Kernels of Polar Codes and Their Applications to Wireless Channels, and Joint Source and Channel Coding Based on LDPC Codes

Download or read book Kernels of Polar Codes and Their Applications to Wireless Channels, and Joint Source and Channel Coding Based on LDPC Codes written by Hsien-Ping Lin and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation contains three topics: Polar codes with optimal exponents based on linear and nonlinear binary kernels of sizes up to 16, a design of rate-compatible polar codes, and a new proposed structure of joint source and channel coding based on low-density-parity-check (LDPC) codes. Polar codes are proposed by Arıkan with construction based on a linear kernel of dimension 2 with polarizing properties. The performance of a polar code is characterized asymptotically in terms of the exponent of its kernel. In this dissertation, constructions of linear and nonlinear binary kernels of dimensions up to 16 are presented. The constructed kernels are proved to have maximum exponents except in the case of nonlinear kernels of dimension 12 where we show that there exists only one possible exponent greater than that of the presented construction. From the results, the minimum dimension where a linear kernel with exponent greater than 0.5, the exponent of the linear kernel proposed by Arıkan, is 15, while this minimum dimension is 14 for nonlinear kernels. We also found that there is a linear kernel with maximum exponent up to dimension 11. The kernels of dimensions 13, 14, 15 with maximum exponents, although nonlinear over GF(2), are shown to be Z4-linear or Z2Z4-linear. In addition to exploring the asymptotic behavior of polar codes, we propose a design of finite block length rate-compatible polar codes suitable for HARQ communications. The central feature of the proposed design is established on the puncturing order chosen with low complexity on a base code of short length, which is then extended to the desired length. With the designed puncturing order, a practical rate-matching system which can be adjusted to any desired rate through puncturing or repetition under polarization is suggested. The proposed rate-matching system combines a channel interleaver and a bit-mapping procedure to preserve the polarization of the rate-compatible polar code family under bit-interleaved coded modulation systems. Simulation results on AWGN and fast fading channels with different modulation orders in both Chase combining and incremental redundancy HARQ communications are listed. For the third topic, we investigate a joint source and channel LDPC coding scheme in which the source compression and the channel coding matrices are designed jointly as two submatrices of a sparse matrix H. The sparse matrix H is constructed algebraically with a structure free of cycles of length 4 and serves as the parity-check matrix for joint decoding of the channel output symbols and untransmitted source symbols. The integrated design of the source and channel coding matrices strengthens the information exchange between the source symbols and the channel output parity-check symbols, which provides a good waterfall error performance of the coded system and low error-foor.