# On the distribution of the number of computations in any finite number of subtrees for the stack algorithm

@article{Johannesson1985OnTD, title={On the distribution of the number of computations in any finite number of subtrees for the stack algorithm}, author={Rolf Johannesson and Kamil Sh. Zigangirov}, journal={IEEE Trans. Inf. Theory}, year={1985}, volume={31}, pages={100-102} }

Multitype branching processes have been employed to determine the stack algorithm computational distribution for one subtree. These results are extended here to the distribution of the number of computations in any finite number of subtrees. Starting from the computational distribution for K-1 subsequent subtrees, a recurrent equation for the distribution for K subsequent subtrees is determined.

## 5 Citations

### Bounds on a probability for the heavy tailed distribution and the probability of deficient decoding in sequential decoding

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A new bound on a probability in the tail of the heavy tailed distribution is given and this bound is used to prove the long-standing conjecture on PG, that is, PG ap constanttimes1/(sigmarhoNrho-1) for a large speed factor sigma of the decoder and for aLarge receive buffer size N whenever the coding rate R and rho satisfy E(rho)=rhoR for 0 les rho les 1.

### Analysis of Sequential Decoding Complexity Using the Berry-Esseen Inequality

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His study presents a novel technique to estimate the computational complexity of sequential decoding using the Berry-Esseen theorem, and finds that the theoretical upper bound for the simplified GDA almost matches the simulation results as the signal-to-noise ratio (SNR) per information bit ($\gamma_b$) is greater than or equal to 8 dB.

### Sequential Decoding of Convolutional Codes

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This article surveys many variants of sequential decoding in literature, and presents the Algorithm A, a general sequential search algorithm, and classes of convolutional codes that are particularly appropriate for sequential decoding are outlined.

### New importance sampling methods for simulating sequential decoders

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- 1993

Two importance sampling techniques are presented for estimating the distribution of computation of sequential decoding for specific convolutional codes (not ensemble averages). Only stack algorithm…

### Wiener odd and even indices on BC-Trees

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It is theoretically that Wiener odd index is not more than its even index for general BC-Trees and closed formulae of the two indices are provided for path BC-tree, star, k-extending star tree and caterpillar BC- tree.

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