Bounds and Constructions of Locally Repairable Codes: Parity-Check Matrix Approach
نویسندگان
چکیده
منابع مشابه
Bounds and Constructions of Locally Repairable Codes: Parity-check Matrix Approach
A code symbol of a linear code is said to have locality r if this symbol could be recovered by at most r other code symbols. An (n, k, r) locally repairable code (LRC) with all symbol locality is a linear code with length n, dimension k, and locality r for all symbols. Recently, there are lots of studies on the bounds and constructions of LRCs, most of which are essentially based on the generat...
متن کاملLow-Density Parity-Check Codes: Constructions and Bounds
Low-density parity-check (LDPC) codes were introduced in 1962, but were almost forgotten. The introduction of turbo-codes in 1993 was a real breakthrough in communication theory and practice, due to their practical effectiveness. Subsequently, the connections between LDPC and turbo codes were considered, and it was shown that the latter can be described in the framework of LDPC codes. In recent...
متن کاملLocally Repairable and Locally Regenerating Codes by Parity-Splitting of HashTag Codes
We construct an explicit family of locally repairable and locally regenerating codes whose existence was proven in a recent work by Kamath et al. about codes with local regeneration but no explicit construction was given. This explicit family of codes is based on HashTag codes. HashTag codes are recently defined vector codes with different vector length α (also called a sub-packetization level)...
متن کاملCodes with a Circulant Parity Check Matrix
In this work we study codes characterized by the property that their parity check matrix is circulant, i.e., that rows are obtained as all the distinct cyclic shifts of the rst row. For these codes, we give simple expressions for their dimension and for a lower bound on their minimum distance. We also present an O(nd) algorithm to solve the problem of deciding whether codes satisfying given con...
متن کاملLocally Repairable Regenerating Code Constructions
In this work, we give locally repairable regenerating code (LRRC) [1]–[4] constructions that can protect the file size promised by the graph analysis of the modified family helper selection (MFHS) scheme [1] at the minimum-bandwidthregenerating (MBR) point. I. RANDOM LINEAR CODE CONSTRUCTION FOR A CLASS OF (n, k, d, r) PARAMETERS In this section, we prove the existence and construction of linea...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: IEEE Transactions on Information Theory
سال: 2020
ISSN: 0018-9448,1557-9654
DOI: 10.1109/tit.2020.3021707