OF THE DISSERTATION Optimizing and Decoding LDPC codes with Graph-Based Techniques

We derive asymptotic expressions for the average distance distributions in ensembles of irregular low-density paritycheck (LDPC) codes. The ensembles are defined by matrices with given profiles of column and row sums.

본 논문은 IEEE 802.16e 표준에서 제시한 효율적인 부호화가 가능한 low-density parity-check (LDPC) 부호에 대하여, 두 가지 대표적인 LDPC 부호의 복호 알고리즘을 기반으로 각각 체크 노드 분할을 이용한 변형된 새로운 복호 방법을 적용하여 수렴 속도 개선을 확인한다. 이는 적은 반복으로 동일한 복호 성능을 보장할 수 있기 때문에, 복호 과정에서 연산의 복잡도를 절반 가량 줄일 수 있는 장점을 갖는다. 또한 IEEE 802.16e 표준에서 제시된 LDPC 부호에 성능과 구현 측면에서 가장 적합한 체크 노드 분할 방법으로 비중복 분할 방법을 제안한다. 새로운 복호 알고리즘은 신뢰할 만한 정보의 복원을 보장하면서도 계산 복잡도를 줄일 수 있다는 의미에서 실제 무선 통신 시스...

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In this paper we consider low-density parity-check (LDPC) codes for the classic bursty channel. We present lower bounds on the maximum resolvable erasure burst length, Lmax, for arbitrary LDPC codes and then present constructions for LDPC codes with good burst erasure correction performance for channels with and without the presence of noise in the guard band.

Turbo-codes provide communications near capacity when very large interleavers (and thus codeword lengths) are used. However, many military communication systems require packet lengths that are too short to exploit the full capability of these codes. We have previously shown that a rectangular parity-check code can be used as an outer code with a turbo code as an inner code in a serial concatena...

Recently, lattice theory has been considered as useful tool for information theory. It has been also shown that lattice codes can be a strong competitor to traditional capacity achieving coding schemes such as LDPC or Turbo codes. Lattice codes are also attractive due to the fact that code space and signal space are equal, instead of traditional codes, where these spaces are different. However,...