How to make JOIN query use index?

I have two tables:

CREATE TABLE `articles` (
  `id` int(11) NOT NULL AUTO_INCREMENT,
  `title` varchar(1000) DEFAULT NULL,
  `last_updated` datetime DEFAULT NULL,
  PRIMARY KEY (`id`),
  KEY `last_updated` (`last_updated`),
) ENGINE=InnoDB AUTO_INCREMENT=799681 DEFAULT CHARSET=utf8 

CREATE TABLE `article_categories` (
  `article_id` int(11) NOT NULL DEFAULT '0',
  `category_id` int(11) NOT NULL DEFAULT '0',
  PRIMARY KEY (`article_id`,`category_id`),
  KEY `category_id` (`category_id`)
) ENGINE=InnoDB DEFAULT CHARSET=utf8 |

This is my query:

SELECT a.*
FROM
    articles AS a,
    article_categories AS c
WHERE
    a.id = c.article_id
    AND c.category_id = 78
    AND a.comment_cnt > 0
    AND a.deleted = 0
ORDER BY a.last_updated
LIMIT 100, 20

And an EXPLAIN for it:

*************************** 1. row ***************************
           id: 1
  select_type: SIMPLE
        table: a
         type: index
possible_keys: PRIMARY
          key: last_updated
      key_len: 9
          ref: NULL
         rows: 2040
        Extra: Using where
*************************** 2. row ***************************
           id: 1
  select_type: SIMPLE
        table: c
         type: eq_ref
possible_keys: PRIMARY,fandom_id
          key: PRIMARY
      key_len: 8
          ref: db.a.id,const
         rows: 1
        Extra: Using index

It uses a full index scan of last_updated on the first table for sorting but does not use any index for join (type: index in explain). This is very bad for performance and kills the whole database server since this is a very frequent query.

I've tried reversing table order with STRAIGHT_JOIN, but this gives filesort, using_temporary, which is even worse.

Is there any way to make MySQL use index for joining and for sorting at the same time?

=== update ===