Victor V. Zyablov. An estimate of the complexity of constructing binary linear cascaded codes. Problemy Peridachi Informatsii, 15(2):58-70, 1971.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....constant) depends exponentially on 1= A result similar to ours was known for the easier problem of decoding from erasures [2] and indeed we use techniques from that paper in our construction. Concatenating these with good binary inner codes enables us to match the so called Zyablov bound [23] with lineartime decoding. One can also use the multilevel concatenation technique of [4] to get linear time codes that match the Blokh Zyablov bound as well. We note that these bounds give essentially the best known rate vs. distance trade o for explicit binary codes. We are able to attain ....

....the unique x in the range 0 x 1=2 that satis es H(x) y) Every code in the family is explicitly speci ed given a constant sized binary linear code which can be constructed in probabilistic O( log(1= or deterministic 2 time. The bound of Equation (3) is half the Zyablov bound [23], and thus these codes match the best error correction performance known for constructive binary concatenated codes. We remark that the rst explicit construction of codes meeting the Zyablov bound for all rates was due to Shen [16] 2.5 Beyond Zyablov bound with linear time codes using ....

Victor V. Zyablov. An estimate of the complexity of constructing binary linear cascaded codes. Problemy Peridachi Informatsii, 15(2):58-70, 1971.

....f1 (R;p) where f 1 (R; p) max RR 0 1 GammaH(p) E(R 0 ; p) 1 Gamma R=R 0 ) Gamma : 1) Here E(R 0 ; p) is the random coding exponent [4] and H( Delta) is the binary entropy function. Thus f 1 (R; p) 0 for all rates R up to the channel capacity. A similar idea was used by Zyablov in [10] to construct codes with polynomial decoding complexity and relative distance arbitrarily close to ffi(R) 1 Gamma R=R 0 )H Gamma1 (1 Gamma R 0 ) R R 0 1) 2) Thus for these codes we have ffi(R) 0 for any value R of the code rate 0 R 1: These results underwent a number of ....

V. V. Zyablov, "An estimate of complexity of constructing binary linear cascade codes," Problems Inform. Transm., 7 (1) (1971), 3-10. 9

....probability P e 2 N(f1 (R;p) where f 1 (R; p) max R R0 1 H(p) E(R 0 ; p) 1 R=R 0 ) 1) Here E(R 0 ; p) is the random coding exponent [4] and H( is the binary entropy function. Thus f 1 (R; p) 0 for all rates R up to the channel capacity. A similar idea was used by Zyablov in [10] to construct codes with polynomial decoding complexity and relative distance (R) 1 R=R 0 )H 1 (1 R 0 ) R R 0 1) 2) Thus for these codes we have (R) 0 for any value R of the code rate 0 R 1: These results underwent a number of improvements (surveyed, for instance, in [2] but ....

V. V. Zyablov, \An estimate of complexity of constructing binary linear cascade codes," Problems Inform. Transm., 7 (1) (1971), 3-10. 9

....method when applied to families of algebraic geometric codes yields precisely the Zyablov bound. However, for the same reason as above this does not yield families of binary ffl Gammabiased arrays. More interesting for our problem is the original semi constructive proof of the Zyablov bound [27]. In fact, apply concatenation to a Reed Solomon code [q m ; rq m ; 1 Gamma r)q m ] q m as outer code and a code [n; m; d] q as inner code, where it is assumed that the inner code asymptotically meets the Gilbert Varshamov bound (d=n = m=n = 1 Gamma H q ( The concatenated code has ....

Zyablov, V. V.: An estimate of the complexity of constructing binary linear cascade codes, Problems in Information transmission 7 (1971), 3-10

....of a conference on Theoretical Aspects of Computer Science. I will deliberately be very brief on the history of LDPC codes since I would like to concentrate more on very recent developments. But no paper on this topic would be complete without mentioning the names of Zyablov and Pinsker [20, 21] and Margulis [12] from the Russian school who had realized the potential of LDPC codes in the 1970 s, and the name of Tanner [19] who re invented and extended LDPC codes. In fact, re invention seems to be a recurring theme: with the advent of the powerful class of Turbo codes [4] many ....

V. V. Zyablov. An estimate of the complexity of constructing binary linear cascade codes. Probl. Inform. Transm., 7:3--10, 1971.

.... (GV) bound [2] Moreover, the same is valid even if A is a fixed MDS (say Reed Solomon) code [3] 9] By making n grow slower than N and taking varying inner and MDS outer codes, it is possible to present families of codes with both nonvanishing rate and distance and low construction complexity [11], 5] Improvements of the parameters of these families are based on multilevel concatenations [3] and the use of algebraic geometry codes [6] A detailed account of the early work is given in [3] see also overviews in [4] 1] For a given rate R 2 [0; 1] denote by ffi 0 = ffi 0 (R) the GV ....

V. V. Zyablov, An estimate of complexity of constructing binary linear cascade codes, Problemy Peredachi Informatsii 7 (1971), no. 1, 3--10.

.... (GV) bound [2] Moreover, the same is valid even if A is a fixed MDS (say Reed Solomon) code [3] 9] By making n grow slower than N and taking varying inner and MDS outer codes, it is possible to present families of codes with both nonvanishing rate and distance and low construction complexity [11], 5] Improvements of the parameters of these families are based on multilevel concatenations [3] and the use of algebraic geometry codes [6] A detailed account of the early work is given in [3] see also overviews in [4] 1] For a given rate R 2 [0; 1] denote by ffi 0 = ffi 0 (R) the GV ....

V. V. Zyablov, An estimate of complexity of constructing binary linear cascade codes, Problemy Peredachi Informatsii 7 (1971), no. 1, 3--10.

No context found.

V.V. Zyablov, "An estimate of complexity of constructing binary linear cascade codes," Problems of Info. Trans., 7 (1) (1971), 3-10.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC