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This paper presents a general and three specific algebraic methods for constructing efficiently encodable non-binary quasi-cyclic LDPC codes. Three classes of quasi-cyclic LDPC codes over nonbinary finite fields are constructed. codes constructed perform very well over the AWGN channel with iterative decoding and achieve large coding gains over the Reed-Solomon codes of the same parameters. Nonbinary...
This paper investigates cyclic codes for correcting bursts of errors from a new point of view. A simple iterative algorithm for correcting bursts of errors is developed. This algorithm is optimal in the sense that it corrects burst of errors of lengths up to the burst-error-correction limit of a cyclic code. Also included in the paper is an iterative process for correcting bursts of erasures.
This paper presents an algebraic method for constructing quasi-cyclic LDPC codes based on the primitive elements of finite fields. The construction gives a class of efficiently encodable quasi-cyclic LDPC codes. Experimental results show that the constructed codes decoded with iterative decoding using the sum-product algorithm perform well over the AWGN channel.
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