We study integrated sensing and communications (ISAC) in an unsourced random access (URA) scenario. In the proposed model, a multi-antenna base station (BS) senses and locates multiple uncooperative objects by leveraging unsourced packets from randomly positioned, single-antenna active users via multi-static sensing. The model is applied in a low-scattering environment, typical for high-frequency channels such as mmWave and Terahertz. Our study explores the tradeoff between sensing and communications, examining the balance between the number of active users supported for reliable communication and the number of objects supported for accurate sensing.

We introduce a novel soft-decision decoding algorithm for binary block codes named ordered reliability direct error pattern testing (ORDEPT). The proposed technique tests a list of partial error patterns (PEP)s that are arranged according to their logistic weight and completed on-the-fly based on the instantaneous received sequence and the code’s parity-check matrix. Our results, obtained for a variety of popular short high-rate codes, demonstrate that ORDEPT outperforms state-of-the-art decoding algorithms such as ordered reliability bits guessing random additive noise decoding (ORBGRAND) in terms of decoding complexity, and is hardware-favorable in terms of latency and energy consumption. The improvements carry on to the iterative decoding of product codes and convolutional product-like codes, where ORDEPT demonstrates the ability to efficiently find multiple candidate codewords and outperform state-of-the art competitors.

In this paper, we propose an approach to construct a fully asynchronous unsourced random access (URA) communication system. In addition to the typical characteristics of a URA system, such as absence of the user identification in the packet and focus on decoding of the message content, there is no limitation on the user transmission timing. The active users can transmit their packets at any time, on demand. The proposed system belongs to the class of preamble-payload URA formats. Contrary to the typical role of the preamble to serve as temporary user identifier in a URA system, in our proposed system the preamble serves the purpose of timing acquisition. The natural transmission asynchronicity reduces packet collisions. The remaining collisions are tackled by use of a small pool of distinct preambles. Our results demonstrate that, over a wide range of signal-to-noise ratios (SNRs), the number of active users supported by the proposed system is close to the number of users supported by an asynchronous URA system with genie-aided nacket timing.

In this work we introduce a novel soft-decision decoding algorithm for high-rate short error-correction codes. Our results demonstrate that the proposed algorithm improves over the state-of-the-art algorithms, including recently proposed Ordered Reliability Bits Guessing Random Additive Noise Decoding (ORBGRAND), in terms of latency and decoding complexity. Specifically, we demonstrate that the ability of the proposed algorithm to find multiple candidate codewords with a reduced number of low-complexity queries makes it an efficient component decoder for iterative decoding of product-like codes.

In this paper we study feedback mechanisms for unsourced random access (URA) communications. We propose an algorithm to construct feedback packets broadcasted to the users by the base station (BS) and a feedback packet format that allows the users to estimate their channels and infer positive or negative feedback based on the presented thresholding algorithms. We show that the proposed feedback technique leads to a substantial reduction in the packet error rates and signal-to-noise ratios (SNRs) required to support various numbers of active users. We also demonstrate that the proposed feedback imposes a much smaller complexity burden on the users compared to the feedback that acknowledges only successful or only all undecoded users. Finally, we present a theoretical analysis framework that closely matches the experimental results.

Existing methods used for the clock distribution of multiple dies employ a balanced tree structure to minimize the impact of the within-die process and loading variations. No topology for die-to-die clock skew compensation of more than two dies has been presented yet. This article presents a novel die-to-die clock skew compensation topology to address these limitations. Unlike existing designs, the proposed topology does not need a phase detector (hence, no dead zone); it only requires one through-silicon via (TSV) to connect a pair of dies and one digitally controlled delay line (DCDL) in each die; thus, there is no skew from extra TSVs and DCDLs. Accordingly, the system has a small chip area and low lock time. The postsynthesis of this work was accomplished in a 65-nm CMOS process. The performance of our design was evaluated theoretically and practically in terms of mismatch/finite resolution of delay lines, buffer mismatch, and TSV delay. Under identical conditions, the residual skew of the proposed design was as low as 13 ps at 1 GHz. This study is the first to obtain the solution for die-to-die clock synchronization of multiple dies (more than two dies) in a three-dimensional (3-D) integrated circuit, while other systems can only support two dies.

We focus on an unsourced random access (URA) system for communication over fading channels where the payload of each packet is encoded for error-correction, repeated, permuted, and scrambled. Each packet is also equipped with a preamble that is used for channel estimation and detection of permutation and scrambling sequences utilized for payload encoding. We propose an algorithm to resolve multiple-access preamble transmission, based on the approximate message-passing (AMP), that is capable to support high numbers of active users and achieve low probabilities of miss-detection. We also develop a parallel interference cancellation technique for payload reception that iteratively refines the channel estimates and attempts to minimize the mean squared error (MSE) of the users’ data via selective error-correction decoding. Finally, we derive a detailed system performance analysis that closely matches the obtained numerical results. We demonstrate that the presented system can more than double the number of active users, supported by the state-of-the-art systems. Large gains in terms of the minimal required signal-to-noise ratios (SNR)s are also demonstrated for a wide range of active user numbers.

This brief presents a power and memory-optimized hardware implementation for the open forward error correction (oFEC) encoder proposed for high-speed fiber optical communications. Instead of storing a large amount of previously encoded data in the memory as suggested in oFEC proposal, we propose an alternative algorithm that requires the knowledge of only a few blocks of preencoded partial parity-check bits with the goal to reduce circuit power consumption. We then present a hardware implementation architecture for both the standard and optimized encoding algorithms and demonstrate that power dissipation and area overhead are reduced multiple times by optimized implementation.

We focus on a hardware implementation of the concatenated forward error-correction (FEC) decoder defined in 400ZR implementation agreement to provide a throughput of 400 Gbps over fiber-optical communication links. We propose a soft-input hard-output low-complexity decoding algorithm for the inner Hamming code. We demonstrate that the algorithm leads to an efficient hardware design with low silicon area and power dissipation. We then propose a hardware implementation architecture of the outer staircase decoder. It features a highly optimized low-power implementation of Bose-Chaudhuri-Hocquenghem (BCH) component decoders and the staircase decoder memory that can be efficiently accessed by either vertical or horizontal component decoders. Finally, we analyze the hardware implementation of the entire 400ZR decoder and investigate the trade-off in terms of power, area, and speed, that results from the inner/outer decoder concatenation and is dictated by the bit-error rate at the output of the inner decoder.

This brief presents a VLSI architecture of a high-throughput, low-latency, and power staircase forward error correction (FEC) encoder. The designed encoder achieves low latency and memory overhead by splitting the parity generation matrix and precomputing partial parity bits for the next staircase block while generating the current staircase block. The proposed encoder is designed with a multistage pipelined architecture that enables high efficiency in terms of throughput and area. Using 65-nm CMOS technology, the synthesized encoder achieves 432 Gb/s when operating at 909 MHz, with the power consumption of 323 mW.

A novel code construction based on spatially coupled low-density parity-check (SC-LDPC) codes is presented. The proposed code ensembles are comprised of several protograph-based chains characterizing individual SC-LDPC codes. We demonstrate that the code ensembles obtained by connecting appropriately chosen individual SC-LDPC code chains at specific points have improved iterative decoding thresholds. In addition, the connected chain ensembles have a smaller decoding complexity required to achieve a specific bit error probability compared to the individual code chains. Moreover, we demonstrate that, like the individual component chains, the proposed constructions have a typical minimum distance that grows linearly with block length. Finally, we show that the improved asymptotic properties of the connected chain ensembles also translate into improved finite length performance.

We consider a signaling format where the information to be communicated from a single or multiple transmitters to a receiver is modulated via a superposition of independent data streams. Each data stream is formed by error-correction encoding, constellation mapping, replication and permutation of symbols, and application of signature sequences. The relations between the data bits and modulation symbols transmitted over the channel can be represented by a sparse graph. In the case where the modulated data streams are transmitted with time offsets the receiver observes spatial coupling of the individual graphs into a graph chain enabling efficient demodulation/decoding. We prove that a two-stage demodulation/decoding method, in which iterative demodulation based on symbol estimation and interference cancellation is followed by parallel error-correction decoding, achieves capacity on the additive white Gaussian noise channel asymptotically. We compare the performance of the two-stage receiver to the receiver which utilizes hard-decision decoding feedback between the error-correction decoders and the iterative demodulator and estimate the gap between the achievable spectral efficiency and the channel capacity.

We analyze a class of high performance, low decoding-data-flow error-correcting codes suitable for high bit-rate optical-fiber communication systems. A spatially coupled split-component ensemble is defined, generalizing from the most important codes of this class, staircase codes and braided block codes, and preserving a deterministic partitioning of component-code bits over code blocks. Our analysis focuses on low-complexity iterative algebraic decoding, which, for the binary erasure channel, is equivalent to a generalization of the peeling decoder. Using the differential equation method, we derive a vector recursion that tracks the expected residual graph evolution throughout the decoding process. The threshold of the recursion, for asymptotically long component codes, is found using potential function analysis. We generalize the analysis to mixture ensembles consisting of more than one type of component code. We give an example of a mixture ensemble consisting of two component codes, which has better performance than spatially-coupled split-component ensembles consisting of only one component code. The analysis extends to the binary symmetric channel by assuming miscorrection-free component-code decoding. Simple upper bounds on the number of errors correctable by the ensemble are derived. Finally, we analyze the threshold of spatially coupled split-component ensembles under beyond bounded-distance component decoding.

We propose a novel encoding/transmission scheme called continuous chain (CC) transmission that is able to improve the finite-length performance of a system using spatially coupled low-density parity-check (SC-LDPC) codes. In CC transmission, instead of transmitting a sequence of independent code words from a terminated SC-LDPC code chain, we connect multiple chains in a layered format, where encoding, transmission, and decoding are performed in a continuous fashion. The connections between chains are created at specific points, chosen to improve the finite-length performance of the code structure under iterative decoding. We describe the design of CC schemes for different SC-LDPC code ensembles constructed from protographs: a (J,K) -regular SC-LDPC code chain, a spatially coupled repeat-accumulate (SC-RA) code, and a spatially coupled accumulate-repeat-jagged-accumulate (SC-ARJA) code. In all cases, significant performance improvements are reported and it is shown that using CC transmission only requires a small increase in decoding complexity and decoding delay with respect to a system employing a single SC-LDPC code chain for transmission.

We consider an asymptotic iterative decoding analysis of spatially-coupled split-component codes used for communication over binary symmetric channel (BSC) with hard-decision decoding at the receiver. The proposed analysis takes into account the impact of mis-corrections that occur in component code decoding. The analysis technique models flows of corrections and mis-corrections that occur throughout the decoding process in the entire coupled code chain. The results for spatially-coupled split-component codes with BCH component codes demonstrate that the analysis provides significantly more accurate estimates of the iterative decoding threshold values.

We analyze a class of high performance, low decoding data-flow codes suitable for high bit-rate optical-fiber communication systems. A spatially-coupled split-component ensemble is defined, encompassing the most representative codes in this class, staircase codes and braided block codes. Our definition preserves two important properties of this class of codes: deterministic partitioning of component-code bits over code blocks and simple iterative algebraic component-code decoding. For the binary erasure channel, we derive a vector recursion for the decoding process and determine its threshold using potential function analysis. We generalize the analysis to mixture ensembles consisting of more than one type of component code. The analysis extends to the binary symmetric channel by assuming mis-correction-free component-code decoding. An intuitive upper-bound on the number of errors correctable by the ensemble is derived. Finally, we analyze the threshold of spatially-coupled split-component ensembles under beyond bounded-distance component decoding.

A novel modulation format based on coupling for streaming data transmissions is proposed. The construction utilizes an infinite parity-check matrix of a low-density parity-check convolutional code which is used for data encoding with real-domain addition instead of modulo-two addition. The demodulation and decoding is accomplished using iterative bit estimation and interference cancellation. We demonstrate that the threshold saturation effect of spatial graph coupling holds for the proposed format and the achievable communication rate approaches the additive white Gaussian noise channel capacity and exceeds the capacities of traditional PAM modulations.

We consider a signaling format where information is modulated via a superposition of independent data streams. Each data stream is formed by replication and permutation of encoded information bits. The relations between data bits and modulation symbols transmitted over the channel can be represented in the form of a sparse graph. The modulated streams are transmitted with time offsets enabling spatial coupling of the sparse modulation graphs. We prove that iterative demodulation based on symbol estimation and interference cancellation followed by parallel error correction decoding is a universal multiple access technique which achieves the entire capacity region of the additive white Gaussian noise (AWGN) multiple access channel.

The finite length performance of codes on graphs constructed by connecting spatially coupled low-density parity-check (SC-LDPC) code chains is analyzed. Successive (peeling) decoding is considered for the binary erasure channel (BEC). The evolution of the undecoded portion of the bipartite graph remaining after each iteration is analyzed as a dynamical system. It is shown that, in addition to superior iterative decoding thresholds, connected chain ensembles have better performance than single chain ensembles of the same rate and length.

Demodulation in a random multiple access channel is considered where the signals are chosen uniformly randomly with unit energy. It is shown that by lifting (replicating) the graph of this system and randomizing the graph connections, a simple iterative cancellation demodulator achieves the same performance as an optimal symbol-by-symbol detector of the original system. The iterative detector has a complexity that is linear in the number of users, while the direct optimal approach is known to be NP-hard. However, the maximal system load of this lifted graph is limited to$\alpha < 2.07$, even for large signal-to-noise ratios (SNRs)—the system is interference limited. Spatial coupling between subsequent lifted graphs is introduced, and anchoring the initial graphs, the achievable system load$\alpha$can go to infinity as the SNR goes to infinity. Our results apply to several well-documented system proposals, such as interleave-division multiple access, partitioned spreading, and certain forms of multiple-input multiple-output communications.

Codes constructed from connected spatially coupled low-density parity-check code (SC-LDPCC) chains are proposed and analyzed. It is demonstrated that connecting coupled chains results in improved iterative decoding performance. The constructed protograph ensembles have better iterative decoding thresholds compared to an individual SC-LDPCC chain and require less computational complexity per bit when operating in the near-threshold region. In addition, it is shown that the proposed constructions are asymptotically good in terms of minimum distance.

In this paper, we study ensembles of connected spatially coupled low-density parity-check codes (SC-LDPCCs), i.e., ensembles described by graphs in which regular SC-LDPCC chains of various lengths serve as edges. We show that, by carefully connecting individual SC-LDPCC chains, we obtain LDPC code ensembles with improved iterative decoding thresholds compared to those of a single coupled chain, in addition to reducing the decoding complexity required to achieve a specific bit error probability. Moreover, we show that, like the component SC-LDPCC chains, the proposed constructions have a typical minimum distance that grows linearly with block length.

Demodulation in a random multiple access channel is considered where the signals are chosen uniformly randomly with unit energy, a model applicable to several modern transmission systems. It is shown that by lifting (replicating) the graph of this system and randomizing the graph connections, a simple iterative cancellation demodulator can be constructed which achieves the same performance as an optimal symbol-by-symbol detector of the original system. The iterative detector has a complexity that is linear in the number of signals (users), while the direct optimal approach is known to be NP-hard. However, the maximal system load of this lifted graph is limited to α <; 2:074, even for signal-to-noise ratios going to infinity - the system is interference limited. We then show that by introducing spatial coupling and anchoring of the lifted graph, this limitation can be avoided and arbitrary system loads are achievable. Our results apply to several well-documented system proposals, such as IDMA, partitioned spreading, and certain forms of MIMO communications.

A multiple packet receiver (MPR), which jointly performs timing acquisition of the incoming packets and decoding of the packet payloads, is analyzed. The payload decoding consists of iteratively performed parallel interference cancellation, followed by individual error control decoding. Timing acquisition is repeated at every stage of the interference cancellation in order to acquire packets that are otherwise covered by interference. The case in which packets are received at multiple power levels is considered, and it is proved that the system is capable to operate close to the multiple access channel capacity. An upper bound on the gap between the achievable spectral efficiency and the channel capacity is derived in terms of the preamble length (timing acquisition window).

Existence type lower bounds on the free distance of periodically time-varying LDPC convolutional codes and on the minimum distance of tail-biting LDPC convolutional codes are derived. It is demonstrated that the bound on free distance of periodically time-varying LDPC convolutional codes approaches the bound on free distance of general (nonperiodic) time-varying LDPC convolutional codes as the period increases. The proof of the bound is based on lower bounding the minimum distance of corresponding tail-biting LDPC convolutional codes, which is of interest in its own right.

Wireless ad hoc networks with nodes capable of simultaneous multiple packet reception are considered. We focus on spread spectrum networks and address the relationship between the packet detection success, probability of the packet success over multiple hops, and asymptotic throughput capacity of the network in terms of power and bandwidth resources as well as the multi-packet detection capability of the nodes. In the second part of the paper we consider network with nodes employing partitioned code division multiple access (CDMA) transmission and joint iterative reception. We study local communication in the network and derive a relationship between the probability of detection success and a fraction of the multiple access channel capacity that can be achieved at any communicating node. We use this result to demonstrate that near optimum throughput and reliable end-to-end communication can be achieved in the network with use of a practical detection method. Finally, we present simulation results which demonstrate the advantage of partitioned CDMA with iterative receivers over CDMA with linear receivers in a network setting.

A new class of binary iteratively decodable codes with good decoding performance is presented. These codes, called braided block codes (BBCs), operate on continuous data streams and are constructed by interconnection of two component block codes. BBCs can be considered as convolutional (or sliding) version of either Elias' product codes or expander codes. In this paper, we define BBCs, describe methods of their construction, analyze code properties, and study asymptotic iterative decoding performance.

Iterative processing for linear matrix channels, aka turbo equalization, turbo demodulation, or turbo code-division multiple access (CDMA), has traditionally been addressed as the concatenation of conventional error control codes with the linear (matrix) channel. However, in several situations, such as CDMA, multiple-input-multiple-output (MIMO) channels, orthogonal frequency-division multiplexing (OFDM), and intersymbol-interference (ISI) channels, the channel itself either contains inherent signal redundancy or such redundancy can readily be introduced at the transmitter. For such systems, iterative demodulation of the linear channel exploiting this redundancy using simple iterative cancellation demodulators, followed by conventional feedforward error control decoding, provides a low-complexity, but extremely efficient decoding alternative. This two-stage demodulator/decoder outperforms more complex turbo CDMA methods for equal power modes (users). Furthermore, it is shown that arbitrary numbers of modes can be supported if an unequal power distribution is adopted. These power distributions are nested, which means that additional modes can be added without disturbing an existing mode population. The main result shows that these nested power distributions enable the two-stage receiver to approach the Shannon capacity of the channel to within less than one bit for any signal-to-noise ratio (SNR).

A key advantage of viewing communications in wireless networks as multiple access rather than a plurality of point-to-point transmissions, is its robustness towards multiple access interference. Concurrent packet transmissions are allowed to coexist thus deviating from the traditional view of enforcing collision-footprints around the transmitter-receiver pairs. What are the performance gains of employing channel access strategy based on a multiple access channel in a multihop wireless network? We consider a wireless multihop network, where nodes have a joint decoding capability to resolve up to K multiple concurrent packet transmissions from other nodes in their range. The basic assumptions are that the packet transmissions are asynchronous, i.e., nodes are completely uncoordinated, and that the packet transmission at each node is based on a probabilistic model. In this paper, we show that a simple random access strategy for communication over such channels offers significant gains in throughput while reducing latency in congested wireless networks. More precisely, we characterize the throughput performance gains through an exact analysis for the case of K=2 and also offer tight approximations for arbitrary K. Furthermore, we study the asymptotic throughput behavior and prove asymptotic optimality of random channel access over multiple access channel.

An ensemble of$(J,K)$-regular low-density parity- check (LDPC) convolutional codes is introduced and existence-type lower bounds on the minimum distance$d _ {\rm L}$of code segments of finite length$L$and on the free distance$d _{\rm free}$are derived. For sufficiently large constraint lengths$\nu$, the distances are shown to grow linearly with$\nu$and the ratio$d_ {\rm L}/\nu$approaches the ratio$d _{ {\rm free}}/\nu$for large$L$. Moreover, the ratio of free distance to constraint length is several times larger than the ratio of minimum distance to block length for Gallager's ensemble of (J,K)-regular LDPC block codes.

We consider two strategies for communication in ad hoc networks with local node cooperation. Groups of adjacent nodes transmit and relay information simultaneously in order to increase the throughput. For the proposed schemes we derive achievability bounds on the communication rates and demonstrate sizable gains over the corresponding time division multiple access based strategies. The obtained bounds closely follow recently derived information theoretic upper bounds on communication rates. Additionally we address the impact of traffic localization on the achievable rates and the receiver complexity.

We consider construction and realization aspects of encoders and decoders for braided block codes (BBCs), which are a powerful class of iteratively decodable codes. An efficient encoder is proposed as well as a pipeline decoder realization. Also, upper and lower bounds on the free distance of BBCs are derived

Traffic demands in networks play a vital role in determining the transmission rate that a network can support between communicating users. We derive information theoretic upper bounds on the rate per communicating source-destination pair in ad-hoc wireless networks with a non-uniform traffic pattern. The upper bounds are tight and closely follow the achievability bounds recently given by Tabet and Knopp. Furthermore, we show that in the case of large signal attenuation, the bounds hold even when the cooperation among the users is limited to certain region of the network domain

Asymptotic iterative decoding performance is analyzed for several classes of iteratively decodable codes when the block length of the codes N and the number of iterations I go to infinity. Three classes of codes are considered. These are Gallager's regular low-density parity-check (LDPC) codes, Tanner's generalized LDPC (GLDPC) codes, and the turbo codes due to Berrou et al. It is proved that there exist codes in these classes and iterative decoding algorithms for these codes for which not only the bit error probability P/sub b/, but also the block (frame) error probability P/sub B/, goes to zero as N and I go to infinity.

Block transmission over noisy communication channels is characterized by two performance criteria: the bit error probability P/sub b/ and the block error probability P/sub B/. If P/sub B/ goes to zero when N/spl rarr//spl infin/ (where N denotes the length of the permutors), P/sub b/ also must go to zero for all symbols in the block but, in general, the reverse is not true. Therefore we formulate the Shannon's condition for reliable communication over noisy channels. In this paper, we address the problem of reliable communication for iterative decoding of turbo codes.

A lower bound on the free distance of LDPC convolutional codes defined by syndrome former matrices comprised of MtimesM permutation matrices is derived. We show that asymptotically, i.e., as Mrarrinfin, for almost all codes in the ensemble the free distance grows linearly with constraint length

A new permutor design for serially concatenated convolutional codes is presented. It is based on the construction of a permutation matrix without short cycles of special types. For such a permutor, we give a lower bound on the minimum distance of the overall code that is significantly larger than that achievable with first-order separation (spreading factors). Additionally, the minimum distance can be attuned to the permutation length. This property may be useful for the construction of codes with moderate block lengths.

Analytic expressions for the exact bit error probabilities of rate R=1/2, memory m=2 convolutional encoders are derived for a maximum-likelihood (ML) decoder and transmission over the binary-symmetric channel (BSC). The resulting expressions are rational functions of the crossover probability of the BSC. In addition to classical nonsystematic encoders without feedback, we consider also recursive systematic encoders, which became especially important as component encoders in concatenated coding schemes. To attest the validity of the results, they are compared to computer simulations. Based on the presented technique also the bit error probability and the probability distribution of the output log-likelihood ratios of the Max-Log-MAP algorithm are derived in analytic form.