## Bounds of redundancy estimates for word-based encoding of sequences produced by a Bernoulli source (1972)

Venue: | Russian), Problemy Peredachi Informacii |

Citations: | 3 - 0 self |

### BibTeX

@INPROCEEDINGS{Khodak72boundsof,

author = {G. L. Khodak},

title = {Bounds of redundancy estimates for word-based encoding of sequences produced by a Bernoulli source},

booktitle = {Russian), Problemy Peredachi Informacii},

year = {1972}

}

### OpenURL

### Abstract

The efficiency of a code is estimated by its redundancy R, while the complexity of a code is estimated by its average delay ¯N. In this work we construct word-based codes, for which R � ¯ N −5/3. Therefore, word-based codes can attain the same redundancy as block-codes while being much less complex. We also consider uniform on the output codes, the benefit of which is the lack of a running synchronization error. For such codes ¯ N −1 � R � ¯ N −1, except for a case when all input symbols are equiprobable, when R � ¯ N −2 for infinitely many ¯ N. 1

### Citations

7146 |
A mathematical theory of communication
- Shannon
- 1948
(Show Context)
Citation Context ...For block codes |Aj| = ¯ N = N (j = 1, . . .,m n ). The efficiency of a code is estimated by using its redundancy: R = ¯ ∑ −1 N j p (Aj) |φ(Aj)| − H log −1 2 n. C. Shannon has shown that 0 � R � N −1 =-=[2]-=-. From the paper of V. M. Sidelnikov [3] ∗ Translation from Russian original: ”Ocenki izbytochnosti pri poslovnom kodirovanii soobscheniy, porojdaemyh bernullievskim istochnikom”, Problemy Peredachi I... |

1053 |
A method for the construction of minimum redundancy codes
- Huffman
- 1952
(Show Context)
Citation Context ... at (36). Observe that (36) is a Kraft inequality for a coding system with code lengths {l (Aj)}. This means, that there exists a decipherable prefix code with |φ(Aj)| = l (Aj) (i = 1, 2, . . .) (see =-=[7]-=-). The redundancy of such a code provides an upper bound for the redundancy of the optimal one, which can be found by using Huffman technique [7]. From (27) it follows that for any j |εj| � 1 (see [2,... |

83 | An introduction to Diophantine approximation, Cambridge Tracts - Cassels - 1957 |

44 |
Two inequalities implied by unique decipherability
- McMillan
- 1956
(Show Context)
Citation Context ...ntroduce the following notation: δ j = 1 − ∑ n −|φ(Aj)| j εj = |φ(Aj)| + logn p (Aj) (j = 1, 2, . . .) (3) ε ′ j = ⎧ ⎨ −1 if εj < −1 , εj if |εj| � 1 , (4) ⎩ 1 if εj > 1 . It is well known (see, e.g. =-=[5]-=-), that the necessary and sufficient condition for the existence of a decipherable code with lengths of codewords |φ(Aj)| (j = 1, 2, . . .) is given by the Kraft inequality δ � 0. Theorem 1. The redun... |

5 |
On Statistical Properties of Transformations Carried out by Finite Automata
- Sidelnikov
- 1965
(Show Context)
Citation Context ... . .,m n ). The efficiency of a code is estimated by using its redundancy: R = ¯ ∑ −1 N j p (Aj) |φ(Aj)| − H log −1 2 n. C. Shannon has shown that 0 � R � N −1 [2]. From the paper of V. M. Sidelnikov =-=[3]-=- ∗ Translation from Russian original: ”Ocenki izbytochnosti pri poslovnom kodirovanii soobscheniy, porojdaemyh bernullievskim istochnikom”, Problemy Peredachi Informacii (Problems of Information Trans... |

2 |
Certain properties of code systems
- Levenšteĭn
- 1961
(Show Context)
Citation Context ...s = t and φ(Aik ) = φ(Ajk ), k = 1, . . .,s. Constructed codes have, in fact, an even more strong property, namely that different messages have different codes. In the terminology of V. I. Levenstein =-=[1]-=-, word-based code is specified by a coding system {A, U, B, V }, where A is the input alphabet, B is the output alphabet, U is the set of words Aj, V = φ(Aj), and it is required that U is strongly (pr... |

1 |
The Length of a Block Necessary for Attaining any
- Krichevski
- 1966
(Show Context)
Citation Context ...letters per each input letter is greater than the minimum necessary. Note, that both redundancy and average delay are continuous functions of probabilities of symbols p1, . . . , pm. R. E. Krichevski =-=[4]-=- has shown that for optimal block-codes R � N −1 (N → ∞), except for the sources with coinciding fractional parts of logn pi 1 . In the present paper, we construct word-based codes, for which R � ¯ N5... |