Parlance's CTC prefix Beam search decoding logic insights

Question

I was looking at Parlance's version of CTCDecoder here. But as I look into the code, eg. here or the below code,

  std::vector<std::pair<size_t, float>> log_prob_idx =
        get_pruned_log_probs(prob, cutoff_prob, cutoff_top_n, log_input);
    // loop over chars
    for (size_t index = 0; index < log_prob_idx.size(); index++) {
      auto c = log_prob_idx[index].first;
      auto log_prob_c = log_prob_idx[index].second;

      for (size_t i = 0; i < prefixes.size() && i < beam_size; ++i) {
        auto prefix = prefixes[i];
        if (full_beam && log_prob_c + prefix->score < min_cutoff) {
          break;
        }
        // blank
        if (c == blank_id) {
          prefix->log_prob_b_cur =
              log_sum_exp(prefix->log_prob_b_cur, log_prob_c + prefix->score);
          continue;
        }
        // repeated character
        if (c == prefix->character) {
          prefix->log_prob_nb_cur = log_sum_exp(
              prefix->log_prob_nb_cur, log_prob_c + prefix->log_prob_nb_prev);
        }
        // get new prefix
        auto prefix_new = prefix->get_path_trie(c, abs_time_step, log_prob_c);

        if (prefix_new != nullptr) {
          float log_p = -NUM_FLT_INF;

          if (c == prefix->character &&
              prefix->log_prob_b_prev > -NUM_FLT_INF) {
            log_p = log_prob_c + prefix->log_prob_b_prev;
          } else if (c != prefix->character) {
            log_p = log_prob_c + prefix->score;
          }

          // language model scoring
          if (ext_scorer != nullptr &&
              (c == space_id || ext_scorer->is_character_based())) {
            PathTrie *prefix_to_score = nullptr;
            // skip scoring the space
            if (ext_scorer->is_character_based()) {
              prefix_to_score = prefix_new;
            } else {
              prefix_to_score = prefix;
            }

            float score = 0.0;
            std::vector<std::string> ngram;
            ngram = ext_scorer->make_ngram(prefix_to_score);
            score = ext_scorer->get_log_cond_prob(ngram) * ext_scorer->alpha;
            log_p += score;
            log_p += ext_scorer->beta;
          }
          prefix_new->log_prob_nb_cur =
              log_sum_exp(prefix_new->log_prob_nb_cur, log_p);
        }
      }  // end of loop over prefix
    }    // end of loop over vocabulary

I couldn't get the intuition on operations done for blank_id or repeated character withing the inner for loop, also there was not enough comments on the code, to convey the intuition.

I surfed through the reference links provided with the repo and a few google searches, but couldn't find a neat explanation stating why. If any of you could guide me to a resource or a basic intuition would be more helpful.

Thanks in advance.