diff --git a/docs/source/decoding-with-langugage-models/index.rst b/docs/source/decoding-with-langugage-models/index.rst
index 577ebbdfb..6e5e3a4d9 100644
--- a/docs/source/decoding-with-langugage-models/index.rst
+++ b/docs/source/decoding-with-langugage-models/index.rst
@@ -4,6 +4,27 @@ Decoding with language models
 This section describes how to use external langugage models 
 during decoding to improve the WER of transducer models.
 
+The following decoding methods with external langugage models are available:
+
+
+.. list-table:: LM-rescoring-based methods vs shallow-fusion-based methods (The numbers in each field is WER on test-clean, WER on test-other and decoding time on test-clean)
+   :widths: 25 50
+   :header-rows: 1
+
+   * - Decoding method
+     - beam=4
+   * - ``modified_beam_search``
+     - Beam search (i.e. really n-best decoding, the "beam" is the value of n), similar to the original RNN-T paper. Note, this method does not use language model. 
+   * - ``modified_beam_search_lm_shallow_fusion``
+     - As ``modified_beam_search``, but interpolate RNN-T scores with language model scores, also known as shallow fusion
+   * - ``modified_beam_search_LODR``
+     - As ``modified_beam_search_lm_shallow_fusion``, but subtract score of a (BPE-symbol-level) bigram backoff language model used as an approximation to the internal language model of RNN-T.
+   * - ``modified_beam_search_lm_rescore``
+     - As ``modified_beam_search``, but rescore the n-best hypotheses with external language model (e.g. RNNLM) and re-rank them.
+   * - ``modified_beam_search_lm_rescore_LODR``
+     - As ``modified_beam_search_lm_rescore``, but also subtract the score of a (BPE-symbol-level) bigram backoff language model during re-ranking.
+
+
 .. toctree::
    :maxdepth: 2
 
diff --git a/docs/source/decoding-with-langugage-models/rescoring.rst b/docs/source/decoding-with-langugage-models/rescoring.rst
index d71acc1e5..de7e700d0 100644
--- a/docs/source/decoding-with-langugage-models/rescoring.rst
+++ b/docs/source/decoding-with-langugage-models/rescoring.rst
@@ -4,7 +4,11 @@ LM rescoring for Transducer
 =================================
 
 LM rescoring is a commonly used approach to incorporate external LM information. Unlike shallow-fusion-based
+<<<<<<< HEAD
+methods (see :ref:`shallow_fusion`, :ref:`LODR`), rescoring is usually performed to re-rank the n-best hypotheses after beam search.
+=======
 methods (see :ref:`shallow-fusion`, :ref:`LODR`), rescoring is usually performed to re-rank the n-best hypotheses after beam search.
+>>>>>>> 80d922c1583b9b7fb7e9b47008302cdc74ef58b7
 Rescoring is usually more efficient than shallow fusion since less computation is performed on the external LM.
 In this tutorial, we will show you how to use external LM to rescore the n-best hypotheses decoded from neural transducer models in
 `icefall <https://github.com/k2-fsa/icefall>`__.
@@ -225,23 +229,23 @@ Here, we benchmark the WERs and decoding speed of them:
      - beam=4
      - beam=8
      - beam=12
-   * - `modified_beam_search`
+   * - ``modified_beam_search``
      - 3.11/7.93; 132s
      - 3.1/7.95; 177s
      - 3.1/7.96; 210s
-   * - `modified_beam_search_lm_shallow_fusion`
+   * - ``modified_beam_search_lm_shallow_fusion``
      - 2.77/7.08; 262s
      - 2.62/6.65; 352s
      - 2.58/6.65; 488s
-   * - LODR
+   * - ``modified_beam_search_LODR``
      - 2.61/6.74; 400s
      - 2.45/6.38; 610s
      - 2.4/6.23; 870s
-   * - `modified_beam_search_lm_rescore`
+   * - ``modified_beam_search_lm_rescore``
      - 2.93/7.6; 156s
      - 2.67/7.11; 203s
      - 2.59/6.86; 255s
-   * - `modified_beam_search_lm_rescore_LODR`
+   * - ``modified_beam_search_lm_rescore_LODR``
      - 2.9/7.57; 160s
      - 2.63/7.04; 203s
      - 2.52/6.73; 263s