Correction Trees as an Alternative to Turbo Codes and Low Density Parity Check Codes

Details Correction Trees as an Alternative to Turbo Codes and Low Density Parity Check Codes Correction Trees as an Alternative to Turbo Codes and Low Density Parity Check Codes

2012-04-24

arxiv.org/abs/1204.5317v1

Computer Science

Information Theory

14 pages, 7 figures

Scientific paper

Quickly increasing performance of modern hardware renders convolutional codes obsolete, and allows for practical implementation of more sophisticated correction codes like Low Density Parity Check (LDPC) and Turbo Codes (TC). Both of them are decoded by iterative algorithms, which require a disproportional computational effort for low channel noise. They are also unable to correct higher noise levels, still below the Shannon's theoretical limit. In this paper, we discuss an enhanced version of a convolutional-like decoding paradigm, which adopts very large spaces of possible system states, of order 2e64. In such conditions, the traditional convolution operation is rendered useless and needs to be replaced by a carefully designed state transition procedure. The size of the system state space completely changes the correction philosophy, as state collisions are virtually impossible and the decoding procedure becomes a correction tree. The proposed decoding algorithm is practically cost-free for low channel noise. As the channel noise approaches the Shannon's limit, there still remains complete correction possibility, yet its cost grows up to infinity. In many applications, the implemented decoder can essentially outperform both LDPC and TC. This paper describes the proposed correction paradigm and theoretically analyzes the asymptotic correction performance. The considered encoder and decoder were verified experimentally for the binary symmetric channel. The correction process remains practically cost-free for channel error rates below 0.05 and 0.13 for the 1/2 and 1/4 rate codes, respectively. For the considered resource limit, the output bit error rates become of order 1e-3 for channel error rates 0.08 and 0.18. The proposed correction paradigm can be easily extended to other communication channels and appropriate generalizations are also discussed in this study.

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