It's basically a bacterial imbalance. Something you are eating is not being digested properly and is fermenting causing the gas. IF you reinstate beneficial bacteria you will improve digestive funtion and eliminate not only the gas, but the stinkiness.
Many things can help, probiotics, enzymes, different dietary choices etc. At the very least I would start with probiotics or fermented foods (kimchi, saurkraut)
Source of enzymes
All digestive enzymes come from two living sources: plants or animals. The plant group includes both those enzymes derived from plant sources (pineapple, papaya, kiwi) and microbial (fungal) sources. In general, plant enzymes are preferable when possible. They offer several advantages over enzymes from animal sources. Plant and microbial enzymes are much more effective in the pH and temperature ranges of the body.
Our pancreas, when working properly, secretes a number of enzymes to digest food as it enters the small intestine. But as we age, or in some disease states, this enzyme secretion may not be adequate to completely digest the food we eat. This can result in pain, cramping, excessive gas, certain food intolerances, and inflammation. Pancreatic enzymes are available by prescription (Creon, Viokase) or over the counter. However, pancreatic enzymes are not stable to the acid conditions found in the stomach, so a good portion of them may be destroyed unless the preparation is treated in such a way, like being enterically coated, so that the enzymes will not be released until they arrive in the small intestine.
Plant and microbial enzymes, however, are stable in acidic conditions. They help digest the cooked and raw foods in the higher pH of the upper part of the stomach, the acidic lower part of the stomach as well as in the alkaline intestines. Digestion in the upper stomach actually mimics the natural process of eating raw foods, which contain some amount of the enzymes needed to break down the food itself. The additional ‘pre-digestion’ provided by plant and microbial enzymes leaves the pancreas to provide the ‘finishing touches’ to the digestive process in a less stressful manner. The intestinal tract will be better able to absorb and assimilate the nutrients and vitamins in the meal.