Hello, for a long while, I've been confused with the rules governing rendaku (連濁 ), and I want to have a clear understanding about this phenomina where the first mora of the second element gains a dakuten.

A modified version of Lyman's Law states that rendaku does not occur when the second element of the compound contains a voiced obstruent in any position. Now what is meant by voiced obstruent? I'm uncertain if it means that the second element contains a mora with a dakuten.

Examples:

[maki]+[sushi] = [makizushi]

[hira]+[kana] =[hiragana]
[furi]+[kana] = [furigana]
[okuri]+[kana] = [okurigana]

yet:

[kata]+[kana] = [katakana]

Why was it omitted for katakana? Is it because it's considered a 'foreign' word?

Also there's rules based on semantics and branching constraints.

Rendaku has no rule as yet discovered. Lyman's law is an approximation that works much of the time but not always.

As far as Japanese is concerned, the "voiced obstruents" are d, g, z, b, and j. "n" is not an obstruent, it's a sonorant.

Quote:Why was it omitted for katakana?

"katakana" is not a foreign word; it's made from native Japanese morphemes just like "hiragana". The reason why one has voice and the other doesn't cannot be explained (or at least not easily).

Quote:I want to have a clear understanding about this phenomina where the first mora of the second element gains a dakuten.

This is not possible; even linguists who study the issue do not have a clear understanding. You just have to memorize the words.

(Lastly I'm being really really picky here but there's no such thing as a "mora with a dakuten" -- kana can have dakuten, mora cannot, since they exist in the spoken language as well as written.)

You can't have a clear understanding of rendaku unless a major breakthrough comes in linguistics. Besides, even native speakers can get confused when dealing with proper nouns and words from dialects. Ask a random Japanese guy on the street if 茨城 is いばらき or いばらぎ. Chances are he doesn't know.

As for voiced obstruents, you can think of them as those moras usually written by kana with dakuten, though technically they only refer to the consonant part of them. So as yudantaiteki says, if you type a kana with d, g, z, b, or j plus either a, i, u, e, or o, you get a mora with a voiced obstruent.

A tricky thing is that their unvoiced versions may be different depending on whether you're talking about grammar or phonetics. For example, t, k, and s are the unvoiced versions of d, g, and z in both phonetic and grammatical senses. But while the unvoiced version of consonant b is p in the phonetic sense, the grammatically unvoiced version of b is h in Japanese. This is because the sound of Japanese has changed rather drastically while renduku grammar etc. haven't changed to the same degree.

It doesn't seem like the Wikipedia article explains this, but the sound change of renduku occurs only when the first consonant of the latter word is either t, k, s, or h. These four guys and their grammatical voiced versions d, g, z, and b also appear other sound change rules like saku+kyoku = sakkyoku. So my advice is you learn these four guys are kind of special and move on.

If you want to learn renduku a little deeper than Wikipedia, here's a blog about rendaku. All posts are about the phenomenon and written in Japanese.

http://rendaku.exblog.jp/

If you really really want to learn it deeply, there are a lot of research results out there. They require native level understanding of the Japanese language though. e.g., you should be able to intuitively tell how a native speaker's mind works differently when he pronounces やまがわ and やまかわ, both of which are 山川.

This really isn't worth worrying about. After a while it just becomes intuative when to do 連濁 or not. Another thing no one mentioned is the common modifacation of two sylable kanji readings がく -> がっ or せつ -> せっ. When つ becomes っ before は行 the はひふへほ becomes ぱぴぷぺぽ. For example 切腹（せっぷく）. But again this will become intuative in time