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Multi-scale fountain encode and decode method based on finite domain

A fountain coding and finite field technology, applied in the field of distributed data storage, can solve problems such as low time efficiency, high decoding complexity of multi-ary fountain codes, and short source length

Inactive Publication Date: 2009-08-19
BEIJING INSTITUTE OF TECHNOLOGYGY
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  • Abstract
  • Description
  • Claims
  • Application Information

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Problems solved by technology

[0011] The present invention aims at the shortcomings of existing binary fountain codes, such as low efficiency and high decoding complexity of multi-ary fountain codes, when the source length is not long, and proposes a multi-ary fountain code and decoding method based on finite fields

Method used

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  • Multi-scale fountain encode and decode method based on finite domain
  • Multi-scale fountain encode and decode method based on finite domain
  • Multi-scale fountain encode and decode method based on finite domain

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Embodiment 1

[0085] Select the source length as K=100, c=0.05, change the parameter δ, use robust solitary wave distribution for the degree of encoding, use the method described in step 1 of the present invention to encode, and then use the method described in step 2 of the present invention to translate code. Selecting two cases of q=2 and q=16, the simulation calculates the relationship between the probability of decoding failure and the coding efficiency as Figure 5 shown. In addition, the coding matrix is ​​randomly and uniformly selected. In the case of q=2 and q=16, the relationship between the probability of decoding failure and the coding efficiency is calculated, and the calculation results are also placed in Figure 5 middle.

[0086] Due to the high density of the random fountain code, it can only be decoded by the conventional Gaussian elimination method, and the decoding complexity is O(K 3 ), which is difficult to apply in practice. This code can be used as a performance...

Embodiment 2

[0093] There is a fountain code with a source length of 5 based on finite field GF(4), let m 1 = 3, m 2 = 2, m 3 = 1, m 4 = 0, m 5 = 1, according to step 1, get:

[0094] 2 m 1 + 3 m 4 = 1 m 2 + 3 m 5 = 1 ...

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Abstract

The invention relates to a multi-system fountain coding and decoding method based on a finite field. Firstly, a fountain code is coded to obtain a fountain coding sequence: a coding-level distribution function Mu(d) is given and a nonnegative integer di is randomly generated according to the distribution function Mu(d), and di is used as the coding level of a coded symbol vi; di different symbols are randomly selected from K information source symbols; di nonzero values are generated in a finite field GF(q) randomly and evenly and used as coding coefficients of the coded symbol vi; weighted sum is obtained for the di different symbols according to the coded coefficients to obtain the value of the coded symbol vi so as to further obtain the fountain coding sequences. Coding sequences with the length of N (N is more than or equal to K) are selected from the fountain coding sequences and designated to be that w equals to (w1, w2, until wN). Decoding is carried out to the coding sequences by pivot selection and pivot in-situ Gauss elimination to obtain a final decoding output sequence. The method greatly improves the fountain coding efficiency, reduces the decoding complexity of the fountain code and is applicable to the fountain codes with various lengths of the information source.

Description

technical field [0001] The present invention relates to a method for encoding and decoding digital fountain codes, in particular to a method for constructing multi-ary digital fountain codes based on finite fields and an efficient decoding method using matrix sparseness, which belongs to wired communication, wireless communication and the Internet Communication data transmission technology field and distributed data storage technology field. Background technique [0002] The digital fountain code is a kind of ratio-free coding. Its basic idea is described by J.Byes, M.Luby, M.Mitzenmacher and A.Rege in "A digital fountain approach to reliable distribution of bulk data" (Proceedings of ACM SIGCOMM'98, Vancouver BC, Canada, pp.56-57, 1998). Digital fountain code is an error correction coding technology applied to erasure channels, and its typical applications include wired and wireless multicast and broadcast services, wireless collaboration and relay, distributed network sto...

Claims

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Application Information

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IPC IPC(8): H03M13/37
Inventor 李祥明安建平
Owner BEIJING INSTITUTE OF TECHNOLOGYGY
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