asymptotic performance analysis using the concept of extrinsic information transfer (EXIT) charts. Compared to the conventional EXIT charts devised to analyze LDPC codes for point to point communication, the proposed EXIT charts have been completely modified to be able to accommodate the systematic nature of the codes as well as the iterative behavior between the two component decoders. Then, the developed modified EXIT charts are deployed to design ensembles for different levels of correlation. Our results show that as the average degree of the designed ensembles grow, the thresholds corresponding to the designed ensembles approach the capacity. In particular, for ensembles with average degree of around 9, the gap to capacity is reduced to about 0.2 dB.

This paper proposes an extrinsic information transfer (EXIT)-chart based optimization technique of LDPC codes for the transmission of quantized Gauss-Markov (GM) source samples over additive white Gaussian (AWGN) noise channels. A joint source and channel (JSC) decoding technique of the proposed code is also devised. In the proposed scheme, no interleaving is performed between the source and the JSC encoder so that the decoder can well exploit the relatively low entropy of the source with memory compared to memory-less sources. At the transmitter, the quantized samples are converted to bit sequences with an injective mapping and the bit sequences are encoded using a systematic binary LDPC code. The proposed JSC decoder is a concatenation of a multi-state BCJR Markov decoder and a sum-product (SP) LDPC decoder. Decoding thresholds of the optimized codes at certain code rates are investigated for both uniform and Lloyd-Max quantizations in different numbers of bits. The decoding thresholds are close to the Gaussian code book Shannon limits for code rate Rc≤ 0.5, although the gap to the Shannon limit notably increases at the higher rates. Finally, the simulation results confirm the significant improvement of coding gain on the bit error rate (BER) performances of the optimized LDPC codes with both the quantization schemes.

We propose a novel joint decoding technique for distributed source-channel (DSC) coded systems for transmission of correlated binary Markov sources over additive white Gaussian noise (AWGN) channels. In the proposed scheme, relatively short-length, low-density parity-check (LDPC) codes are independently used to encode the bit sequences of each source. To reconstruct the original bit sequence, a joint source-channel decoding (JSCD) technique is proposed which exploits the knowledge of both temporal and source correlations. The JSCD technique is composed of two stages, which are iteratively performed. First, a sum-product (SP) decoder is serially concatenated with a BCJR decoder, where the knowledge of source memory is utilized during local (horizontal) iterations. Then, the estimate of correlation between the sources is used to update the concatenated decoder during global (vertical) iterations. Therefore, the correlation of the sources is assumed as side information in the subsequent global iteration of each concatenated decoder. From the simulation results of frame/bit error rate (FER/BER), we note that significant gains are achieved by the proposed decoding scheme with respect to the case where the correlation knowledge is not completely utilized at the decoder.

We propose a technique to design finite-length irregular low-density parity-check (LDPC) codes over the binary-input additive white Gaussian noise (AWGN) channel with good performance in both the waterfall and the error floor region. The design process starts from a protograph which embodies a desirable degree distribution. This protograph is then lifted cyclically to a certain block length of interest. The lift is designed carefully to maximize the components of the approximate cycle extrinsic message degree (ACE) spectrum of the code's Tanner graph in a greedy fashion. As a consequence, the designed code would perform well in the error floor region. Moreover, the proposed construction results in quasi-cyclic codes which are attractive in practice due to simple encoder and decoder implementation. Simulation results are provided to demonstrate the effectiveness of the proposed construction in comparison with similar existing constructions.

A new approach for the approximation of the channel log-likelihood ratio (LLR) for wireless channels based on Taylor series is proposed. The approximation is applied to uncorrelated flat fading channels with unknown channel state information at the receiver. It is shown that the proposed approximation greatly simplifies the calculation of channel LLRs, and yet provides results almost identical to those based on the exact calculation of channel LLRs. The results are obtained in the context of bit-interleaved coded modulation (BICM) schemes with low-density parity-check (LDPC) codes, and include threshold calculations and error rate performance of finite-length codes. Compared to the existing approximations, the proposed method is either significantly less complex, or considerably more accurate.

A new approach for the approximation of the channel log-likelihood ratio (LLR) for wireless channels based on Taylor series is proposed. The approximation is applied to the uncorrelated flat Rayleigh fading channel with unknown channel state information at the receiver. It is shown that the proposed approximation greatly simplifies the calculation of channel LLRs, and yet provides results almost identical to those based on the exact calculation of channel LLRs. The results are obtained in the context of bit-interleaved coded modulation (BICM) schemes with low-density parity-check (LDPC) codes, and include threshold calculations and error rate performance of finite-length codes. Compared to the existing approximations, the proposed method is either significantly less complex, or considerably more accurate.

We propose a technique to design finite-length irregular low-density parity-check (LDPC) codes over the binary-input additive white Gaussian noise (AWGN) channel with good performance in both the waterfall and the error floor region. The design process starts from a protograph which embodies a desirable degree distribution. This protograph is then lifted cyclically to a certain block length of interest. The lift is designed carefully to satisfy a certain approximate cycle extrinsic message degree (ACE) spectrum. The target ACE spectrum is one with extremal properties, implying a good error floor performance for the designed code. The proposed construction results in quasi-cyclic codes which are attractive in practice due to simple encoder and decoder implementation. Simulation results are provided to demonstrate the effectiveness of the proposed construction in comparison with similar existing constructions.

Cyclic liftings are proposed to lower the error floor of low-density parity-check (LDPC) codes. The liftings are designed to eliminate dominant trapping sets of the base code by removing the short cycles which are part of the trapping sets. We derive a necessary and sufficient condition for the cyclic permutations assigned to the edges of a cycle ξ of lengthl(ξ) in the base graph such that the inverse image of ξ in the lifted graph consists of only cycles of length strictly larger thanl(ξ). The proposed method is universal in the sense that it can be applied to any LDPC code over any channel and for any iterative decoding algorithm. It also preserves important properties of the base code such as degree distributions, and in some cases, the code rate. The constructed codes are quasi-cyclic and thus attractive from a practical point of view. The proposed method is applied to both structured and random codes over the binary symmetric channel (BSC). The error floor improves consistently by increasing the lifting degree, and the results show significant improvements in the error floor compared to the base code, a random code of the same degree distribution and block length, and a random lifting of the same degree. Similar improvements are also observed when the codes designed for the BSC are applied to the additive white Gaussian noise (AWGN) channel.

A new approach for the approximation of the channel log-likelihood ratio (LLR) for wireless channels based on Taylor series is proposed. The approximation is applied to the uncorrelated flat Rayleigh fading channel with unknown channel side information at the receiver. It is shown that the proposed approximation greatly simplifies the calculation of channel LLRs, and yet provides results almost identical to those based on the exact calculation of channel LLRs. The results are obtained in the context of iterative decoding of low-density parity-check (LDPC) codes and include threshold calculations and error rate performance of finite-length codes. Compared to the existing approximations, the proposed method is either significantly less complex, or considerably more accurate.

Cyclic liftings are proposed to lower the error floor of low-density parity-check (LDPC) codes. The liftings are designed to eliminate dominant trapping sets of the base code by removing the short cycles which form the trapping sets. We derive a necessary and sufficient condition for the cyclic permutations assigned to the edges of a cycle c of length ℓ(c) in the base graph such that the inverse image of c in the lifted graph consists of only cycles of length strictly larger than ℓ(c). The proposed method is universal in the sense that it can be applied to any LDPC code over any channel and for any iterative decoding algorithm. It also preserves important properties of the base code such as degree distributions. The proposed method is applied to both structured and random codes over the binary symmetric channel (BSC). The error floor improves consistently by increasing the lifting degree, and the results show significant improvements in the error floor compared to the base code, a random code of the same degree distribution and block length, and a random lifting of the same degree. Similar improvements are also observed when the codes designed for the BSC are applied to the additive white Gaussian noise (AWGN) channel.