The prophecy in Ezekiel 4 is a prophecy whose symbols are portrayed via the prophet's own actions. What Ezekiel does must be understood as symbolic, typifying the events foretold.
As with the dreams of the baker and the butler, a similar method of interpretation to Ezekiel's prophecy applies. In the dreams Joseph interpreted for the two men, the three baskets of bread represented days until the fulfillment of the dream was to occur--not days of the baker's punishment. The days of Ezekiel's laying on his side do not indicate years of Israel's punishment, but rather, years of probation until that punishment would come.
As another answer has suggested, the 390 years represented by the 390 days in Ezekiel's demonstration that were given for the "iniquity of Israel," began with the first year of the reign of Jeroboam who split away from Rehoboam with 10 of the tribes, also called the "Northern Kingdom" and "Israel." Solomon's son Rehoboam was left to govern just two tribes: Judah and Benjamin, the latter being so small and insignificant in comparison to the former that it became called simply "Judah" (the Southern Kingdom).
The entire prophecy, for both Israel and for Judah, is directed at the city of Jerusalem, however; not to the tribes generally. The siege predicted was to come to Jerusalem, and Jerusalem was in the Southern Kingdom. Therefore, to assume that the Northern Kingdom (Israel) would be punished for 390 years is incorrect for another specific reason: Jerusalem was not within the boundaries of the Northern Kingdom.
At the end of the 390 years, Jerusalem is broken up and Solomon's temple is destroyed. Judah's sin happens much later in time, is much greater in significance, and less probation is granted afterward before the temple, the second one, is again destroyed. It was 40 years after Christ's crucifixion that Jerusalem was broken up and the temple destroyed.
While the total of 390 and 40 is 430, the twin prophecies are not fulfilled in back-to-back fashion, and many mistakenly attempt to combine and correlate them to the years noted in Exodus 12:40-41 for the sojourn of the Israelites in Egypt. Ezekiel's prophecies are not contiguous; they are parallel prophecies, having parallel sins (the rejection of God and the worship of God) and parallel fulfillments (the destruction of the temple at the end of a siege).
The defiled bread applies to the fact that the siege would be so severe as to cause the people to eat defiled food (e.g. their own boiled children). Most of the chapter focuses on the severity of the siege, such as the drinking of water by ration, and the cooking of food over dung. But the siege is not predicted to last 390 or 40 years--those numbers point to the time of fulfillment of the prophecy, not the duration of these conditions.
