Code Block Length Research Articles

SWIPT-Enabled Relaying in IoT Networks Operating With Finite Blocklength Codes

This paper considers simultaneous wireless information and power transfer (SWIPT) mechanisms in a relaying-assisted ultra-reliable low latency communication network operating with finite blocklength codes. The reliability of the network is maximized by the optimal selection of SWIPT parameters under both a power splitting (PS) protocol and a time switching (TS) protocol. In addition, we propose a protocol to improve the reliability performance by introducing a tradeoff between the PS and TS protocols. To further improve the reliability, a joint design is provided, which aligns the optimal selection of SWIPT parameters together with a blocklength allocation between two relaying hops. Via simulations, we validate our analytical model and show that the proposed algorithm achieves the same performance as that obtained with exhaustive search. In addition, we evaluate the considered network, and characterize the impact of blocklength, transmit power, and packet size on the reliability of the considered SWIPT-enabled relaying network. Finally, the performance advantages of the proposed protocol (in comparison with the PS and TS protocols) and the proposed joint designs are investigated.

On the Throughput of Large-but-Finite MIMO Networks Using Schedulers

This paper studies the sum throughput of the {multi-user} multiple-input-single-output (MISO) networks in the cases with large but finite number of transmit antennas and users. Considering continuous and bursty communication scenarios with different users' data request probabilities, we derive quasi-closed-form expressions for the maximum achievable throughput of the networks using optimal schedulers. The results are obtained in various cases with different levels of interference cancellation. Also, we develop an efficient scheduling scheme using genetic algorithms (GAs), and evaluate the effect of different parameters, such as channel/precoding models, number of antennas/users, scheduling costs and power amplifiers' efficiency, on the system performance. Finally, we use the recent results on the achievable rates of finite block-length codes to analyze the system performance in the cases with short packets. As demonstrated, the proposed GA-based scheduler reaches (almost) the same throughput as in the exhaustive search-based optimal scheduler, with substantially less implementation complexity. Moreover, the power amplifiers' inefficiency and the scheduling delay affect the performance of the scheduling-based systems significantly.

Resource allocation for ultra-reliable low latency communications in sparse code multiple access networks

In this paper, we propose an optimal resource allocation policy for sparse code multiple access (SCMA) networks supporting ultra-reliable low-latency communications (URLLC). The network is assumed to operate with finite blocklength (FBL) codes, which is opposed to the classical information-theoretic works with infinite blocklength (IBL) codes. In particular, we aim at maximizing the average transmission rate in the FBL regime while guaranteeing the transmission reliability. A joint design is proposed, which combines the power allocation with the codebook assignment. The convexity of the corresponding optimization problem is analyzed and an iterative search algorithm is further provided. We study the impact of reliability and short blocklength constraints on the performance of the proposed optimal resource allocation policy through numerical simulations. In addition, we evaluate the FBL performance of the proposed joint design in comparison to the scenario with an IBL assumption.

Short block length trellis‐based codes for interference channels

In this study, the authors consider Gaussian interference channels and fading interference channels, and design short block length codes based on trellis-based constructions. For both joint maximum likelihood (JML) decoding and single user minimum distance decoding, they obtain error-rate bounds to assess the code performance. Then they employ the obtained bounds for code design and present several design examples. For the case of quasi-static fading, they note that while the simple version of the derived bound is not sufficiently tight for code search purposes, one can obtain a tight performance bound with a higher complexity that can be used for a theoretical performance investigation. For the Gaussian case under JML decoding, they show that the newly designed codes provide significant improvements over point-to-point (P2P) trellis-based codes and off-the-shelf low density parity check codes. They also demonstrate that, for the case of independent and identically distributed fading, the best codes obtained by performing code search are P2P optimal ones, which is also verified by simulation results.

Ultra-Reliable Short-Packet Communications: Half-Duplex or Full-Duplex Relaying?

This letter analyzes and compares the performance of full-duplex relaying (FDR) and half-duplex relaying (HDR) for ultra-reliable short-packet communications. Specifically, we derive both approximate and asymptotic closed-form expressions of the block error rate (BLER) for FDR and HDR using short packets with finite blocklength codes. We define and attain a closed-form expression of a critical BLER, which can be used to efficiently determine the optimal duplex mode for ultra-reliable low latency communication scenarios. Our results unveil that FDR is more appealing to the system with relatively lower transmit power constraint, less stringent BLER requirement and stronger loop interference suppression.

Continuity of Channel Parameters and Operations under Various DMC Topologies.

We study the continuity of many channel parameters and operations under various topologies on the space of equivalent discrete memoryless channels (DMC). We show that mutual information, channel capacity, Bhattacharyya parameter, probability of error of a fixed code and optimal probability of error for a given code rate and block length are continuous under various DMC topologies. We also show that channel operations such as sums, products, interpolations and Arıkan-style transformations are continuous.

Randomized generation of error control codes with automata and transducers

We introduce the concept of an -maximal error-detecting block code, for some parameter in (0,1), in order to formalize the situation where a block code is close to maximal with respect to being error-detecting. Our motivation for this is that it is computationally hard to decide whether an error-detecting block code is maximal. We present an output-polynomial time randomized algorithm that takes as input two positive integers N, ℓ and a specification of the errors permitted in some application, and generates an error-detecting, or error-correcting, block code of length ℓ that is 99%-maximal, or contains N words with a high likelihood. We model error specifications as (nondeterministic) transducers, which allow one to represent any rational combination of substitution and synchronization errors. We also present some elements of our implementation of various error-detecting properties and their associated methods. Then, we show several tests of the implemented randomized algorithm on various error specifications. A methodological contribution is the presentation of how various desirable error combinations can be expressed formally and processed algorithmically.

Fundamental Tradeoff Between Doppler Diversity and Channel Estimation Errors in SIMO High Mobility Communication Systems

This paper studies the fundamental performance limits of a single-input multiple-output (SIMO) high mobility wireless communication systems with imperfect channel state information (CSI). The fundamental limits are quantified in terms of the maximum diversity order (including both Doppler diversity and antenna diversity) that can be achieved by a high mobility system, and the loss in coding gain due to channel estimation errors. Due to severe Doppler effects caused by fast time-varying fading in high mobility systems, channel estimation errors are usually inevitable and might cause significant performance losses. On the other hand, Doppler effect provides potential Doppler diversity that can be harnessed to improve system performance. To quantify this fundamental tradeoff between Doppler diversity and channel estimation errors, we perform analytical studies of the asymptotic error performance of SIMO high mobility systems when the signal-to-noise ratio and the coding block length is large. The analytical results are obtained by analyzing and quantifying the impacts of channel estimation errors on the system performance. With the help of pilot-aided channel estimation and a simple repetition code, we identified the maximum diversity order achievable by a SIMO high mobility system with imperfect CSI and the loss in coding gains due to the inevitable channel estimation errors. The analytical results are then used to optimally allocate transmission energy to pilot symbols and data symbols to simultaneously maximize the Doppler diversity order and minimize the loss coding gain loss due to channel estimation errors. The results reveal the fundamental tradeoff between Doppler diversity and channel estimation errors and can be used to serve as a guide in the design of practical high mobility systems.

Serially Concatenated Polar Codes

Simulation results show that the performance of polar codes is improved vastly by using polar codes as inner codes in serially concatenated coding schemes. Furthermore, this performance improvement is achieved using a relatively short cyclic redundancy check as the outer code and a practically implementable successive cancellation list decoder for decoding the overall code. This paper offers a theoretical analysis of such schemes by employing a random-coding method on the selection of the outer code and assuming that the channel is memoryless. It is shown that the probability of error for the concatenated coding scheme decreases exponentially in the code block length at any fixed rate below the symmetric capacity. Applications of this result include the design of polar codes for communication systems that require high reliability at small to moderate code lengths, such as control channels in wireless systems and machine-type communications for industrial automation.

Delay-Sensitive Area Spectral Efficiency: A Performance Metric for Delay-Constrained Green Networks

This paper introduces a new metric, referred to as delay-sensitive area spectral efficiency (DASE), to analyze the performance of delay-constrained wireless networks. We study DASE in different point-to-point, spectrum sharing, interference, and Poisson-point process-based dense network configurations and with different levels of channel state information (CSI) at the transmitters. Also, we determine the optimal rates/powers optimizing DASE. Finally, we use some recent results on finite block-length codes to analyze the effect of the codewords length on the network DASE. As demonstrated, DASE is a useful metric for analyzing delay-sensitive green networks. Moreover, adaptive power allocation and partial CSI feedback are powerful tools for performance improvement in green networks.

On the VLSI Energy Complexity of LDPC Decoder Circuits

Sequences of randomly generated bipartite configurations are analyzed; under mild conditions almost surely such configurations have minimum bisection width proportional to the number of vertices. This implies an almost sure $\Omega (n^{2}/d^{2}_{\mathrm {max}})$ scaling rule for the energy of directly-implemented low-density parity-check (LDPC) decoder circuits for codes of block length $n$ and maximum node degree $d_{\mathrm {max}}$ . It also implies an $\Omega (n^{3/2}/d_{\mathrm {max}})$ lower bound for serialized LDPC decoders. It is also shown that all (as opposed to almost all) capacity-approaching, directly-implemented non-split-node LDPC decoding circuits, have energy, per iteration, that scales as $\Omega \left ({\chi ^{2}\ln ^{3} \chi }\right )$ , where $\chi =(1-R/C)^{-1}$ is the reciprocal gap to capacity, $R$ is code rate, and $C$ is channel capacity.

Delay Minimization in Real-Time Communications With Joint Buffering and Coding

We present a closed-form expression for the minimal delay that is achievable in a setting that combines a buffer and an erasure code, used to mitigate the packet delay variance. The erasure code is modeled according to the recent information-theoretic results on finite block length codes. Evaluations reveal that accurate knowledge of the network parameters is essential for optimal operation. Moreover, it is shown that, when the network packet delay variance is large, the buffer delay becomes negligible. Therefore, in this case, the delay budget should be spent mainly on the erasure code.

High-Rate Locally Correctable Codes via Lifting

We present a general framework for constructing high-rate error correcting codes that are locally correctable (and hence locally decodable if linear) with a sublinear number of queries, based on lifting codes with respect to functions on the coordinates. Our approach generalizes the lifting of affine-invariant codes (of Guo, Kopparty, and Sudan) and its generalization automorphic lifting (alluded to in the work of Ben-Sasson et al., but distinct from their degree lifting), which lifts algebraic geometry codes with respect to a group of automorphisms of the code. Our notion of lifting is a natural alternative to the degree lifting of Ben-Sasson et al. and it carries two advantages. First, it overcomes the rate barrier inherent in degree lifting. Second, it requires no special properties (e.g. linearity and invariance) of the base code, and requires a very little structure on the set of functions on the coordinates of the code. As an application, we construct new explicit families of locally correctable codes by lifting algebraic geometry codes. Like the multiplicity codes of Kopparty, Saraf, Yekhanin, and the affine-lifted codes of Guo, Kopparty, and Sudan, our codes of block length $N$ can achieve $N^\epsilon $ query complexity and $1-\alpha $ rate for any given $\epsilon , \alpha > 0$ , while correcting a constant fraction of errors, in contrast to the Reed–Muller codes and the degree-lifted AG codes of Ben-Sasson et al., which face a rate barrier of $\epsilon ^{O(1/\epsilon )}$ . However, like the degree-lifted AG codes, our codes are over an alphabet significantly smaller than that obtained by Reed–Muller codes, affine-lifted codes, and multiplicity codes.

Unified Scaling of Polar Codes: Error Exponent, Scaling Exponent, Moderate Deviations, and Error Floors

Consider the transmission of a polar code of block length $N$ and rate $R$ over a binary memoryless symmetric channel $W$ and let $P_{\mathrm{ e}}$ be the block error probability under successive cancellation decoding. In this paper, we develop new bounds that characterize the relationship of the parameters $R$ , $N$ , $P_{\mathrm{ e}}$ , and the quality of the channel $W$ quantified by its capacity $I(W)$ and its Bhattacharyya parameter $Z(W)$ . In previous work, two main regimes were studied. In the error exponent regime, the channel $W$ and the rate $R are fixed, and it was proved that the error probability $P_{\mathrm{ e}}$ scales roughly as $2^{-\sqrt {N}}$ . In the scaling exponent approach, the channel $W$ and the error probability $P_{\mathrm{ e}}$ are fixed and it was proved that the gap to capacity $I(W)-R$ scales as $N^{-1/\mu }$ . Here, $\mu $ is called scaling exponent and this scaling exponent depends on the channel $W$ . A heuristic computation for the binary erasure channel (BEC) gives $\mu =3.627$ and it was shown that, for any channel $W$ , $3.579 \le \mu \le 5.702$ . Our contributions are as follows. First, we provide the tighter upper bound $\mu \le 4.714$ valid for any $W$ . With the same technique, we obtain the upper bound $\mu \le 3.639$ for the case of the BEC; this upper bound approaches very closely the heuristically derived value for the scaling exponent of the erasure channel. Second, we develop a trade-off between the gap to capacity $I(W)-R$ and the error probability $P_{\mathrm{ e}}$ as the functions of the block length $N$ . In other words, we neither fix the gap to capacity (error exponent regime) nor the error probability (scaling exponent regime), but we do consider a moderate deviations regime in which we study how fast both quantities, as the functions of the block length $N$ , simultaneously go to 0. Third, we prove that polar codes are not affected by error floors . To do so, we fix a polar code of block length $N$ and rate $R$ . Then, we vary the channel $W$ and study the impact of this variation on the error probability. We show that the error probability $P_{\mathrm{ e}}$ scales as the Bhattacharyya parameter $Z(W)$ raised to a power that scales roughly like ${\sqrt {N}}$ . This agrees with the scaling in the error exponent regime.

Wireless Energy and Information Transmission Using Feedback: Infinite and Finite Block-Length Analysis

In this paper, we propose and analyze a wireless energy and information transfer system. To reduce the outage probability, compared with open-loop communication, we implement retransmission protocols both in the energy and in the information transmission phases. We use some recent results on finite block-length codes to analyze the effect of the energy and information signals lengths on the system outage probability/throughput. Finally, under a packet transmission delay constraint, we derive the optimal power allocation and time sharing between the energy and information signals, such that the energy-constrained outage probability is minimized. The simulation and analytical results demonstrate that the retransmission-based protocols are efficient techniques to reduce the energy-limited outage probability of wireless energy and information transmission systems.

Energy-Efficient Packet Scheduling With Finite Blocklength Codes: Convexity Analysis and Efficient Algorithms

This paper considers an energy-efficient packet scheduling problem over quasi-static block fading channels. The goal is to minimize the total energy for transmitting a sequence of data packets under the first-in-first-out rule and strict delay constraints. Conventionally, such design problem is studied under the assumption that the packet transmission rate can be characterized by the classical Shannon capacity formula, which, however, may provide inaccurate energy consumption estimation, especially when the code blocklength is finite. In this paper, we formulate a new energy-efficient packet scheduling problem by adopting a recently developed channel capacity formula for finite blocklength codes. The newly formulated problem is fundamentally more challenging to solve than the traditional one because the transmission energy function under the new channel capacity formula neither can be expressed in closed form nor possesses desirable monotonicity and convexity in general. We analyze conditions on the code blocklength for which the transmission energy function is monotonic and convex. Based on these properties, we develop efficient offline packet scheduling algorithms as well as a rolling-window based online algorithm for real-time packet scheduling. Simulation results demonstrate not only the efficacy of the proposed algorithms but also the fact that the traditional design using the Shannon capacity formula can considerably underestimate the transmission energy for reliable communications.

Design of LDPC Codes Based on Multipath EMD Strategies for Progressive Edge Growth

Low-density parity-check (LDPC) codes are capable of achieving excellent performance and provide a useful alternative for the high-performance applications. However, at medium to high signal-to-noise ratios, an observable error floor arises from the loss of independence of messages passed under iterative graph-based decoding. In this paper, the error floor performance of the short block length codes is improved by the use of a novel candidate selection metric in code graph construction. The proposed multipath extrinsic message degree (EMD) approach avoids harmful structures in the graph by evaluating certain properties of the cycles introduced in each edge placement. We present multipath EMD-based designs for several structured LDPC codes, including quasi-cyclic and the irregular repeat accumulate codes. In addition, an extended class of the diversity-achieving codes on the challenging block fading channel is proposed and considered with the multipath EMD design. This combined approach is demonstrated to provide the gains in decoder convergence and error rate performance. A simulation study evaluates the performance of the proposed and existing state-of-the-art methods.

A New Construction Method for Large Girth Quasi-Cyclic LDPC Codes with Optimized Lower Bound using Chinese Remainder Theorem

This paper presents a new construction algorithm of Quasi-cyclic low-density parity-check (QC-LDPC) codes of medium to large block-length by combining QC-LDPC codes of small block-length as their component codes, via Chinese remainder theorem. Such component codes were constructed by permuting each column block sequentially to attain the desire local girth. After combining all component codes to generate an expanded parity-check matrix, the resulting girth is greater than or at least equal to the highest girth of component codes. We investigate a lower bound for circulant permutation matrices in the proposed method, which provides efficient and fast encoding for a desired girth, and has very simple structure and more economical in terms of hardware implementation. As already proven, a high girth parameter of the parity-check matrix ensures a good error correcting performance. Thus, simulation results show that our proposed construction method of the parity-check matrix significantly outperforms the other well-known existing methods, has low error-floor, and can reduce encoding complexity for medium to large block-length QC-LDPC codes.

An Information Theory Perspective for the Binary STT-MRAM Cell Operation Channel

Spin-torque transfer magnetic random access memory (STT-MRAM) has emerged as a promising nonvolatile memory technology, with advantages, such as scalability, speed, endurance, and power consumption. This paper presents an STT-MRAM cell operation channel model with write and read operations for information theorists and error correction code designers. This model considers the effects of process variations and thermal fluctuations and considers all principle flaws during the fabrication and operation processes. With this model, evaluations are not only made for the write channel, the read channel, but also the write and read channel with metrics, such as operation failure rate, bit error rate, channel ergodic capacity, and channel outage probability at certain outage capacity. Moreover, it is proved that the distributions of written-in bit states are not uniformly distributed and are proportional to their respective write success probabilities. Finally, simulation results show that practical code rates and code block lengths can guarantee reliable performances only if the operation success rate difference between state 1 and state 0 is small enough.

Optimization of LDPC Codes over the Underwater Acoustic Channel

To combat severe intersymbol interference incurred by multipath propagation of sound waves in the underwater acoustic environment, we introduce an iterative equalization and decoding scheme by iteratively exchanging soft information between a low-density parity check (LDPC) decoder and a decision feedback equalizer. We apply extrinsic information transfer (EXIT) charts to analyze performance of LDPC codes over the acoustic multipath channel. Furthermore, using differential evolution technique, we develop an EXIT-aided method to optimize LDPC codes for the underwater acoustic channel. Design examples are presented for two different realizations of the underwater acoustic channel that are generated by an acoustic ray tracing model. Computer simulations show that the optimized LDPC codes outperform its regular counterpart or Turbo codes under the same coding rate and block length, with gains of 1.0 and 0.8 dB, respectively, at the bit error rate of 10−5.