Reliable Memories with Subline Accesses

Abstract

We study memories protected with error control codes, in which the memory's contents are organized in lines which are read and written to in isolation from other lines. In these memories the available redundancy is structured so as to protect individual lines rather than the entire memory as a whole. Often designers wish to read and write only parts of the memory line, as in some instances this leads to various favorable system design tradeoffs, including better power consumption, increased data access concurrency, etc. (alternatively one may say that designers sometimes would prefer smaller line sizes). Nevertheless when designing systems with such subline accesses it is often found that in order to mantain a given level of reliability, the total amount of redundancy allocated in the memory needs to be increased beyond desirable levels. In this work, we initiate a study of the problem of structuring error control codes to allow subline accesses with good tradeoffs between reliability and redundancy. We motivate and explore a setting in which a "double-lookup" protocol is used in conjunction with certain types of two-level codes, whereby error detection is attained in a first level and error correction using the second level is performed whenever errors are detected in the first level. We obtain lower bounds on redundancy for a given level of reliability and offer a code construction that attains this bound for a certain important class of parameters. We also introduce an alternate construction which allows us to find longer codes under restrictions of the Galois Field size used in the codes.

Optimal locally repairable codes with local minimum storage regeneration via rank-metric codes

“…Subsequently, the work by Prakash et al extends the bound to a more general definition of scalar LRCs [11]. (Han and Lastras-Montano [18] provide a similar upper bound which is coincident with the one in [11] for small minimum distances, and also present codes that attain this bound in the context of reliable memories.) In [10], Papailiopoulos and Dimakis generalize the bound in [9] to vector codes, and present locally repairable coding schemes which exhibits MDS property at the cost of small amount of additional storage per node.…”

“…only information symbols satisfy the locality constraint. However, an explicit construction of optimal scalar LRCs with all-symbols locality is known only for the case n = M r (r + δ − 1) [11], [18]. Towards optimal scalar LRCs for broader range of parameters, given field size |F| > Mn M , [11] establishes the existence of scalar codes with all-symbols locality for the setting when (r + δ − 1)|n.…”

A Tight Rate Bound and Matching Construction for Locally Recoverable Codes With Sequential Recovery From Any Number of Multiple Erasures

“…The notion of codes with locality was introduced in [4] (See also [5], [6], [7]) to design codes such that the number of nodes accessed to repair a failed node is much smaller than the dimension k of the code . Let C be an [n, k, d min ] linear code over F q having block length n, dimension k and minimum distance d min .…”

Codes with local regeneration

“…b) Parity-Splitting Codes Optimal codes with all-symbol locality can be obtained for some parameter sets through a process known as paritysplitting. The parity-splitting construction appeared first in [21] and was subsequently rediscovered in [19]. The general construction is optimal whenever n = κ r (r + δ − 1) and the required field size is q = n + 1.…”