Construction of Near-Optimum Burst Erasure Correcting Low-Density Parity-Check Codes

In this paper, a simple, general-purpose and effective tool for the design of low-density parity-check (LDPC) codes for iterative correction of bursts of erasures is presented. The design method consists in starting from the parity-check matrix of an LDPC code and developing an optimized parity-check matrix, with the same performance on the memory-less erasure channel, and suitable also for the iterative correction of single bursts of erasures. The parity-check matrix optimization is performed by an algorithm called pivot searching and swapping (PSS) algorithm, which executes permutations of carefully chosen columns of the parity-check matrix, after a local analysis of particular variable nodes called stopping set pivots. This algorithm can be in principle applied to any LDPC code. If the input parity-check matrix is designed for achieving good performance on the memory-less erasure channel, then the code obtained after the application of the PSS algorithm provides good joint correction of independent erasures and single erasure bursts. Numerical results are provided in order to show the effectiveness of the PSS algorithm when applied to different categories of LDPC codes.Comment: 15 pages, 4 figures. IEEE Trans. on Communications, accepted (submitted in Feb. 2007

Generalized Stability Condition for Generalized and Doubly-Generalized LDPC Codes

In this paper, the stability condition for low-density parity-check (LDPC) codes on the binary erasure channel (BEC) is extended to generalized LDPC (GLDPC) codes and doublygeneralized LDPC (D-GLDPC) codes. It is proved that, in both cases, the stability condition only involves the component codes with minimum distance 2. The stability condition for GLDPC codes is always expressed as an upper bound to the decoding threshold. This is not possible for D-GLDPC codes, unless all the generalized variable nodes have minimum distance at least 3. Furthermore, a condition called derivative matching is defined in the paper. This condition is sufficient for a GLDPC or DGLDPC code to achieve the stability condition with equality. If this condition is satisfied, the threshold of D-GLDPC codes (whose generalized variable nodes have all minimum distance at least 3) and GLDPC codes can be expressed in closed form.Comment: 5 pages, 2 figures, to appear in Proc. of IEEE ISIT 200

On the LoRa Modulation for IoT: Waveform Properties and Spectral Analysis

An important modulation technique for Internet of Things (IoT) is the one proposed by the low power long range (LoRa) alliance. In this paper, we analyze the M -ary LoRa modulation in the time and frequency domains. First, we provide the signal description in the time domain, and show that LoRa is a memoryless continuous phase modulation. The cross-correlation between the transmitted waveforms is determined, proving that LoRa can be considered approximately an orthogonal modulation only for large M. Then, we investigate the spectral characteristics of the signal modulated by random data, obtaining a closed-form expression of the spectrum in terms of Fresnel functions. Quite surprisingly, we found that LoRa has both continuous and discrete spectra, with the discrete spectrum containing exactly a fraction 1/M of the total signal power

Massive Grant-Free Access with Massive MIMO and Spatially Coupled Replicas

Massive multiple access schemes, capable of serving a large number of uncoordinated devices while fulfilling reliability and latency constraints, are proposed. The schemes belong to the class of grant-free coded random access protocols and are tailored to massive multiple input multiple output (MIMO) base station processing. High reliability is obtained owing to an intra-frame spatial coupling effect, triggered by a simple device access protocol combined with acknowledgements (ACKs) from the base station. To provide system design guidelines, analytical bounds on error floor and latency are also derived. The proposed schemes are particularly interesting to address the challenges of massive machine-type communications in the framework of next generation massive multiple access systems

Identification-detection group testing protocols for COVID-19 at high prevalence

Group testing allows saving chemical reagents, analysis time, and costs, by testing pools of samples instead of individual samples. We introduce a class of group testing protocols with small dilution, suited to operate even at high prevalence (5–10%), and maximizing the fraction of samples classified positive/negative within the first round of tests. Precisely, if the tested group has exactly one positive sample then the protocols identify it without further individual tests. The protocols also detect the presence of two or more positives in the group, in which case a second round could be applied to identify the positive individuals. With a prevalence of 5 % and maximum dilution 6, with 100 tests we classify 242 individuals, 92 % of them in one round and 8 % requiring a second individual test. In comparison, the Dorfman’s scheme can test 229 individuals with 100 tests, with a second round for 18.5 % of the individuals

Pragmatic Space-Time Codes for Cooperative Relaying in Block Fading Channels

We address the problem of construction of space-time codes for cooperative communications in block fading channels. More precisely, we consider a pragmatic approach based on the concatenation of convolutional codes and BPSK/QPSK modulation to obtain cooperative codes for relay networks, for which we derive the pairwise error probability, an asymptotic bound for frame error probability, and a design criterion to optimize both diversity and coding gain. Based on this framework, we set up a code search procedure to obtain a set of good pragmatic space-time codes (P-STCs) with overlay construction, suitable for cooperative communication with a variable number of relays in quasistatic channel, which outperform in terms of coding gain other space-time codes (STCs) proposed in the literature. We also find that, despite the fact that the implementation of pragmatic space-time codes requires standard convolutional encoders and Viterbi decoders with suitable generators and branch metric, thus having low complexity, they perform quite well in block fading channels, including quasistatic channel, even with a low number of states and relays

Layered Video Transmission on Adaptive OFDM Wireless Systems

Future wireless video transmission systems will consider orthogonal frequency division multiplexing (OFDM) as the basic modulation technique due to its robustness and low complexity implementation in the presence of frequency-selective channels. Recently, adaptive bit loading techniques have been applied to OFDM showing good performance gains in cable transmission systems. In this paper a multilayer bit loading technique, based on the so called "ordered subcarrier selection algorithm," is proposed and applied to a Hiperlan2-like wireless system at 5 GHz for efficient layered multimedia transmission. Different schemes realizing unequal error protection both at coding and modulation levels are compared. The strong impact of this technique in terms of video quality is evaluated for MPEG-4 video transmission