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1. Compress-and-Forward via Multilevel Coding

   Wan, H.; Host-Madsen, A.; Nosratinia, A. (July 2019, IEEE International Symposium on Information Theory)

   We investigate the performance of discrete (coded) modulations in the full-duplex compress-forward relay channel using multilevel coding. We numerically analyze the rates assigned to component binary codes of all levels. LDPC codes are used as the component binary codes to provide error protection. The compression at the relay is done via a nested scalar quantizer whose output is mapped to a codeword through LDPC codes. A compound Tanner graphical model and information-exchange algorithm are described for joint decoding of both messages sent from the source and relay. Simulation results show that the performance of the proposed system based on multilevel coding is better than that based on BICM, and is separated from the SNR threshold of the known CF achievable rate by two factors consisting approximately of the sum of the shaping gain (due to scalar quantization) and the separation of the LDPC code implementation from AWGN capacity. 

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2. Decoder Error Propagation Mitigation for Spatially Coupled LDPC Codes

   Zhu, Min; Mitchell, D; Lentmaier, M; Costello, D (March 2021, International Symposium on Information Theory and its Applications)

   In this paper, we introduce two new methods of mitigating decoder error propagation for low-latency sliding window decoding (SWD) of spatially coupled low-density parity-check (SC-LDPC) codes. Building on the recently introduced idea of check node (CN) doping of regular SC-LDPC codes, here we employ variable node (VN) doping to fix (set to a known value) a subset of variable nodes in the coupling chain. Both of these doping methods have the effect of allowing SWD to recover from error propagation, at a cost of a slight rate loss. Experimental results show that, similar to CN doping, VN doping improves performance by up to two orders of magnitude compared to un-doped SC-LDPC codes in the typical signal-to-noise ratio operating range. Further, compared to CN doping, VN doping has the advantage of not requiring any changes to the decoding process. In addition, a log-likelihood-ratio based window extension algorithm is proposed to reduce the effect of error propagation. Using this approach, we show that decoding latency can be reduced by up to a significant fraction without suffering any loss in performance. 

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3. Decoder Error Propagation Mitigation for Spatially Coupled LDPC Codes

   Zhu, M; Mitchell, D; Lentmaier, M; Costello, D (October 2020, Proc. International Symposium on Information Theory and Its Applications)

   null (Ed.)

   In this paper, we introduce two new methods of mitigating decoder error propagation for low-latency sliding window decoding (SWD) of spatially coupled low density parity check (SC-LDPC) codes. Building on the recently introduced idea of check node (CN) doping of regular SC-LDPC codes, here we employ variable node (VN) doping to fix (set to a known value) a subset of variable nodes in the coupling chain. Both of these doping methods have the effect of allowing SWD to recover from error propagation, at a cost of a slight rate loss. Experimental results show that, similar to CN doping, VN doping improves performance by up to two orders of magnitude compared to undoped SC-LDPC codes in the typical signal-to-noise ratio operating range. Further, compared to CN doping, VN doping has the advantage of not requiring any changes to the decoding process.In addition, a log-likelihood-ratio based window extension algorithm is proposed to reduce the effect of error propagation. Using this approach, we show that decoding latency can be reduced by up to a significant fraction without suffering any loss in performance 

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4. A Joint Detection and Decoding Receiver Design for Polar Coded MIMO Wireless Transmissions

   https://doi.org/10.1109/ISIT.2018.8437879  

   Jalali, Amin; Ding, Zhi (June 2018, 2018 IEEE International Symposium on Information Theory (ISIT))

   This work develops a novel design of joint detection and decoding receiver for multiple-input multiple output (MIMO) wireless transmissions that utilizes polar codes in forward error correction (FEC). To optimize the overall receiver performance, we integrate the polar code constraints during signal detection by relaxing and transforming FEC code constraints from the original Galois field to the real field. We propose a novel joint linear programming (LP) optimization formulation that takes into consideration the transformed polar code constraints when designing a novel receiver robust against practical obstacles including channel state information (CSI) errors, additive noises, co-channel interferences, and pilot contamination. Our newly proposed joint LP formulation can also be integrated with reduced complexity polar decoders such as successive cancellation (SC) and successive cancellation list (SCL) decoders to deliver superior receiver performance at low cost. 

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5. Polar Codes with Local-Global Decoding

   Zhu, Ziyuan; Wu, Wei; Siegel, Paul H. (March 2023, Proceedings of 14th Annual Non-Volatile Memories Workshop)

   Error correction coding schemes with local-global decoding are motivated by practical data storage applications where a balance must be achieved between low latency read access and high data reliability. As an example, consider a 4KB codeword, consisting of four 1KB subblocks, that supports a local-global decoding architecture. Local decoding can provide reliable, low-latency access to individual 1KB subblocks under good channel conditions, while global decoding can provide a “safety-net” for recovery of the entire 4KB block when local decoding fails under bad channel conditions. Recently, Ram and Cassuto have proposed such local-global decoding architectures for LDPC codes and spatially coupled LDPC codes. In this paper, we investigate a coupled polar code architecture that supports both local and global decoding. The coupling scheme incorporates a systematic outer polar code and a partitioned mapping of the outer codeword to semipolarized bit-channels of the inner polar codes. Error rate simulation results are presented for 2 and 4 subblocks. 

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