The performance of a code under the maximum-likelihood (ML) decoder highly depends on the weight enumerating function (WEF). However, how to compute efficiently the WEF of a polar code or a polarization-adjusted convolutional (PAC) code is still an open problem. For the design of stand-alone polar codes, we consider enumerating the number of minimum-weight non-zero codewords of the polar code. The block error rate (BLER) under the ML decoder can be approximated as a function of the minimum weight of non-zero codewords and its multiplicity. On the other hand, for the design of PAC codes, we consider enumerating the WEF averaged over the ensemble of random PAC codes. The ML-BLER upper bound can be represented as a function of the WEF. The bit-channel selection algorithms for polar codes and PAC codes are proposed, which take both utilization of the polarization effect and the ML decoding performance as selection criteria. Simulation results show that the proposed stand-alone polar codes are competitive when the block length gets larger. Also, simulation results show that the proposed PAC codes yield excellent performance for a wide range of code rates and block lengths and outperform the 5G polar codes.

Ultra-reliable low-latency communication (URLLC) is an important feature brought by 5G New Radio (NR). By using a block code, the low-latency requirement in general requires a short block length in order to reduce the latency of transmitting the entire code block. The ultra-reliable communication requires a low-rate code to achieve high decoding reliability even under low signal-to-noise ratios (SNRs). This paper proposes a new class of coding and modulation schemes, termed permutation-coded modulations, for low-rate and short-block-length applications, such as URLLC. We show that permutation-coded modulations under maximum-likelihood (ML) decoding have remarkable performance levels that achieve the dispersion bounds with normal approximation (NA) for short block lengths. However, their encoding and ML-decoding complexities are prohibitive if the number of message bits transmitted per code block increases. To reduce the encoding and decoding complexities, we propose a trapezoidal permutation-coded modulation scheme which can be decoded efficiently by successive cancellation list (SCL) decoders. We also show that the trapezoidal permutation-coded modulations under SCL decoding can achieve the dispersion bounds with NA for short block lengths.

Private information retrieval (PIR) schemes allow a user to retrieve entries of a database without revealing the index of the desired item. The focus of this paper lies on constructions of PIR schemes with optimal computational complexity for the servers, which play a crucial part in fast retrieval. This paper first proposes a generic construction of t-private PIR schemes using circulant permutation matrices (CPMs), which can protect the user’s perfect privacy from any collusion of up to t servers. Then this paper takes Byzantine and unresponsive servers into account in the t-private PIR schemes using CPMs and proposes a generic construction of t-private robust PIR schemes using CPMs. The proposed constructions of PIR schemes enjoy the advantages of optimal computational complexity for the servers, competitive user computational complexity, acceptable communication complexity, low memory space for storing all possible queries for the user, and low encoding complexity upon encoding the database.

Private information retrieval (PIR) protocols allow a user to retrieve entries of a database without revealing the index of the desired item. Information-theoretical privacy can be achieved by the use of several servers and specific retrieval algorithms. In this paper, we investigate the problem of PIR under erasure-coded distributed storage systems and construct PIR protocols with optimal computational complexity for the servers, reasonable communication complexity, and low storage overhead. The proposed constructions also enjoy the advantages of low encoding complexity and low memory requirement for storing all possible queries for the user. More specifically, we concentrate on the study of using circulant permutation matrices or the zero matrix to construct PIR protocols for noncommunicating servers.

The main purpose of this paper is to construct pliable fractional repetition (FR) codes that are locally recoverable for distributed storage systems (DSSs). FR codes are integral in constructing a class of distributed storage codes with exact repair by transfer. Pliable FR codes are a new type of FR codes in which both the per-node storage and repetition degree can easily be adjusted simultaneously; thus, pliable FR codes are vital for DSSs in which parameters can dynamically change over time. However, the constructions of pliable FR codes with repair locality remain unknown. In addition, the tradeoffs between the code minimum distance of an FR code and its repair locality are not fully understood. To address these problems, this paper first presents general results regarding FR codes. Subsequently, this paper presents an improved Singleton-like bound for locally recoverable FR codes under an additional requirement that each node must be part of a local structure that, upon failure, allows it to be exactly recovered by a simple download process. Moreover, this paper proposes a construction of locally recoverable FR codes that can achieve the proposed Singleton-like bound; this construction is based on bipartite graphs with a given girth. In particular, this paper also proposes a general bipartite-graph-based approach to constructing optimal pliable FR codes with and without repair localities; in this approach, a new family of bipartite graphs, called matching-feasible graphs, is introduced. Finally, this paper proposes the explicit constructions of optimal pliable FR codes by using a family of matching-feasible graphs with arbitrary large girth. Notably, in addition to attaining a Singleton-like bound for FR codes, the explicit pliable FR codes are optimal locally recoverable FR codes from two perspectives of repair locality. The explicit pliable FR codes can also be used as FR batch codes to provide load balancing in DSSs.

The paper focuses on fractional repetition (FR) codes that are the key to constructing distributed storage codes with uncoded repair (i.e., a helper node reads the exact amount of data it needs to send to a replacement node and forwards it without any processing). Pliable FR codes are a new type of FR codes with the property that the per-node storage and repetition degree can easily be adjusted simultaneously, and are of vital importance for distributed storage systems where the parameters can dynamically change over time. A major drawback of existing pliable FR codes is that the supported file size is not large enough to meet a Singleton-like bound with equality when the number of storage nodes required to reconstruct the original file is large. To address this problem, this paper presents some general results on FR codes, including the exact file size of FR codes and sufficient conditions for FR codes to be optimal with respect to a Singleton-like bound. Based on bipartite graphs with arbitrary large girth, this paper also proposes a class of optimal pliable FR codes that attains a Singleton-like bound with equality. Examples are also provided to illustrate the proposed optimal pliable FR codes.

A distributed storage system (DSS) is one of the most vital components of a cloud computing system used for storing and sharing big data among authorized users. A typical DSS consists of n storage nodes each with a storage capacity of α units of data such that the entire file stored on the DSS can be recovered by accessing any kn-1/ ρ-1; 3) the constructed codes also meet a Singleton-like bound on the minimum distance at least for 1 ≤ k <; 3, which demonstrates their optimality; 4) the computational complexity necessary for determining the file size or the minimum distance of the constructed codes can be greatly reduced when it is hard to exactly determine them; and 5) the constructed codes can be used as fractional repetition batch codes to provide load balancing in DSSs, for which the batch size (i.e., the number of symbols that can be read in parallel) can be exactly determined.

This paper considers the construction of fractional repetition (FR) codes with flexible storage capacity and repair for distributed storage systems (DSSs). FR codes are the key to constructing a class of distributed storage codes with exact repair by transfer, where, upon failure, a failed storage node is exactly regenerated by simply downloading symbols from the surviving nodes. A major drawback of existing FR codes is that their parameters are not flexible enough to adapt to system changes in DSSs. To address this issue, this paper proposes two constructions of FR codes, called adaptive-and-resolvable FR codes, based on circulant permutation matrices and affine permutation matrices. In the proposed FR codes, the storage capacity per node and repetition degree of the symbols can be varied simultaneously in a simple manner. Some results on the exact file size that can be supported by the proposed FR codes are provided, based on the girth of the corresponding Tanner graph. Furthermore, the proposed FR codes are also shown to meet a Singleton-like bound on the minimum distance for certain parameter ranges.

Motivated by applications involving hot data, the notion of (r, t)-availability was introduced, where a symbol is said to have (r, t)-availability if it can be reconstructed, respectively, from t disjoint repair alternatives of other symbols, each of size at most r. The key to constructing a family of locally repairable codes with (r, t)-availability is the design of a membership matrix for dividing global parities into local ones such that each repair group contains only one parity symbol. Although explicit designs of membership matrices are available, it remains unclear whether membership matrices with significantly better parameters can be constructed, which was a question left open. To tackle the open problem, this paper first provides a connection between the design of membership matrices and the design of a combinatorial object in the well-known combinatorial design theory, called resolvable configurations. This paper then proposes several direct designs of membership matrices based on Euclidean geometry, finite fields, circulant permutation matrices, affine permutation matrices, and Reed-Solomon codes. By leveraging the notion of resolvable configurations and the Kronecker product, this paper further proposes a two-step design of membership matrices. The proposed direct and two-step designs of membership matrices are shown to have significantly better parameters than those recently available.

This paper is concerned with the construction of local parities for optimal locally repairable codes (LRCs) with (r, t)-availability in distributed storage, where a symbol is said to have (r, t)-availability if it can be reconstructed from t disjoint repair alternatives of other symbols, each of size at most r. The key to constructing a family of optimal LRCs with (r, t)-availability that can support a scaling number of parallel reads while keeping the rate to be an arbitrarily high constant is the design of a (0,1)-matrix R, called a membership matrix, for dividing global parities into local ones. Although explicit designs of R are available, it remains unclear whether R with significantly better parameters can be constructed, which was a question left open. To tackle the open problem, this paper first provides a connection between designs of R and a combinatorial object in the well-known combinatorial design theory, called resolvable configurations. This paper then proposes several designs of R based respectively on Euclidean geometry, circulant permutation matrices, and affine permutation matrices, which, to the best knowledge of the author of this paper, are also new to resolvable configurations. The proposed designs of R are shown to have significantly better parameters than those in the literature.

Topology-transparent scheduling (TTS) via the Chinese remainder theorem (CRT) has succeeded in providing guaranteed collision-free transmissions in each schedule without the need to know the maximum nodal degree of the graph representing connectivity of a mobile ad hoc network. Its main limitation is due to the restriction on the moduli imposed by the CRT. To address the shortcoming, this letter proposes an application of the general Chinese remainder theorem (GCRT) to TTS, which provides a unified framework for TTS that is developed via the CRT. The proposed GCRT-based scheme not only employs integer sequences to form the moduli, but also repeats the moduli to enhance TTS via the CRT. To determine how to repeat moduli in a systematic way, this letter formulates an integer programming problem, which is solved by the branch-and-bound technique. Numerical results are presented, demonstrating that the proposed GCRT-based scheme outperforms earlier works with much shorter schedule lengths.

In this paper, we address the issue of unequal missing protection (UMP) for the design of grouping of radio-frequency identification (RFID) tags. While relying on group generation matrices, grouping of RFID tags allows verifying the integrity of a collection of RFID tags without the requirement for accessing external systems, and can be extended to identify missing RFID tags. Motivated by application needs that call for UMP among RFID tags, we first introduce the concepts of UMP for grouping of RFID tags and its extended counterpart. We then present a simple scheme to realize extended grouping of RFID tags with UMP. Simulation results are presented to demonstrate the efficiencies of the proposed UMP scheme for extended grouping of RFID tags.

In this paper, we address the issue of unequal missing protection (UMP) for the design of grouping of radio-frequency identification (RFID) tags. While relying on group generation matrices, grouping of RFID tags allows verifying the integrity of a collection of tags without the requirement for accessing external systems, and can be extended to identify missing tags. Motivated by application needs that call for UMP among the tags, we first introduce the concepts of UMP for grouping of RFID tags and its extended counterpart, with which missing tags with high missing protection levels are more easily counted or identified than those with low missing protection levels. We then present simple yet effective schemes to realize grouping of RFID tags with UMP and its extended counterpart. The proposed schemes not only can easily fulfill the requirement of UMP among the tags, but also offer flexibility in constructing UMP group generation matrices. We also characterize key objects in order to further study grouping of RFID tags with UMP and its extended counterpart, called consistent and unidentifiable sets, respectively. This characterization in turn enables theoretical analysis of the error rate from the perspective of a tag. Theoretical and simulation results are presented to demonstrate the efficiencies of the proposed schemes for the design of grouping of RFID tags with UMP.

This paper proposes a novel scheme for the design of topology-transparent scheduling (TTS) in mobile ad hoc networks (MANETs), based on the Chinese remainder theorem (CRT). TTS can provide each node with guaranteed success in each schedule without any detailed topology information and yields a guaranteed upper bound on the transmission delay of each packet at every node in a MANET. In general, TTS requires two global constraints on the number of nodes in the MANET and the maximum nodal degree of the graph representing connectivity of the MANET. Due to the inherent mobility of MANETs, the maximum nodal degree, however, cannot be available or easily estimated. To eliminate the requirement for the maximum nodal degree, this paper proposes TTS via the CRT. By the redundancy property of the Chinese remainder representation, the proposed CRT-based scheme not only preserves the advantages of providing guaranteed success in each schedule with only the global constraint on the number of nodes in the MANET, but also offers flexibility in constructing TTS. To have a better transmission delay bound for a node with lower interference, this paper also introduces two threaded counterparts of the proposed CRT-based scheme. This paper provides performance analyses for the proposed CRT-based scheme and its threaded counterparts. Numerical results demonstrate that TTS via the CRT can outperform existing schemes, especially in scenarios with harsh interference, and is a versatile approach for the design of TTS.

This letter presents a novel scheme for the design of extended grouping of radio-frequency identification (RFID) tags, based on resolvable transversal designs (RTDs). Extended grouping of RFID tags allows identifying missing objects without the requirement for accessing external systems. The original scheme relies on Gallager's parity-check matrices and, as such, it cannot easily achieve designated decoding guarantees due to its pseudo-random nature. In view of the Gallager's parity-check matrix form of incidence matrices of RTDs, this letter proposes extended grouping of RFID tags based on RTDs. The proposed scheme proves to provide designated decoding guarantees more easily than the original scheme. In addition, this letter introduces a simple method, termed group splitting (GS), to improve the performance of extended grouping of RFID tags. Theoretical and simulation results demonstrate that the proposed scheme with or without GS is an efficient approach for the design of extended grouping of RFID tags.

In this paper, we propose a novel scheme for the design of grouping of radio-frequency identification (RFID) tags, based on the Chinese remainder theorem (CRT). Grouping allows verifying the integrity of a collection of objects without the requirement for accessing external systems, and can be extended to identify missing objects. Motivated by the redundancy property of the Chinese remainder representation, we propose grouping of RFID tags via the CRT. The proposed scheme not only provides designated decoding guarantees, but also offers flexibility in constructing group generation matrices. We also characterize the key objects needed to study decoding guarantees of grouping and its extended counterpart, called rank-deficient and dead-end sets, respectively, which enable theoretical analyses of error rates. The two key objects are related to the minimum and stopping distances of a linear code, respectively. As such, the characterization offers direct connection with coding theory that helps in the understanding of the verification/identification problems being studied. Theoretical and simulation results are presented, demonstrating that the proposed scheme is an efficient approach to the design of grouping of RFID tags.

This paper investigates network-wide spectrum allocation based on the cross-entropy (CE) method in cognitive radio network (CRN). A few spatial spectrum allocation techniques in CRN have been proposed in the literature. However, the optimum spectrum allocation requires an exhaustive search over all combinations of available channels and constraints on secondary users, whose complexity increases exponentially with the number of users and channels. Simulation results show that the proposed modified CE-based scheme is an efficient method to greatly reduce the complexity while still reaching optimal network utility. Most of the solutions generated by the modified CE algorithm are equal to the optimal values.

In this paper, decoding of LDPC convolutional codes with rational parity-check matrices (LDPC-CC-RPCM) is investigated. We show that Tanner graph of every LDPC-CC-RPCM can always be transformed into an equivalent one with enlarged girth and finite memory order suitable for practical pipeline decoder. Based on the transformed graph, a dynamic scheduling-aided decoding scheme with the enhancement of signal perturbation and error cancellation is presented to improve the convergence speed and bit-error-rate performance in both of the waterfall and error-floor regions. Simulation results also reveal that LDPC-CC-RPCM may outperform ordinary LDPC-CC with polynomial parity-check matrices in some cases under the same code rate and decoding complexity.

In the literature, a class of iterative decoding algorithms which combine the traditional reliability-based decoding (RBD) with the adaptive belief propagation (ABP) have been validated to be applicable for Reed-Solomon codes. However, in the original design of the iterative decoding, the soft-information is passed only from the ABP-part to the RBD-part such that the decoding performance is somewhat limited. In this study, we first present a new reliability updating scheme for the bidirectional exchange of soft-information in the iterative decoding, which can guarantee the correction of the most errors in both of the reliable and unreliable bits. A simple bit-flipping mechanism is also proposed to refine the initialization of the ABP-part for further performance improvement. Revealed by the simulation results, our proposed scheme can outperform the conventional design in terms of the bit-error-rate performance.

In this paper, we study medium access control (MAC) protocols with quality-of-service (QoS) support, that is, topology-independent link activation transmission scheduling, for mobile code-division multiple-access (CDMA) ad hoc networks. QoS provisioning for each communication link is guaranteed without the need to adopt transmission schedules in mobile environments. An interference model, which captures the difference between transmission and interference ranges, is considered. Under this interference model, an approach to guaranteeing conflict-free transmission slots in each frame (QoS provisioning) for each communication link is proposed. Compared with the previously known method, superior performance is obtained. We then present a topology-independent link activation scheduling framework based on the theory of group-divisible (GD) designs. By the mathematical properties of GD designs, the proposed framework guarantees conflict-free transmission slots in each frame for each communication link, without the overhead due to the recomputation of transmission schedules when the network topology changes. With the proposed framework, we study and evaluate one series of GD design constructions. Based on the results derived, topology-independent link activation scheduling algorithms are then presented. The proposed schemes are designed for different objectives: maximizing the minimum system throughput and/or minimizing the schedule frame length. Numerical results show that the proposed algorithms outperform previously known schemes. The average performance of the proposed schemes is also derived.

In this paper, we study topology-independent link activation transmission scheduling protocols for multihop code-division multiple-access (CDMA) packet radio networks. We focus on quality-of-service (QoS) provisioning for each communication link in mobile environments. An interference model for wireless multihop packet radio networks, which is more practical than that adopted in earlier literature, is considered. Under this interference model, an approach to guaranteeing conflict-free transmission slots in each frame for each communication link is proposed. We then present a topology-independent link activation scheduling framework based on the theory of group divisible (GD) designs. The proposed framework guarantees conflict-free transmission slots in each frame for each communication link by mathematical properties of GD designs. With the proposed framework, we study and evaluate one series of GD design construction. We then propose topology-independent link activation scheduling algorithms based on the results derived. The proposed schemes are designed for different objectives: maximizing the minimum system throughput and minimizing the schedule frame length. Analysis results show that the proposed algorithms outperform previously known schemes.

We study topology-transparent link activation transmission scheduling protocols for multihop CDMA ad hoc networks. We focus on quality-of-service (QoS) provisioning for each communication link, particularly when node mobility is considered. An interference model, which is more practical than that adopted in earlier literature, is proposed. Under the presented interference model, two methods are proposed to guarantee conflict-free transmission slots for each communication link in each frame. After that, we present two frameworks for topology-transparent link activation scheduling which are based on resolvable balanced incomplete block (RBIB) designs and group-divisible (GD) designs. respectively. These schemes address and resolve primary and secondary conflicts through the mathematical properties of block designs. The proposed schemes maximize the minimum system throughput and analysis results show that the proposed algorithms can outperform the previously known algorithm.