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1. Sparse Regression LDPC Codes

   https://doi.org/10.1109/TIT.2024.3496486  

   Ebert, Jamison R; Chamberland, Jean-Francois; Narayanan, Krishna R (January 2025, IEEE Transactions on Information Theory)

   This article introduces a novel concatenated coding scheme called sparse regression LDPC (SR-LDPC) codes. An SR-LDPC code consists of an outer non-binary LDPC code and an inner sparse regression code (SPARC), whose respective field size and section sizes are equal. For such codes, an efficient decoding algorithm is proposed based on approximate message passing (AMP) that dynamically shares soft information between inner and outer decoders. This dynamic exchange of information is facilitated by a denoiser that runs belief propagation (BP) on the factor graph of the outer LDPC code within each AMP iteration. It is shown that this BP denoiser falls within the framework of non-separable denoising functions and subsequently, that state evolution holds for the proposed AMP-BP algorithm. Leveraging the rich structure of SR-LDPC codes, this article proposes an efficient low-dimensional approximate state evolution recursion that can be used for efficient hyperparameter tuning, thus paving the way for future work on optimal code design. Finally, numerical simulations demonstrate that SR-LDPC codes outperform contemporary codes over the AWGN channel for parameters of practical interest. SR-LDPC codes are shown to be viable means for obtaining shaping gains over the AWGN channel. 

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2. New Dual Relationships for Error-Correcting Wiretap Codes

   https://doi.org/10.1109/ITW48936.2021.9611443  

   Shoushtari, Morteza; Harrison, Willie K. (October 2021, 2021 Information Theory Workshop (ITW))

   In this paper, we consider the equivocation of finite blocklength coset codes when used over binary erasure wiretap channels. We make use of the equivocation matrix in comparing codes that are suitable for scenarios with noisy channels for both the intended receiver and an eavesdropper. Equivocation matrices have been studied in the past only for the binary erasure wiretap channel model with a noiseless channel for the intended recipient. In that case, an exact relationship between the elements of equivocation matrices for a code and its dual code was identified. The majority of work on coset codes for wiretap channels only addresses the noise-free main channel case, and extensions to noisy main channels require multi-edge type codes. In this paper, we supply a more insightful proof for the noiseless main channel case, and identify a new dual relationship that applies when two-edge type coset codes are used for the noisy main channel case. The end result is that the elements of the equivocation matrix for a dual code are known precisely from the equivocation matrix of the original code according to fixed reordering patterns. Such relationships allow one to study the equivocation of codes and their duals in tandem, which simplifies the search for best and/or good finite blocklength codes. This paper is the first work that succinctly links the equivocation/error correction capabilities of dual codes for two-edge type coset coding over erasure-prone main channels. 

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3. On Sparse Regression LDPC Codes

   https://doi.org/10.1109/ISIT54713.2023.10206818  

   Ebert, Jamison R; Chamberland, Jean-Francois; Narayanan, Krishna R (August 2023, IEEE)

   Iterative decoding of graph-based codes and sparse recovery through approximate message passing (AMP) are two research areas that have seen monumental progress in recent decades. Inspired by these advances, this article introduces sparse regression LDPC codes (SR-LDPC codes) and their decoding. Sparse regression codes (SPARCs) are a class of error correcting codes that build on ideas from compressed sensing and can be decoded using AMP. In certain settings, SPARCs are known to achieve capacity; yet, their performance suffers at finite block lengths. Likewise, low-density parity-check (LDPC) codes can be decoded efficiently using belief propagation and can also be capacity achieving. This article introduces a novel concatenated coding structure that combines an LDPC outer code with a SPARC-inspired inner code. Efficient decoding for such a code can be achieved using AMP with a denoiser that performs belief propagation on the factor graph of the outer LDPC code. The proposed framework exhibits performance improvements over SPARCs and standard LDPC codes for finite block lengths and results in a steep waterfall in error performance, a phenomenon not observed in uncoded SPARCs. 

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4. Rate-Compatible, Bandwidth-Efficient, Low-Density Parity-Check (LDPC) Codes for Aeronautical Telemetry

   https://doi.org/10.3390/e26121045  

   Cummins, Andrew D; Mitchell, David G; Perrins, Erik (December 2024, Entropy)

   Low-density parity-check (LDPC) codes form part of the IRIG-106 standard and have been successfully deployed for the Telemetry Group version of shaped-offset quadrature phase shift keying (SOQPSK-TG) modulation. Recently, LDPC code solutions have been proposed and optimized for continuous phase modulations (CPMs), including pulse code modulation/frequency modulation (PCM/FM) and the multi-h CPM developed by the Advanced-Range TeleMetry program (ARTM CPM), the latter of which was shown to perform around one dB from channel capacity. In this paper, we consider the effect of the random puncturing and shortening of these LDPC codes to further improve spectrum efficiency. We perform asymptotic analyses of the ARTM0 code ensembles and present numerical simulation results that affirm the robust decoding performance promised by LDPC codes designed for ARTM CPM. 

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5. Secrecy Coding in the Integrated Network Enhanced Telemetry (iNET)

   Shoushtari, Morteza; Harrison, Willie (October 2021, Proceedings International Telemetering Conference US)

   Data security plays a crucial role in all areas of data transmission, processing, and storage. This paper considers security in eavesdropping attacks over wireless communication links in aeronautical telemetry systems. Data streams in these systems are often encrypted by traditional encryption algorithms such as the Advanced Encryption Standard (AES). Here, we propose a secure coding technique for the integrated Network Enhanced Telemetry (iNET) communications system that can be coupled with modern encryption schemes. We consider a wiretap scenario where there are two telemetry links between a test article (TA) and a legitimate receiver, or ground station (GS). We show how these two links can be used to transmit both encrypted and unencrypted data streams while keeping both streams secure. A single eavesdropper is assumed who can tap into both links through its noisy channel. Since our scheme does not require encryption of the unencrypted data stream, the proposed scheme offers the ability to reduce the size of the required secret key while keeping the transmitted data secure. 

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