In this paper, we present a reliability-based iterative proportionality-logic decoding algorithm for two classes of structured low-density parity-check (LDPC) codes. The main contributions of this paper include: 1) Sy...
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In this paper, we present a reliability-based iterative proportionality-logic decoding algorithm for two classes of structured low-density parity-check (LDPC) codes. The main contributions of this paper include: 1) Syndrome messages instead of extrinsic messages are processed and exchanged between variable nodes and check nodes, which can reduce the decoding complexity;2) a more flexible decision mechanism is developed in which the decision threshold can be self-adjusted during the iterative process. Such decision mechanism is particularly effective for decoding the majority-logic decodable codes;3) only part of the variable nodes satisfying the pre-designed criterion are involved for the presented algorithm, which is in the proportionality-logic sense and can further reduce the computational complexity. Simulation results show that, when combined with factor correction techniques and appropriate proportionality parameter, the presented algorithm performs well and can achieve fast decoding convergence rate while maintaining relative low decoding complexity, especially for small quantized levels (3-4 bits). The presented algorithm provides a candidate for those application scenarios where the memory load and the energy consumption are extremely constrained.
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CHEN, CHResearch Department
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Arithmetic codes use a structured redundancy technique for binary number representation such that errors in an arithmetic operation of a digital computer can be detected or corrected. This correspondence studies the c...
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Arithmetic codes use a structured redundancy technique for binary number representation such that errors in an arithmetic operation of a digital computer can be detected or corrected. This correspondence studies the code structures by treating the set of redundant coded binary representations as a finite Abelian group. An algebraic model of arithmetic codes is developed, which shows that an arithmetic code is a pair of cyclic group isomorphisms. Two theorems are derived which describe the necessary and sufficient conditions for the existence of an arithmetic code. It is also shown that the group of redundant coded binary numbers is isomorphic to a cyclic group, or the direct sum of two cyclic groups. For a given code generator A and the information cardinality m, the two theorems may be applied to find all existing arithmetic codes up to an isomorphism. The algebraic structures of all codes published to date are covered by the mathematical model described in this correspondence.
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