查看更多>>摘要：Product-like codes are widely used in high-speed communication systems since they can be decoded with low-complexity hard decision decoders (HDDs). To meet the growing demand of data rates, enhanced HDDs are required. In this paper, we propose a novel soft-aided HDD (SA-HDD), termed iterative bounded distance decoding with random flipping (iBDD-RF), for product-like codes. In iBDD-RF, the soft reliability of a bit is a weighted sum of the output of bounded distance decoder (BDD) and the channel log-likelihood ratio (LLR). When the amplitude of the soft reliability of a bit is less than a given threshold, it is flipped with a given probability. This random flipping may make the decoder escape from the local optimum. To optimize the threshold and the flipping probability, we derive the density evolution (DE) equations of iBDD-RF for product codes (PCs) and staircase codes (SCs). Our extensive numerical results show that iBDD-RF outperforms iBDD with scaled reliability (iBDD-SR) over the binary-input additive white Gaussian noise (Bi-AWGN) channel. Particularly, for a PC with (255,239,2) Bose-Chaudhuri-Hocquenghem (BCH) code and an SC with (254,230,3) BCH code, iBDD-RF performs about 0.25 dB and 0.28 dB better than iBDD-SR, respectively.
查看更多>>摘要：In this paper, we focus on Singleton-optimal $(r,\delta)$ LRCs with disjoint local repair groups. We provide an improved bound for the length of q-ary Singleton-optimal $(r,\delta)$ LRCs based on the parity-check matrix approach. Specifically, for $d \geq 3\delta $ , we prove that $n\le O(q^{\delta })$ when $d-3\delta \lt r\le d-2\delta +1$ . We also show that the code length $n\le q+\delta +2$ when $r=2$ and $d=3\delta +2$ . We present a sufficient and necessary condition for the existence of Singleton-optimal $(n,k,d;r,\delta)$ LRCs with disjoint local repair groups, where the minimum distance satisfies $3\delta +1\le d \le 3\delta +2$ and locality $r=2$ . This condition imposes an upper bound on the code length, $n\le O(q^{2})$ , and indicates the existence of a code length approximately given by $n\approx \sqrt {2}q$ when $d=3\delta +1$ and $r=2$ . Finally, we utilize blocking sets to provide a general construction of Singleton-optimal $(n,k,d=2\delta +2,r=2,\delta)$ LRC with code length $n\approx O\left ({{q^{\frac {h+1}{h}}}}\right)$ for any $h\ge 3$ . To the best of our knowledge, this is the first family of Singleton-optimal $(n,k,d=2\delta +2,r=2,\delta)$ LRC with super-linear code length.
查看更多>>摘要：This paper proposes a novel binary code to correct one insertion and at most two consecutive deletion errors simultaneously occurring in a codeword. Our proposed code is intended first to isolate the possible error cases among all the error scenarios, and then correct the errors. Furthermore, we provide detailed descriptions of the code construction and also suggest a decoding strategy for the proposed code. According to the proposed code, $5\log _{2} n +O(1)$ redundancy bits are required to correct one insertion and at most two consecutive deletion errors occurring in a codeword. In addition, a decoding procedure of the proposed code is comprehensively presented for all error scenarios including a single insertion error, an insertion and a deletion error, and an insertion and two consecutive deletion errors.
查看更多>>摘要：Maximum distance separable (MDS) codes in distributed storage systems provide the optimal tradeoff between fault tolerance and storage overhead. As a kind of MDS codes, minimum storage regenerating (MSR) codes have attracted a lot of attention since they are also optimal in terms of repair bandwidth. However, MSR codes suffer from a high repair degree, meaning many helper nodes are needed in the node repair process. Compared to MSR codes, locally repairable codes (LRCs) can significantly reduce the repair degree at the cost of increased storage overhead. The recently introduced concept of vector LRCs combines the advantages of MSR codes and LRCs, providing a tradeoff between repair degree/repair bandwidth and storage overhead. Most existing vector LRCs are built on MSR codes or their shortened versions. However, existing MSR codes have an unavoidably large sub-packetization levels, which also result in large sub-packetization levels in the corresponding vector LRCs. In this paper, we propose a new vector LRC structure, where MDS array codes (without shortening) can be employed as the local codes. Based this new structure, we propose three constructions of vector LRCs with small sub-packetization levels and small repair bandwidth, whose required field sizes are comparable to the code lengths. Additionally, the first two constructions offer a flexible tradeoff between the sub-packetization level and the repair bandwidth, while the third construction has a sub-packetization level of 2, making it easy to implement. Compared to existing vector LRCs, the new vector LRCs provide significantly smaller sub-packetization levels and support a wider range of parameters.
查看更多>>摘要：In a real-time transmission scenario, messages are transmitted through a channel that is subject to packet loss. The destination must recover the messages within the required deadline. In this paper, we consider a setup where two different types of messages with distinct decoding deadlines are transmitted through a channel model that introduces either one burst erasure of length at most B, or N random erasures in any fixed-sized sliding window. The message with a short decoding deadline $T_{\mathrm {u}}$ is referred to as an urgent message, while the other one with a decoding deadline $T_{\mathrm {v}}$ ( $T_{\mathrm {v}} \gt T_{\mathrm {u}}$ ) is referred to as a less urgent message. We consider the scenario where $T_{\mathrm {v}} \gt T_{\mathrm {u}} + B$ and propose a non-trivial achievable region $\mathcal {R}$ for the aforementioned channel model. We propose a novel merging approach to encode two message streams of different urgency levels into a single flow and present explicit constructions for encoding, contributing to the establishment of the achievability of region $\mathcal {R}$ . Our comprehensive analysis demonstrates that this region encompasses the rate pairs of existing encoding schemes and coincides with the capacity region in burst channel scenarios. Lastly, we investigate the property of the achievable region $\mathcal {R}$ , proving that it is the largest one obtained from all the rate pairs under the merging method.
查看更多>>摘要：Ensuring signal confidentiality against eavesdroppers is particularly challenging, especially with imperfect channel state information (CSI). To address this, we propose a novel approach leveraging reconfigurable intelligent surfaces (RISs) to enhance security and optimize transmission performance. This paper focuses on secure communication in symbiotic radio (SR) systems by investigating cooperative jamming-assisted transmission with RISs, providing a robust solution to these challenges. RIS-I, acting as a secondary transmitter (STx), multicasts confidential signals from the primary transmitter (Alice) to a primary user (Bob), protecting against eavesdropping by Eve. Additionally, RIS-I transmits its own signals to a secondary user (SU) using backscattering radio technology. Meanwhile, RIS-II serves as a cooperative jammer, converting received confidential signals from Alice into jamming signals by strategically adjusting its reflection coefficients to disrupt Eve’s reception. These RISs can operate cooperatively; when RIS-II transmits as an STx, RIS-I functions as a cooperative jammer. We explore two scenarios: 1. With perfect CSI for the wiretap channel, we propose a joint SDR(Semi-definite relaxation)+MM(Minorization-maximization) optimization algorithm to simultaneously optimize Alice’s beamforming vector and the RISs’ reflection coefficients. 2. With imperfect CSI, we derive the secrecy outage probability formula and evaluate the scheme’s performance across different scenarios. Numerical results demonstrate that RIS-assisted cooperative jamming significantly enhances the secrecy rate and reduces the secrecy outage probability for Bob, outperforming traditional RIS-assisted SR systems.
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