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Geometry based designs of LDPC codes

In this paper we construct three types of low-density parity-check codes with column weight j = 3 based on geometries in graphical models. Low-density parity-check codes with j > 2 are desired because their minimum distance improves linearly with the code block length n. The codes we present here have girth 8 and girth 10. All codes are regular and well-structured. These codes have flexible block lengths and code rates, and may be used in the area of communications and data storage. Our simulation results show that they have better bit-error-rate decoding performance and lower error floors in additive white Gaussian noise channels than randomly constructed low-density parity-check codes.