Abstract：This paper describes a class of rate-compatible nonbinary low-density parity-check (LDPC) codes based on an improved extension method. The check symbols for lower code rates involve not only the codewords of the highest-rate code but also the check symbols of moderate-rate codes. The construction process optimizes the masking matrix and the base matrix with random replacement of nonbinary elements. This paper also describes an algebraic method to design the parity matrices to further reduce the design complexity. The codes are not only rate compatible, but also have a quasi-cyclic structure which will benefit hardware implementations of the encoder and decoder. Numerical tests show that the codes can achieve good performance within a wide range of code rates in both the waterfall region and in the error-floor region.
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