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Recently, neural networks have improved MinSum message-passing decoders for low-density parity-check (LDPC) codes by multiplying or adding weights to the messages, where the weights are determined by a neural network. The neural network complexity to determine distinct weights for each edge is high, often limiting the application to relatively short LDPC codes. Furthermore, storing separate weights for every edge and every iteration can be a burden for hardware implementations. To reduce neural network complexity and storage requirements, this paper proposes a family of weight-sharing schemes that use the same weight for edges that have the same check node degree and/or variable node degree. Our simulation results show that node-degree-based weight-sharing can deliver the same performance requiring distinct weights for each node. This paper also combines these degree-specific neural weights with a reconstruction-computation-quantization (RCQ) decoder to produce a weighted RCQ (W-RCQ) decoder. The W-RCQ decoder with node-degree-based weight sharing has a reduced hardware requirement compared with the original RCQ decoder. As an additional contribution, this paper identifies and resolves a gradient explosion issue that can arise when training neural LDPC decoders.

Non-uniform message quantization techniques such as reconstruction-computation-quantization (RCQ) improve error-correction performance and decrease hardware complexity of low-density parity-check (LDPC) decoders that use a flooding schedule. Layered MinSum RCQ (L-msRCQ) enables message quantization to be utilized for layered decoders and irregular LDPC codes. We investigate field-programmable gate array (FPGA) implementations of L-msRCQ decoders. Three design methods for message quantization are presented, which we name the Lookup, Broadcast, and Dribble methods. The decoding performance and hardware complexity of these schemes are compared to a layered offset MinSum (OMS) decoder. Simulation results on a (16384, 8192) protograph-based raptor-like (PBRL) LDPC code show that a 4-bit L-msRCQ decoder using the Broadcast method can achieve a 0.03 dB improvement in error-correction performance while using 12% fewer registers than the OMS decoder. A Broadcast-based 3-bit L-msRCQ decoder uses 15% fewer lookup tables, 18% fewer registers, and 13% fewer routed nets than the OMS decoder, but results in a 0.09 dB loss in performance., Comment: 6 pages, 5 figures, submitted to GLOBECOM 2021

Protograph-based Raptor-like low-density parity-check codes (PBRL codes) are a recently proposed family of easily encodable and decodable rate-compatible LDPC (RC-LDPC) codes. These codes have an excellent iterative decoding threshold and performance across all design rates. PBRL codes designed thus far, for both long and short block-lengths, have been based on optimizing the iterative decoding threshold of the protograph of the RC code family at various design rates. In this work, we propose a design method to obtain better quasi-cyclic (QC) RC-LDPC codes with PBRL structure for short block-lengths (of a few hundred bits). We achieve this by maximizing an upper bound on the minimum distance of any QC-LDPC code that can be obtained from the protograph of a PBRL ensemble. The obtained codes outperform the original PBRL codes at short block-lengths by significantly improving the error floor behavior at all design rates. Furthermore, we identify a reduction in complexity of the design procedure, facilitated by the general structure of a PBRL ensemble., Comment: Longer version of a submission to 2017 IEEE International Symposium on Information Theory

This paper presents a general approach for optimizing the number of symbols in increments (packets of incremental redundancy) in a feedback communication system with a limited number of increments. This approach is based on a tight normal approximation on the rate for successful decoding. Applying this approach to a variety of feedback systems using non-binary (NB) low-density parity-check (LDPC) codes shows that greater than 90% of capacity can be achieved with average blocklengths fewer than 500 transmitted bits. One result is that the performance with ten increments closely approaches the performance with an infinite number of increments. The paper focuses on binary- input additive-white Gaussian noise (BI-AWGN) channels but also demonstrates that the normal approximation works well on examples of fading channels as well as high-SNR AWGN channels that require larger QAM constellations. The paper explores both variable-length feedback codes with termination (VLFT) and the more practical variable length feedback (VLF) codes without termination that require no assumption of noiseless transmitter confirmation. For VLF we consider both a two-phase scheme and CRC-based scheme.

We consider the problem of constructing $(3,L)$ quasi-cyclic low-density parity-check (LDPC) codes from complete protographs. A complete protograph is a small bipartite graph with two disjoint vertex sets such that every vertex in the variable-node set is connected to every vertex in the check-node set by a unique edge. This paper analyzes the required lifting factor for achieving girths of six or eight in the resulting quasi-cyclic codes with constraints on lifting. The required lifting factors provide lower bounds on the block-length of such codes., Comment: 6 pages, 2 figures, 5-page version to appear in the Proceedings of 2015 IEEE International Symposium on Information Theory. Update 1 - 05/29/2015 - Minor changes and added a reference

This paper proposes a class of rate-compatible LDPC codes, called protograph-based Raptor-like (PBRL) codes. The construction is focused on binary codes for BI-AWGN channels. As with the Raptor codes, additional parity bits are produced by exclusive-OR operations on the precoded bits, providing extensive rate compatibility. Unlike Raptor codes, the structure of each additional parity bit in the protograph is explicitly designed through density evolution. The construction method provides low iterative decoding thresholds and the lifted codes result in excellent error rate performance for long-blocklength PBRL codes. For short-blocklength PBRL codes the protograph design and lifting must avoid undesired graphical structures such as trapping sets and absorbing sets while also seeking to minimize the density evolution threshold. Simulation results are shown in information block sizes of $k=192$, $16368$ and $16384$. Comparing at the same information block size of $k=16368$ bits, the PBRL codes outperform the best known standardized code, the AR4JA codes in the waterfall region. The PBRL codes also perform comparably to DVB-S2 codes even though the DVB-S2 codes use LDPC codes with longer blocklengths and are concatenated with outer BCH codes., Comment: 12 pages, 9 figures

In this paper we design and analyze an end-to-endcommunication system between a lander/rover on the surface ofthe lunar South Pole and an Earth station. Various communicationsystems on the lander or rover could be used for the Earthto-Moon communication in both the uplink and downlink direction.To communicate to and from the lander/rover on the lunarSouth Pole, low and/or medium directional antennas onboardthe lander/rover will have to be pointed at low elevation anglesbetween 2 to 10 degrees, thus causing multipath fading effectsdue to reflection of a portion of the transmitted electromagneticwaves from the surface of the Moon. These are not commonlyencountered in traditional deep space communications betweena spacecraft and a ground station.We investigate various design methods and analyze such communicationsystems, in the presence of multipath fading. Wemodel the fading channel based on existing and simulated data.For coherent reception, the acquisition and tracking loop shouldacquire and track incoming carrier phase in presence of Ricianmultipath fading. For this communication system in additionto estimating the received carrier phase, the amplitude of thefading signal should also be estimated, in particular to be used inthe decoder. We consider simple modulation and coding schemesin particular those specified in the CCSDS standards for spaceapplications.After designing various components of the communication system,we use Simulink models to obtain the end-to-end performanceof the communication link under investigation. Basedon the available data, the fading channel can be accuratelymodeled as a Rician fading channel with various Rician parametersdepending on the Earth elevation angle, which alsoaffects the Doppler spread. Therefore, the challenge is todesign a communication system robust in the presence of themultipath fading where the channel conditions change in timeand thus produce fading. In summary, this paper comparespossible communication system designs, performance analysis,and simulations for coded system with/without interleaving withhard/soft decision and with/without channel state information(CSI), over a communication link between a lander/rover at theLunar south pole and a Deep Space Network station in presenceof Rician fading.

This letter produces a family of rate-compatible protograph-based LDPC codes approaching the independent and uniformly distributed (i.u.d.) capacity of inter-symbol interference (ISI) channels. This problem is highly nontrivial due to the joint design of structured (protograph-based) LDPC codes and the state structure of ISI channels. We describe a method to design nested high-rate protograph codes by adding variable nodes to the protograph of a lower rate code. We then design a family of rate-compatible protograph codes using the extension method. The resulting protograph codes have iterative decoding thresholds close to the i.u.d. capacity. Our results are supported by numerical simulations., Comment: 4 pages, 5 figures

This paper produces a rate-compatible protograph LDPC code at 1k information blocklength with superior performance in both waterfall and error floor regions. The design of such codes has proved difficult in the past because the constraints imposed by structured design (protographs), rate-compatibility, as well as small block length, are not easily satisfied together. For example, as the block length decreases, the predominance of decoding threshold as the main parameter in coding design is reduced, thus complicating the search for good codes. Our rate-compatible protograph codes have rates ranging from 1/3 to 4/5 and show no error floor down to $10^{-6}$ FER.

Despite encouraging advances in the design of relay codes, several important challenges remain. Many of the existing LDPC relay codes are tightly optimized for fixed channel conditions and not easily adapted without extensive re-optimization of the code. Some have high encoding complexity and some need long block lengths to approach capacity. This paper presents a high-performance protograph-based LDPC coding scheme for the half-duplex relay channel that addresses simultaneously several important issues: structured coding that permits easy design, low encoding complexity, embedded structure for convenient adaptation to various channel conditions, and performance close to capacity with a reasonable block length. The application of the coding structure to multi-relay networks is demonstrated. Finally, a simple new methodology for evaluating the end-to-end error performance of relay coding systems is developed and used to highlight the performance of the proposed codes., Comment: Accepted in IEEE Trans. Wireless Comm

A new coding scheme for image transmission over noisy channel is proposed. Similar to standard image compression, the scheme includes a linear transform followed by successive refinement scalar quantization. Unlike conventional schemes, in the proposed system the quantized transform coefficients are linearly mapped into channel symbols using systematic linear encoders. This fixed-to-fixed length "linear index coding" approach avoids the use of an explicit entropy coding stage (e.g., arithmetic or Huffman coding), which is typically fragile to channel post-decoding residual errors. We use linear codes over GF(4), which are particularly suited for this application, since they are matched to the dead-zone quantizer symbol alphabet and to the QPSK modulation used on the deep-space communication channel. We optimize the proposed system where the linear codes are systematic Raptor codes over GF(4). The rateless property of Raptor encoders allows to achieve a "continuum" of coding rates, in order to accurately match the channel coding rate to the transmission channel capacity and to the quantized source entropy rate for each transform subband and refinement level. Comparisons are provided with respect to the concatenation of state-of-the-art image coding and channel coding schemes used by Jet Propulsion Laboratories (JPL) for the Mars Exploration Rover (MER) Mission., Comment: 36 pages, 5 figures, to be submitted to IEEE Trans. on Communications

Recent results by Chen et al. and Polyanskiy et al. explore using feedback to approach capacity with short blocklengths. This paper explores Chernoff bounding techniques to extend the rate-compatible sphere-packing (RCSP) analysis proposed by Chen et al. to scenarios involving numerous retransmissions and different step sizes in each incremental retransmission. Williamson et al. employ exact RCSP computations for up to six transmissions. However, exact RCSP computation with more than six retransmissions becomes unwieldy because of joint error probabilities involving numerous chi-squared distributions. This paper explores Chernoff approaches for upper and lower bounds to provide support for computations involving more than six transmissions. We present two versions of upper and lower bounds for the two-transmission case. One of the versions is extended to the general case of $m$ transmissions where $m \geq 1$. Computing the general bounds requires minimization of exponential functions with the auxiliary parameters, but is less complex and more stable than multiple rounds of numerical integration. These bounds also provide a good estimate of the expected throughput and expected latency, which are useful for optimization purposes., Comment: Submitted to 2012 Information Theory Workshop

This paper presents an adaptive-sweep algorithm that can be used in conjunction with a Phased-Lock Loop to acquire and track the carrier of a Binary Phase-shift Keying signal with residual carrier. This algorithm is useful in proximity links where no Doppler pre-compensation is available at the transmitter, and allows the receiver to acquire the incoming carrier even if the experienced Doppler shift is several orders of magnitude larger than the PLL bandwidth. Other applications for this algorithm include Multiple Uplink per Antenna at the Deep Space Network, and generation of observables (Doppler shift, Doppler rate, range rate) for in-situ navigation purposes. This paper enhances a previously presented adaptive-sweep algorithm and its performance analysis in two fronts. First, the algorithm now uses the direction function to automatically estimate the required frequency jump to achieve PLL lock. This enables a fully adaptive-sweep scheme in which system implementer does not need to manually select thresholds. On the other hand, we study the system performance in the presence of Additive White Gaussian Noise and derive necessary conditions for the system to operate at low signal-to-noise conditions. This allows us to create design rules that specify all parameters of the algorithm given a set of system-level requirements. To test the performance of the proposed algorithm, we implement it in GNU Radio, an open-source Software-Defined Radio that interfaces with several commercial radio peripherals. We use this implementation to demonstrate carrier lock and quantify system performance under different noise conditions. We also test the algorithm using open-loop recordings of two downlinks between the Lunar Reconnaissance Orbiter and the Deep Space Network. We show that even after large frequency jumps (tens of kHz), the proposed system is able to rapidly reacquire the carrier and continue operation.

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This paper presents machine learning-based approaches to automate and optimize the detection of volume loss for the downlink process of telemetry data from the Mars Curiosity Rover. The Curiosity observes volume loss and data corruption, requiring re-transmits from the rover and Ground Data System Analysts (GDSA) to monitor the data flow. To resolve this issue, we created a data pipeline to accumulate data from various data sources in the downlink process and detect where the data is missed. In this paper, we benchmarked different methodologies based on the accuracy and excitability of them to identify whether a downlink data that is received to the ground system is complete or incomplete. Our results show that machine learning methods can improve the performance of the GDSA by 55% while the user can diagnose why data is missed and provide an explanation for the data accountability problem.

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Digital communication coding methods for designing protograph-based bit-interleaved code modulation that is general and applies to any modulation. The general coding framework can support not only multiple rates but also adaptive modulation. The method is a two stage lifting approach. In the first stage, an original protograph is lifted to a slightly larger intermediate protograph. The intermediate protograph is then lifted via a circulant matrix to the expected codeword length to form a protograph-based low-density parity-check code.

Digital communication coding methods resulting in rate-compatible low density parity-check (LDPC) codes built from protographs. Described digital coding methods start with a desired code rate and a selection of the numbers of variable nodes and check nodes to be used in the protograph. Constraints are set to satisfy a linear minimum distance growth property for the protograph. All possible edges in the graph are searched for the minimum iterative decoding threshold and the protograph with the lowest iterative decoding threshold is selected. Protographs designed in this manner are used in decode and forward relay channels.

Theoretical analysis has long indicated that feedback improves the error exponent but not the capacity of pointto- point memoryless channels. The analytic and empirical results indicate that at short blocklength regime, practical rate-compatible punctured convolutional (RCPC) codes achieve low latency with the use of noiseless feedback. In 3GPP, standard rate-compatible turbo codes (RCPT) did not outperform the convolutional codes in the short blocklength regime. The reason is the convolutional codes for low number of states can be decoded optimally using Viterbi decoder. Despite excellent performance of convolutional codes at very short blocklengths, the strength of convolutional codes does not scale with the blocklength for a fixed number of states in its trellis.