In this thesis, error correcting codes for future storage with distributed nature are suggested and theoretically analyzed. For not only traditional storage systems like hard-disk-drive (HDD) and solid-state-drive (SSD) but also recent massive cloud system, error-correcting codes with distributed nature are promising for achieving dynamic system performance targets. In this thesis, three different error-correcting codes with distributed nature are proposed for various types of storage systems. In Chapter 2, two-dimensional (2D) cyclic codes are proposed which correct any single occurrence of known 2D error patterns. First, the code construction procedure begins with designing 2D code theoretically to have distinct syndrome sets for all target 2D patterns. After that, syndrome set for each pattern is further designed to have distinct elements for all possible pattern locations. In Chapter 3, practical concatenated coding scheme with multiple short component polar codes and single-parity-check codes is proposed. As for hardware-complexity, required memory is significantly reduced by utilizing small decoding unit geared to serial decoding of short component polar codes. In theoretic analysis, each short component polar code shows much improved error-rate scaling-behavior thanks to simple single-parity-check decoding, i.e., the error rate decays as fast as a long single polar code along with overall code-length while retaining considerable memory advantage. In the last chapter, storage-repair bandwidth trade-off for distributed storage system with knowledge of coding connectivity is analyzed. Conventional distributed storage system is based on repair of failures with randomly chosen $d$-helper nodes and random linear network coding. If the repair process of a failed node is based on knowledge of local connections, failure can be repaired by the connected helper nodes only. Information flow analysis of sparsely-coded distributed storage system is presented in numerical sense. Through the approach, improved storage-repair bandwidth pair is obtained with much less helper nodes.
본 논문에서는 차세대 스토리지 환경에 적합한 분산형 구조의 오류정정부호 구조를 설계하고 이론적 분석을 진행하였다. 첫 번째 챕터에서는, 높은 집적도의 하드디스크 드라이브에서 발생하는 이차원 간섭채널에 적합한 이차원 오류패턴정정부호를 설계하고 기반 이론을 정립하였다. 두 번째 챕터에서는, 스토리지 환경뿐만 아니라 차세대 네트워크 환경에서 주목받고 있는 폴라부호 연구를 다룬다. 리스트복호는 폴라부호의 정정능력을 위해 널리 사용되지만, 복호기에 매우 큰 메모리 버퍼를 요구한다. 본 논문에서는 짧은 길이의 행단위 폴라부호들을 열단위 단일 패리티 체크 부호와 연접하여 작은 메모리 버퍼로 복호가 가능한 실용적인 폴라부호를 제안한다. 마지막 챕터에서는 분산 스토리지 환경에서 부호기반의 노드 연결성을 이용해 소실 노드를 복구하여 향상된 스토리지-복구대역폭 트레이드오프를 달성할 수 있는 가능성을 제시한다.
