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The Consultative Committee for Space Data Systems (CCSDS) standard for high photon efficiency uses a serially-concatenated (SC) code to encode pulse position modulated laser light. A convolutional encoder serves as the outer code and an accumulator serves as the inner code. These two component codes are connected through an interleaver. This coding scheme is called Serially Concatenated convolutionally coded Pulse Position Modulation (SCPPM) and it is used for NASA's Deep Space Optical Communications (DSOC) experiment. For traditional decoding that traverses the trellis forwards and backwards according to the Bahl Cocke Jelinek and Raviv (BCJR) algorithm, the latency is on the order of the length of the trellis, which has 10,080 stages for the rate 2/3 DSOC code. This paper presents a novel alternative approach that simultaneously processes all trellis stages, successively combining pairs of stages into a meta-stage. This approach has latency that is on the order of the log base-2 of the number of stages. The new decoder is implemented using the Compute Unified Device Architecture (CUDA) platform on an Nvidia Graphics Processing Unit (GPU). Compared to Field Programmable Gate Array (FPGA) implementations, the GPU implementation offers easier development, scalability, and portability across GPU models. The GPU implementation provides a dramatic increase in speed that facilitates more thorough simulation as well as enables a shift from FPGA to GPU processors for DSOC ground stations. 

Free-space optical (FSO) links are sensitive to channel fading caused by atmospheric turbulence, varying weather conditions, and changes in the distance between the transmitter and receiver. To mitigate FSO fading, this paper applies linear and quadratic prediction to estimate fading channel conditions and dynamically select the appropriate low-density parity check (LDPC) code rate. This adaptivity achieves reliable communication while efficiently utilizing the available channel mutual information. Protograph-based Raptor-like (PBRL) LDPC codes supporting a wide range of rates are designed, facilitating convenient rate switching. When channel state information (CSI) is known without delay, dynamically selecting LDPC code rate appropriately maximizes throughput. This work explores how such prediction behaves as the feedback delay is increased from no delay to a delay of 4 ms for a channel with a coherence time of 10 ms. 

In the short blocklength regime, serial list decoding of tail-biting (TB) convolutional codes concatenated with an expurgating linear function (ELF) can approach the random coding union bound on frame error rate (FER) performance. Decoding complexity for a particular received word depends on how deep in the list the decoder must search to find a valid TB-ELF codeword. The average list size is close to one at low-FER operating points such as 10^−6, and serial list decoding provides a favorable average complexity compared to other decoders with similar performance for these cases. However, the average list size can be on the order of a hundred or a thousand at higher, but still practically important, FER operating points such as 10−3. It is useful to study the tradeoff between how deep the decoder is willing to search and the proximity to the frame error rate (FER) achieved by an ML decoder. Often, this tradeoff is framed in terms of a maximum list depth. However, this paper frames the tradeoff in terms of a maximum allowable metric between the received word and the trellis paths on the list. We consider metrics of Euclidean distance and angle. This new approach draws on the wealth of existing literature on bounded-metric decoding to provide characterizations of how the choice of maximum allowable metric controls the tradeoffs between FER performance and both decoding complexity and undetected error rate. These characterizations lead to an example of an ELF-TB convolutional code that outperforms recent results for polar codes in terms of the lowest SNR that simultaneously achieves both a total error rate less than T = 10^−3 and an undetected error rate below U = 10^−5. 

Free-space optical (FSO) links are sensitive to channel fading caused by atmospheric turbulence, varying weather conditions, and changes in the distance between the transmitter and receiver. To mitigate FSO fading, this paper applies linear and quadratic prediction to estimate fading channel conditions and dynamically select the appropriate low-density parity check (LDPC) code rate. This adaptivity achieves reliable communication while efficiently utilizing the available channel mutual information. Protograph-based Raptor-like (PBRL) LDPC codes supporting a wide range of rates are designed, facilitating convenient rate switching. When channel state information (CSI) is known without delay, dynamically selecting LDPC code rate appropriately maximizes throughput. This work explores how such prediction behaves as the feedback delay is increased from no delay to a delay of 4 ms for a channel with a coherence time of 10 ms. 

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. 

The Consultative Committee for Space Data Systems (CCSDS) 141.11-O-1 Line Product Code (LPC) provides a rare opportunity to compare maximum-likelihood decoding and message passing. The LPC considered in this paper is intended to serve as the inner code in conjunction with a (255,239) Reed Solomon (RS) code whose symbols are bytes of data. This paper represents the 141.11-O-1 LPC as a bipartite graph and uses that graph to formulate both maximum likelihood (ML) and message passing algorithms. ML decoding must, of course, have the best frame error rate (FER) performance. However, a fixed point implementation of a Neural-Normalized MinSum (N-NMS) message passing decoder closely approaches ML performance with a significantly lower complexity. 

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.