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On lower bounds for the minimum distance of LDPC codes constructed by combinatorial design

智治 澁谷, Tomoharu Shibuya

Published Jan 1, 2002• 0 citations
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On tightness of Tanner's lower bound for the minimum distance of regular LDPC codes

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Short-length codes may play a crucial role in delay-sensitive scenarios. Low-density parity-check (LDPC) codes, as a class of Shannon limit approaching codes, perform well with long code length. However, the design of short-length LDPC codes with good performance is still challenging. This paper investigates the construction of short-length LDPC codes based on the combinatorial design theory. Specifically, Kirkman triple systems (KTS), as a type of balanced incomplete block design (BIBD) techniques, are used to construct the parity-check matrices of LDPC codes, which are guaranteed to be 4-cycles free. Some other properties of such designed LDPC codes are also investigated. For instance, a lower bound on the girth, the code rate and minimum code distance. The simulation results show that the designed short-length LDPC codes based on KTS outperform that of randomly constructed ones.
An independent tree-based method for lower bounding the minimum distance of low-density parity-check (LDPC) codes is presented. This lower-bound is then used as the decision criterion during the iterative construction of regular LDPC codes. The new construction algorithm results in LDPC codes with greater girth and improved minimum-distance bounds when compared to regular LDPC codes constructed using the progressive edge-growth (PEG) construction and the approximate cycle extrinsic message degree (ACE)-constrained PEG construction. Simulation results of codes constructed with the new method show improved performance on the additive white Gaussian noise channel at moderate signal-to-noise ratios.