A construction of expander codes is presented with the following three properties: i) the codes lie close to the Singleton bound, ii) they can be encoded in time complexity that is linear in their code length, and iii...
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A construction of expander codes is presented with the following three properties: i) the codes lie close to the Singleton bound, ii) they can be encoded in time complexity that is linear in their code length, and iii) they have a linear-time bounded-distance decoder. By using a version of the decoder that corrects also erasures, the codes can replace maximum-distance separable (MDS) outer codes in concatenated constructions, thus resulting in linear-time encodable and decodable codes that approach the Zyablov bound or the capacity of memoryless channels. The presented construction improves on an earlier result by Guruswami and Indyk in that any rate and relative minimum distance that lies below the Singleton bound is attainable for. a significantly smaller alphabet size.
In this paper, we present an efficient systematic encoding algorithm for quasi-cyclic (QC) low-density parity-check (LDPC) codes that are related to cyclic maximum-distance separable (MDS) codes. The algorithm offers ...
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In this paper, we present an efficient systematic encoding algorithm for quasi-cyclic (QC) low-density parity-check (LDPC) codes that are related to cyclic maximum-distance separable (MDS) codes. The algorithm offers lineartime complexity, and it can be easily implemented by using polynomial multiplication and division circuits. We show that the division polynomials can be completely characterized by their zeros and that the sum of the respective numbers of their zeros is equal to the parity-length of the codes.
Powerful rate-compatible codes are essential for achieving high throughput in hybrid automatic repeat request (ARQ) systems for networks utilising packet data transmission. The paper focuses on the construction of eff...
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Powerful rate-compatible codes are essential for achieving high throughput in hybrid automatic repeat request (ARQ) systems for networks utilising packet data transmission. The paper focuses on the construction of efficient rate-compatible low-density parity-check (RC-LDPC) codes over a wide range of rates. Two LDPC code families are considered;namely, regular LDPC codes which are known for good performance and low error floor, and semi-random LDPC codes which offer performance similar to regular LDPC codes with the additional property of linear-time encoding. An algorithm for the design of punctured regular RC-LDPC codes that have low error floor is presented. Furthermore, systematic algorithms for the construction of semi-random RC-LDPC codes are proposed based on puncturing and extending. The performance of a type-II hybrid ARQ system employing the proposed RC-LDPC codes is investigated. Compared with existing hybrid ARQ systems based on regular LDPC codes, the proposed ARQ system based on semi-random LDPC codes offers the advantages of linear-time encoding and higher throughput.
In this paper, we present an efficient systematic encoding algorithm for quasi-cyclic (QC) low-density parity-check (LDPC) codes that are related to cyclic maximum-distance separable (MDS) codes. The algorithm offers ...
详细信息
ISBN:
(纸本)9781424420698
In this paper, we present an efficient systematic encoding algorithm for quasi-cyclic (QC) low-density parity-check (LDPC) codes that are related to cyclic maximum-distance separable (MDS) codes. The algorithm offers lineartime complexity, and it can be easily implemented by using polynomial multiplication and division circuits. We show that the division polynomials can be completely characterized by their zeros and that the sum of the respective numbers of their zeros is equal to the parity-length of the codes.
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