Now it's time to apply a little entropy encoding to our signal. Remember that we did use wavelet transformations to create the sub-bands. This means we have wavelet coefficients. JPEG 2000 uses the Elias entropy code to do this. In the Elias entropy code, a positive integer x is represented by 1 + floor(log(2) x) in unary, followed by the binary representation of x without its most significant bit. This means that it is not necessary to transmit the entropy coding table with the compressed file. A utility that decompresses the file will already know how the data was manipulated.
Again, since the image is broken up into sub-bands and tiles, we can apply the entropy encoding to every tile in parallel. This means we can significantly decrease the time needed to compress or decompress the file while retaining the same level of quality. However, we should also note that this Elias coding is not great for extremely large integers. But, since we are only dealing with 32-bit and 64-bit computers, the Elias coding should suffice. In the future, when we have 1-kbit and greater processors, we can switch to the Second Elias Code, or the Delta Code, which is optimized for extremely large integers.