  The rapidly improving performance of modern hardware renders convolutional
codes obsolete, and allows for the practical implementation of more
sophisticated correction codes such as low density parity check (LDPC) and
turbo codes (TC). Both 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 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
the order of $2^{64}$. Under 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 limit, it is still possible to perform correction,
although its cost increases 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 reach the order of $10^{-3}$ for channel error rates 0.08 and
0.18. The proposed correction paradigm can be easily extended to other
communication channels; the appropriate generalizations are also discussed in
this study.
