Ying Yu Tai

Construction of Quasi-Cyclic LDPC Codes for AWGN and Binary Erasure Channels: A Finite Field Approach

In the late 1950s and early 1960s, finite fields were successfully used to construct linear block codes, especially cyclic codes, with large minimum distances for hard-decision algebraic decoding, such as Bose-Chaudhuri-Hocquenghem (BCH) and Reed-Solomon (RS) codes. This paper shows that finite fields can also be successfully used to construct algebraic low-density parity-check (LDPC) codes for iterative soft-decision decoding. Methods of construction are presented. LDPC codes constructed by these methods are quasi-cyclic (QC) and they perform very well over the additive white Gaussian noise (AWGN), binary random, and burst erasure channels with iterative decoding in terms of bit-error probability, block-error probability, error-floor, and rate of decoding convergence, collectively. Particularly, they have low error floors. Since the codes are QC, they can be encoded using simple shift registers with linear complexity.

Transactions Papers - Constructions of Nonbinary Quasi-Cyclic LDPC Codes: A Finite Field Approach

This paper is concerned with construction of efficiently encodable nonbinary quasi-cyclic LDPC codes based on finite fields. Four classes of nonbinary quasi-cyclic LDPC codes are constructed. Experimental results show that codes constructed perform well with iterative decoding using a fast Fourier transform based q-ary sum-product algorithm and they achieve significant coding gains over Reed-Solomon codes of the same lengths and rates decoded with either algebraic hard- decision Berlekamp-Massey algorithm or algebraic soft-decision Kotter-Vardy algorithm.

Algebraic construction of quasi-cyclic LDPC codes for the AWGN and erasure channels

This paper is concerned with construction of quasi-cyclic (QC) low-density parity-check (LDPC) codes for three different types of channels: the additive white Gaussian noise, the binary random erasure, and the binary burst erasure channels. Two algebraic methods for systematic construction of QC-LDPC codes are presented. Codes constructed perform well over all three types of channels

Construction of nonbinary cyclic, quasi-cyclic and regular LDPC codes: a finite geometry approach

This paper presents five methods for constructing nonbinary LDPC codes based on finite geometries. These methods result in five classes of nonbinary LDPC codes, one class of cyclic LDPC codes, three classes of quasi-cyclic LDPC codes and one class of structured regular LDPC codes. Experimental results show that constructed codes in these classes decoded with iterative decoding based on belief propagation perform very well over the AWGN channel and they achieve significant coding gains over Reed-Solomon codes of the same lengths and rates with either algebraic hard-decision decoding or Kotter-Vardy algebraic soft-decision decoding at the expense of a larger decoding computational complexity.

New constructions of quasi-cyclic LDPC codes based on special classes of BIBD's for the AWGN and binary erasure channels

This paper presents new methods for constructing efficiently encodable quasi-cyclic LDPC codes based on special balanced incomplete block designs (BIBDs). Codes constructed perform well over both the AWGN and binary erasure channels with iterative decoding.

High Performance Non-Binary Quasi-Cyclic LDPC Codes on Euclidean Geometries LDPC Codes on Euclidean Geometries

This paper presents algebraic methods for constructing high performance and efficiently encodable non-binary quasi-cyclic LDPC codes based on flats of finite Euclidean geometries and array masking. Codes constructed based on these methods perform very well over the AWGN channel. With iterative decoding using a fast Fourier transform based sum-product algorithm, they achieve significantly large coding gains over Reed-Solomon codes of the same lengths and rates decoded with either algebraic hard-decision Berlekamp-Massey algorithm or algebraic soft-decision Kotter-Vardy algorithm. Due to their quasi-cyclic structure, these non-binary LDPC codes on Euclidean geometries can be encoded using simple shift-registers with linear complexity. Structured non-binary LDPC codes have a great potential to replace Reed-Solomon codes for some applications in either communication or storage systems for combating mixed types of noise and interferences.

A trellis-based method for removing cycles from bipartite graphs and construction of low density parity check codes

This letter presents a trellis-based iterative method for removing short cycles from bipartite graphs. This method can be used to improve the performance of low density parity check (LDPC) codes or to construct new LDPC codes.

Dispersed Reed-Solomon codes for iterative decoding and construction of q-ary LDPC codes

This paper presents three algebraic methods for constructing q-ary LDPC codes. The first method gives a class of dispersed Reed-Solomon codes as LDPC codes. The second method gives a class of q-ary quasi-cyclic LDPC codes. The third method gives two classes of q-ary finite geometry LDPC codes. Codes constructed by these methods perform very well with iterative decoding, even for short codes.

CTH08-1: Construction of High Performance and Efficiently Encodable Nonbinary Quasi-Cyclic LDPC Codes

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 LDPC codes may be used to replace Reed-Solomon codes in some communication environments or storage systems for combating mixed types of noises and interferences.

Constructions of quasi-cyclic LDPC codes for the AWGN and binary erasure channels based on finite fields and affine mappings

This paper presents two algebraic methods for constructing efficiently encodable quasi-cyclic (QC) LDPC codes that perform well on both the AWGN and binary erasure channels with iterative decoding in terms of bit-error performance, block error performance and error-floor, collectively. The constructions are based on the cyclic subgroups of the multiplicative groups of finite fields and affine mappings