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aThe proposed technique is also applicable to other BICM-ID techniques, so far as they use LP for degree allocation optimization.
Hence, the process for determining the optimal degree allocation using LP [13, 14] is also included in the repeat-until loop in EBSA.
The proposed EBSA is applicable to BICM-ID techniques using other codes, so far as the degree allocation optimization can be performed using LP.
EBSA is composed of node degree allocation optimization using linear programming (LP) and labeling optimization based on adaptive binary switching algorithm jointly.
More details are given in Appendix 1. Furthermore, to find the optimal check node degree d c, this article proposes a brute-force search (all possible value search),c as summarized in Algorithm 1. Algorithm 1 Optimal degree allocation algorithm.
With the EBSA framework, the labeling pattern used in the LP-based degree allocation optimization for DSI-BICM-ID-EM are obtained by lowering the cost of Z ℓ map - 1 (at right-most MI point corresponding to the case with full a priori information) as much as possible, while still keeping the vertical gap smaller than the predefined value δ w.
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This is mainly because the EBSA algorithm jointly optimize the labeling patterns and degree allocations as a systematic framework.
The repetition times d v, referred to as variable node degree, may take different values in a block (transmission frame); if d v takes several different values in a block, such code is referred to as having irregular degree allocations.
Tables 1 and 2 show the node degree allocations before and after performing LP for ℓmap = 5 and SNR = 0.8 dB, where the simplex algorithm was used as a tool for LP.
With the same initial degree allocations and ϵ settings, EBSA was performed for SNR = 3.1 dB. Figure 7 show with and without optimization the EXIT curves for SNR = 0.8 dB and 3.1 dB, respectively, for SI-BICM-ID-EM.
We investigated in [14] that linear programming (LP) technique can be applied for SI-BICM-ID-EM to determine the optimal degree allocations for the IRC code with the aim of achieving desired convergence property.
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