The read() call on the receiving side can use a buffer of arbitrary
length- you might just have to call read() more often if you use a very
small buffer.
Note that the read() call will most probably NOT fill a 1-Mbyte buffer,
but will return after reading less data. So you have to interpret the
return value of your InputStream.read() call ! (If you know that there
is a 1Mbyte chunk coming, you have to call read() in a loop until all
data is read.
The following piece of code might help you:
public static void readCompleteBlocking(InputStream is,byte[] target)
                       throws IOException
  {
     int readBytes=0;
     while(readBytes<target.length){
        int read=is.read(target,readBytes,target.length-readBytes);
        if(read<1)throw new IOException("read() returned 0 or
negative");
        readBytes+=read;
     }
  }