compression and decompression of string data in java

This is because of

String outStr = obj.toString("UTF-8");

Send the byte[] which you can get from your ByteArrayOutputStream and use it as such in your ByteArrayInputStream to construct your GZIPInputStream. Following are the changes which need to be done in your code.

byte[] compressed = compress(string); //In the main method

public static byte[] compress(String str) throws Exception {
    ...
    ...
    return obj.toByteArray();
}

public static String decompress(byte[] bytes) throws Exception {
    ...
    GZIPInputStream gis = new GZIPInputStream(new ByteArrayInputStream(bytes));
    ...
}