We demonstrated that these codes can outperform the rate-adaptive LDPCA codes when employed in a high-correlation scenario using short block lengths.
The proposed codes have been analyzed in a high-correlation scenario, where the marginal probability of each symbol, X i in X, given Y is highly skewed (unbalanced).
In the high-correlation scenario, with short block length, for lower values of p, longer block lengths are more efficient, but for higher error probabilities, shorter block lengths are preferable.
The main motivations of the study on RA BCH codes is the relatively low efficiency of LDPCA (and Turbo) codes when using a short packet length in a high-correlation scenario and the fact that the analysis of the performance of the RA BCH codes is simpler.
An initial study on RA BCH codes was presented in [15], where we proposed a model for RA BCH codes: we demonstrated that BCH codes were able to outperform LDPCA codes in the high-correlation scenario, and we validated the correctness of the results of our model.
In this work, we focused on a high-correlation scenario p ≤ 0.04 (H(X|Y) ≤ 0.24), but we also assessed the performance of our code for p = 0.1 (H(X|Y) = 0.47) in order to assess the robustness of the proposed code in terms of the ability of the proposed codes (including checking strategy) to perform reasonably well outside the error interval they have been developed for.
In Figure 4, the outage probability is plotted against the correlation coefficient of the channels for the low, medium, and high spatial correlation scenarios in the channels.
We focused on a high correlation (low entropy) scenario; hence, we chose low values of p. Among all the possible strategies, some can be inefficient, i.e. there are strategies having the same (or higher) rate but still achieving worse BER than another strategy.
They correspond to a high and a low correlation scenario, respectively [29].
In general, the algorithm average efficiency increases with heritability but some exceptions can be found, particularly under data structure S10. Figure 1 shows the marginal posterior distributions and trace plots for the overall mean of the threshold level obtained in one replication in the scenarios of high correlation and low, medium and high heritabilities when the data structure was S10.
