This paper proposes a syndrome sphere decoding (SSD) algorithm. SSD achieves the frame error rate (FER) of maximum likelihood (ML) decoding for a tail-biting convolutional code (TBCC) concatenated with an expurgating linear function (ELF) with significantly lower average and maximum decoding complexity than serial list Viterbi decoding (SLVD). SSD begins by using a Viterbi decoder to find the closest trellis path, which may not be tail-biting and may not satisfy the ELF. This trellis path has a syndrome comprised of the difference between the received ELF and the ELF computed from the received message and the difference between the beginning and ending state of the trellis path. This syndrome is used to find all valid tail-biting codewords that satisfy the ELF constraint and lie within a specified distance from the closest trellis path. The proposed algorithm avoids the complexity of SLVD at the cost of a large table containing all the offsets needed for each syndrome. A hybrid decoder combines SSD and SLVD with a fixed maximum list size, balancing the maximum list size for SLVD against the size of the SSD offset table.
Nanopore sequencers are a strong contender for the practical retrieval and decoding of information stored in DNA. In this paper, we provide two graph constructions of codes that satisfy the restrictions on sequences desirable for nanopore sequencers including GC-content, run length limit, and secondary structure avoidance. Moreover, we show that our constructions have error detecting capability with respect to single deletions, insertions, and substitutions.
We show that optimized message update scheduling can enhance both the error-rate performance and the throughput of layered BP decoding of LDPC codes. As an exemplary attempt, optimized scheduling accelerates BP decoding and leads to approximately 2x throughput enhancement when compared to top-to-bottom row-layered BP decoding of 5G LDPC codes. Furthermore, scheduling enhances the error-rate performance of short-length LDPC codes via ensemble decoding. For short-length 5G LDPC codes, coding gains of up to 0.7 dB and 1.6 dB at BLER of 10(-3)-10(-4) for both AWGN and Rayleigh fading channels can be achieved when compared to conventional BP decoders. Additionally, we show that the same concept applies to general linear block codes (e.g., polar/RM codes) facilitating a unified decoding architecture based on row-layered BP decoders ("one-silicon fits all").
This article studies the Hermitian hulls of linear codes from algebraic plane curves of a special type. We provide lower bounds on the hull dimension of one-point algebraic geometry codes. We derive two families of entanglement-assisted quantum codes from one-point algebraic geometry codes, using the Hermitian approach.
We propose a generalization of the recently proposed quantum Tanner codes by Leverrier and Zemor. These codes can be constructed equivalently from groups, Cayley graphs, or square complexes constructed from groups. In a recent work, we enlarged this to group actions on finite sets, Schreier graphs, and a family of square complexes. We extend the class of quantum Tanner codes further by replacing the tensor product code in the construction with a Tanner code on any bipartite graph. A stricter property on the other underlying graphs is required, and we show that a common variation of the construction can always be taken to satisfy this condition. This results in improved codes compared to the ones constructed based on Schreier graphs.
