Decoder-in-the-Loop: Genetic Optimization-based LDPC Code Design

LDPC code design tools typically rely on asymptotic code behavior and are affected by an unavoidable performance degradation due to model imperfections in the short length regime. We propose an LDPC code design scheme based on an evolutionary algorithm, the Genetic Algorithm (GenAlg), implementing a "decoder-in-the-loop" concept. It inherently takes into consideration the channel, code length and the number of iterations while optimizing the error-rate of the actual decoder hardware architecture. We construct short length LDPC codes (i.e., the parity-check matrix) with error-rate performance comparable to, or even outperforming that of well-designed standardized short length LDPC codes over both AWGN and Rayleigh fading channels. Our proposed algorithm can be used to design LDPC codes with special graph structures (e.g., accumulator-based codes) to facilitate the encoding step, or to satisfy any other practical requirement. Moreover, GenAlg can be used to design LDPC codes with the aim of reducing decoding latency and complexity, leading to coding gains of up to $0.325$ dB and $0.8$ dB at BLER of $10^{-5}$ for both AWGN and Rayleigh fading channels, respectively, when compared to state-of-the-art short LDPC codes. Also, we analyze what can be learned from the resulting codes and, as such, the GenAlg particularly highlights design paradigms of short length LDPC codes (e.g., codes with degree-1 variable nodes obtain very good results).Comment: in IEEE Access, 201

Decoder-in-the-Loop: Genetic Optimization- Based LDPC Code Design

LDPC code design tools typically rely on asymptotic code behavior and are affected by an unavoidable performance degradation due to model imperfections in the short length regime. We propose an LDPC code design scheme based on an evolutionary algorithm, the Genetic Algorithm (GenAlg), implementing a ``decoder-in-the-loop\u27\u27 concept. It inherently takes into consideration the channel, code length and the number of iterations while optimizing the error-rate of the actual decoder hardware architecture. We construct short length LDPC codes (i.e., the parity-check matrix) with error-rate performance comparable to, or even outperforming that of well-designed standardized short length LDPC codes over both AWGN and Rayleigh fading channels. Our proposed algorithm can be used to design LDPC codes with special graph structures (e.g., accumulator-based codes) to facilitate the encoding step, or to satisfy any other practical requirement. Moreover, GenAlg can be used to design LDPC codes with the aim of reducing decoding latency and complexity, leading to coding gains of up to 0:325 dB and 0:8 dB at BLER of 10¯⁵ for both AWGN and Rayleigh fading channels, respectively, when compared to state-of-the-art short LDPC codes. Also, we analyze what can be learned from the resulting codes and, as such, the GenAlg particularly highlights design paradigms of short length LDPC codes (e.g., codes with degree-1 variable nodes obtain very good results)

CRC-Aided Belief Propagation List Decoding of Polar Codes

Although iterative decoding of polar codes has recently made huge progress based on the idea of permuted factor graphs, it still suffers from a non-negligible performance degradation when compared to state-of-the-art CRC-aided successive cancellation list (CA-SCL) decoding. In this work, we show that iterative decoding of polar codes based on the belief propagation list (BPL) algorithm can approach the error-rate performance of CA-SCL decoding and, thus, can be efficiently used for decoding the standardized 5G polar codes. Rather than only utilizing the cyclic redundancy check (CRC) as a stopping condition (i.e., for error-detection), we also aim to benefit from the error-correction capabilities of the outer CRC code. For this, we develop two distinct soft-decision CRC decoding algorithms: a Bahl-Cocke-Jelinek-Raviv (BCJR)-based approach and a sum product algorithm (SPA)-based approach. Further, an optimized selection of permuted factor graphs is analyzed and shown to reduce the decoding complexity significantly. Finally, we benchmark the proposed CRC-aided belief propagation list (CA-BPL) to state-of-the-art 5G polar codes under CA-SCL decoding and, thereby, showcase an error-rate performance not just close to the CA-SCL but also close to the maximum likelihood (ML) bound as estimated by ordered statistic decoding (OSD).Comment: Submitted to IEEE for possible publicatio