Cyclic Codes Suitable for an Iterative Decoding Based on the Sum-Product Algorithm

Nguyen Thi Hong Nhung, Pham Xuan Nghia, The Cuong Dinh +2 more

Qilin Zhang, Shinsuke Ibi, Takumi Takahashi +1 more

This paper proposes a deep unfolding-aided sum-product algorithm (SPA) for error correction decoding of cyclic redundancy check (CRC) coded short message. SPA is a practical decoding algorithm for linear codes without requiring enormous computational complexity. However, if the SPA is used as it is for CRC codes, belief correlation and outliers will be induced in the iterative decoding process, resulting in lousy correction capability. To compensate for this drawback, we design a SPA-based decoding process for CRC code that incorporates a data-driven design based on deep learning and learning optimization of in-ternal trainable parameters. Considering the operation principle of soft-decision decoder, a novel loss function based on a weighted average of negentropy, which is a key measure to evaluate the Gaussianity, and BCE of the decoder output is proposed. Numerical results show that the proposed algorithm improves the bit error rate (BER) performance with deep unfolding and negentropy-aware loss function.

P. Heijnen, Henk C. A. van Tilborg

Shumei Song, Lan Lan, Shu Lin +1 more

This paper presents an algebraic method for constructing quasi-cyclic LDPC codes based on the primitive elements of finite fields. The construction gives a class of efficiently encodable quasi-cyclic LDPC codes. Experimental results show that the constructed codes decoded with iterative decoding using the sum-product algorithm perform well over the AWGN channel.

Li Guo Zhang, Qin Huang, Shu Lin

Codes constructed based on finite geometries form a large class of cyclic codes with large minimum distances which can be decoded with simple majority-logic decoding in one or multiple steps. In 2001, Kou, Lin and Fossorier showed that the one-step majority-logic decodable finite geometry codes form a class of cyclic LDPC codes whose Tanner graphs are free of cycles of length 4. These cyclic finite geometry LDPC codes perform very well over the AWGN channel using iterative decoding based on belief propagation (IDBP) and have very low error-floors. However, the standard IDBP is not effective for decoding other cyclic finite geometry codes because their Tanner graphs contain too many short cycles of length 4 which severely degrade the decoding performance. This paper investigates iterative decoding of two-step majority-logic decodable finite geometry codes. Three effective algorithms for decoding these codes are proposed. These algorithms are devised based on the orthogonal structure of the parity-check matrices of the codes to avoid or reduce the degrading effect of the short cycles of length 4. These decoding algorithms provide significant coding gains over the standard IDBP using either the sum-product or the min-sum algorithms.

Pascal O. Vontobel