H denotes HSPA (High Speed Packet Access). It is one of 3G network type and not 4G. H provides upto 14Mbps download Speed.
3G provides transfer rate of atleast .2Mbps. However, many services advertised as 3G provide higher speed than the minimum technical requirements for a 3G service.
EDGE is 2G connection.
Do you have issue with Internet Access? Then look at the symbols.
4G,H+,H,3G,EDGE(2G) and GPRS = You have got Mobile Internet Connection!
4g, h+,h,3g,edge and gprs = You can only make call.You cannot access Internet.