Ja n 20 06 Improved Nearly - MDS Expander Codes ∗
نویسندگان
چکیده
A construction of expander codes is presented with the following three properties: (i) the codes lie close to the Singleton bound, (ii) they can be encoded in time complexity that is linear in their code length, and (iii) they have a linear-time bounded-distance decoder. By using a version of the decoder that corrects also erasures, the codes can replace MDS outer codes in concatenated constructions, thus resulting in linear-time encodable and decodable codes that approach the Zyablov bound or the capacity of memoryless channels. The presented construction improves on an earlier result by Guruswami and Indyk in that any rate and relative minimum distance that lies below the Singleton bound is attainable for a significantly smaller alphabet size.
منابع مشابه
Nearly MDS expander codes with reduced alphabet size
Recently, Roth and Skachek proposed two methods for constructing nearly maximum-distance separable (MDS) expander codes. We show that through the simple modification of using mixed-alphabet codes derived from MDS codes as constituent codes in their code designs, one can obtain nearly MDS codes of significantly smaller alphabet size, albeit at the expense of a (very slight) reduction in code rate.
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 کامل1 8 Ja n 20 07 On decomposability of 4 - ary distance 2 MDS codes , double - codes , and n - quasigroups of order 4 ∗
A subset S of {0, 1, . . . , 2t − 1}n is called a t-fold MDS code if every line in each of n base directions contains exactly t elements of S. The adjacency graph of a t-fold MDS code is not connected if and only if the characteristic function of the code is the repetition-free sum of the characteristic functions of t-fold MDS codes of smaller lengths. In the case t = 2, the theory has the foll...
متن کاملJa n 20 09 IS THE CRITICAL PERCOLATION PROBABILITY LOCAL ?
We show that the critical probability for percolation on a d-regular nonamenable graph of large girth is close to the critical probability for percolation on an infinite d-regular tree. This is a special case of a conjecture due to O. Schramm on the locality of pc. We also prove a finite analogue of the conjecture for expander graphs.
متن کامل