Error-trellis state complexity of LDPC convolutional codes based on circulant matrices

Abstract

We consider the decoding of convolutional codes using an error trellis constructed based on a submatrix of a given check matrix. In the proposed method, the syndromesubsequence computed using the remaining submatrix is utilized as auxiliary information for decoding. Then the ML error path is correctly decoded using the degenerate error trellis. We also show that the decoding complexity of the proposed method is basically identical with that of the conventional one based on the original error trellis. Next, we apply the method to check matrices with monomial entries proposed by Tanner et al. By choosing any row of the check matrix as the submatrix for errortrellis construction, a 1-state error trellis is obtained. Noting the fact that a likelihood-concentration on the all-zero state and the states with many 0's occurs in the error trellis, we present a simplified decoding method based on a 1-state error trellis, from which decoding-complexity reduction is realized.

Asymptotic freedom in inflationary cosmology with a non-minimally coupled Higgs field

“…However, this pessimistic conclusion, which contradicts the widely accepted range 115 GeV≤ M H ≤ 180 GeV, did not take into account O(1) contributions due to running logarithms in the quantum effective action, which can qualitatively improve the situation. 2 This was nearly simultaneously observed in [4,5,23] where the renormalization group (RG) improvement of the one-loop results of [3] was considered and it was found that the Higgs-mass range compatible with the CMB data almost coincides with the conventional one.…”