| 1. |
- Avgustinovich, S. V., et al.
(författare)
-
On partitions of an n-cube into nonequivalent perfect codes
- 2007
-
Ingår i: Problems of Information Transmission. - : Pleiades Publishing Ltd. - 0032-9460 .- 1608-3253. ; 43:4, s. 310-315
-
Tidskriftsartikel (refereegranskat)abstract
- We prove that for all n = 2(k)-1, k >= 5. there exists a partition of the set of all binary vectors of length n into pairwise nonequivalent perfect binary codes of length n with distance 3.
|
|
| 2. |
- Avgustinovich, S. V., et al.
(författare)
-
On the structure of symmetry groups of Vasil'ev codes
- 2005
-
Ingår i: Problems of Information Transmission. - : Springer Science and Business Media LLC. - 0032-9460 .- 1608-3253. ; 41:2, s. 105-112
-
Tidskriftsartikel (refereegranskat)abstract
- The structure of symmetry groups of Vasil'ev codes is studied. It is proved that the symmetry group of an arbitrary perfect binary non-full-rank Vasil'ev code of length n is always nontrivial; for codes of rank n - log(n + 1) + 1, an attainable upper bound on the order of the symmetry group is obtained.
|
|
| 3. |
- Bocharova, Irina, et al.
(författare)
-
Dual convolutional codes and the MacWilliams identities
- 2012
-
Ingår i: Problems of Information Transmission. - 0032-9460. ; 48:1, s. 21-30
-
Tidskriftsartikel (refereegranskat)abstract
- A recursion for sequences of spectra of truncated as well as tailbitten convolutional codes and their duals is derived. The order of this recursion is shown to be less than or equal to the rank of the weight adjacency matrix (WAM) for the minimal encoder of the convolutional code. It is sufficient to know finitely many spectra of these terminated convolutional codes in order to obtain an infinitely long sequence of spectra of their duals.
|
|
| 4. |
|
|
| 5. |
- Bocharova, Irina, et al.
(författare)
-
Woven convolutional graph codes with large free distances
- 2011
-
Ingår i: Problems of Information Transmission. - 0032-9460. ; 47:1, s. 1-14
-
Tidskriftsartikel (refereegranskat)abstract
- Constructions of woven graph codes based on constituent convolutional codes are studied and examples of woven convolutional graph codes are presented. The existence of codes, satisfying the Costello lower bound on the free distance, within the random ensemble of woven graph codes based on s-partite, s-uniform hypergraphs, where s depends only on the code rate, is shown. Simulation results for Viterbi decoding of woven graph codes are presented and discussed.
|
|
| 6. |
- Boyvalenkov, P., et al.
(författare)
-
Refinements of Levenshtein Bounds in q-ary Hamming Spaces
- 2018
-
Ingår i: Problems of Information Transmission. - : Pleiades Publishing. - 0032-9460 .- 1608-3253. ; 54:4, s. 329-342
-
Tidskriftsartikel (refereegranskat)abstract
- We develop refinements of the Levenshtein bound in q-ary Hamming spaces by taking into account the discrete nature of the distances versus the continuous behavior of certain parameters used by Levenshtein. We investigate the first relevant cases and present new bounds. In particular, we derive generalizations and q-ary analogs of the MacEliece bound. Furthermore, we provide evidence that our approach is as good as the complete linear programming and discuss how faster are our calculations. Finally, we present a table with parameters of codes which, if exist, would attain our bounds.
|
|
| 7. |
- Handlery, Marc, et al.
(författare)
-
A distance approach to window decoding
- 2002
-
Ingår i: Problems of Information Transmission. - 0032-9460. ; 38:3, s. 169-181
-
Tidskriftsartikel (refereegranskat)abstract
- In convolutional coding, code sequences have infinite length; thus, a maximum-likelihood decoder implies an infinite delay. Due to memory and delay constraints in practical coding schemes, convolutional codes often are either terminated or decoded by a window decoder. When a window decoder is used, the convolutional code sequence is not terminated; instead, the window decoder estimates information digits after receiving a finite number of noise-corrupted code symbols, thereby keeping the decoding delay short. An exact characterization of the error-correcting capability of window decoded convolutional codes is given by using active distances of convolutional codes.
|
|
| 8. |
- Handlery, Marc, et al.
(författare)
-
Encoder and distance properties of woven convolutional codes with one tailbiting component code
- 2002
-
Ingår i: Problems of Information Transmission. - 0032-9460. ; 38:1, s. 41-49
-
Tidskriftsartikel (refereegranskat)abstract
- Woven convolutional codes with one tailbiting component code are studied and their generator matrices are given. It is shown that, if the constituent encoders are identical, a woven convolutional encoder with an outer convolutional warp and one inner tailbiting encoder (WIT) generates the same code as a woven convolutional encoder with one outer tailbiting encoder and an inner convolutional warp (WOT). However, for rate R tb < 1 tailbiting encoders, the WOT cannot be an encoder realization with a minimum number of delay elements. Lower bounds on the free distance and active distances of woven convolutional codes with a tailbiting component code are given. These bounds are equal to those for woven codes consisting exclusively of unterminated convolutional codes. However, for woven convolutional codes with one tailbiting component code, the conditions for the bounds to hold are less strict.
|
|
| 9. |
- Höst, Stefan, et al.
(författare)
-
A distance measure tailored to tailbiting codes
- 2002
-
Ingår i: Problems of Information Transmission. - 0032-9460. ; 38:4, s. 280-295
-
Tidskriftsartikel (refereegranskat)abstract
- The error-correcting capability of tailbiting codes generated by convolutional encoders is described. In order to obtain a description beyond what the minimum distance d min of the tailbiting code implies, the active tailbiting segment distance is introduced. The description of correctable error patterns via active distances leads to an upper bound on the decoding block error probability of tailbiting codes. The necessary length of a tailbiting code so that its minimum distance is equal to the free distance d free of the convolutional code encoded by the same encoder is easily obtained from the active tailbiting segment distance. This is useful when designing and analyzing concatenated convolutional codes with component codes that are terminated using the tailbiting method. Lower bounds on the active tailbiting segment distance and an upper bound on the ratio between the tailbiting length and memory of the convolutional generator matrix such that d min equals d free are derived. Furthermore, affine lower bounds on the active tailbiting segment distance suggest that good tailbiting codes are generated by convolutional encoders with large active-distance slopes.
|
|
| 10. |
- Höst, Stefan, et al.
(författare)
-
Nonequivalent cascaded convolutional codes obtained from equivalent constituent convolutional encoders
- 1998
-
Ingår i: Problems of Information Transmission. - 0032-9460. ; 34:4, s. 291-299, s. 338-338
-
Forskningsöversikt (refereegranskat)abstract
- Cascaded convolutional codes with conventional convolutional codes as constituent codes are powerful and attractive to use in communication systems where very low error probabilities are needed. This paper clearly demonstrates the dramatic effect the replacement of the inner convolutional encoder by an equivalent one could have on the cascaded convolutional code
|
|
