probabilities sum to 1.000000 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 0 0.000000 0 0.084337 0 0.216867 1 0.369478 1 0.566265 2 0.742972 2 0.963855 3 1.168675 3 1.385542 4 1.634538 4 1.911647 5 2.144578 6 2.413655 6 2.650602 6 2.895582 6 3.180723 7 3.473896 8 3.759036 8 4.028112 8 4.361446 9 1 ------------- 0.000000 0 0.092369 1 0.236948 2 0.401606 2 0.574297 3 0.791165 3 0.995984 3 1.180723 4 1.429719 4 1.702811 5 1.931727 6 2.200803 6 2.437751 6 2.682731 6 2.963855 8 3.228916 8 3.514056 8 3.783133 8 4.116466 10 2 ------------- ------------- 0.000000 0 0.100402 2 0.257028 3 0.393574 3 0.610442 3 0.807229 5 0.987952 5 1.204819 5 1.477912 5 1.706827 6 1.975904 8 2.208835 8 2.445783 8 2.726908 8 2.991968 8 3.244980 9 3.514056 9 3.847390 10 3 ------------- ------------- ------------- 0.000000 0 0.108434 3 0.244980 3 0.417671 4 0.610442 5 0.791165 5 1.008032 6 1.240964 6 1.465863 6 1.730924 8 1.963855 8 2.200803 8 2.481928 8 2.746988 8 2.995984 10 3.228916 10 3.562249 10 4 ------------- ------------- ------------- ------------- 0.000000 0 0.096386 4 0.253012 5 0.409639 5 0.590361 5 0.791165 6 1.024096 6 1.216867 7 1.477912 8 1.706827 9 1.943775 9 2.212851 9 2.477912 9 2.726908 10 2.959839 10 3.261044 11 5 ------------- ------------- ------------- ------------- ------------- 0.000000 0 0.100402 5 0.248996 6 0.385542 6 0.582329 6 0.803213 8 0.995984 8 1.216867 8 1.441767 9 1.678715 9 1.947791 9 2.204819 10 2.449799 10 2.682731 10 2.975904 12 6 ------------- ------------- ------------- ------------- ------------- ------------- 0.000000 0 0.108434 6 0.244980 6 0.409639 7 0.622490 8 0.815261 8 1.036145 8 1.228916 9 1.465863 9 1.726908 10 1.983936 10 2.228916 10 2.461847 10 2.755020 12 7 ------------- ------------- ------------- ------------- ------------- ------------- ------------- 0.000000 0 0.092369 7 0.236948 8 0.409639 8 0.590361 9 0.803213 9 0.995984 9 1.192771 10 1.453815 11 1.702811 11 1.947791 11 2.172691 12 2.461847 12 8 ------------- ------------- ------------- ------------- ------------- ------------- ------------- ------------- 0.000000 0 0.096386 8 0.253012 9 0.401606 9 0.610442 10 0.799197 10 0.987952 10 1.216867 11 1.465863 11 1.706827 12 1.931727 12 2.212851 14 9 ------------- ------------- ------------- ------------- ------------- ------------- ------------- ------------- ------------- 0.000000 0 0.112450 9 0.261044 9 0.425703 10 0.614458 10 0.803213 10 1.028112 12 1.240964 12 1.477912 12 1.702811 12 1.983936 14 10 ------------- ------------- ------------- ------------- ------------- ------------- ------------- ------------- ------------- ------------- 0.000000 0 0.104418 10 0.261044 10 0.409639 11 0.598394 11 0.811245 12 1.024096 12 1.228916 13 1.453815 13 1.726908 14 11 ------------- ------------- ------------- ------------- ------------- ------------- ------------- ------------- ------------- ------------- ------------- 0.000000 0 0.100402 11 0.244980 11 0.385542 12 0.590361 12 0.795181 14 0.991968 14 1.180723 14 1.453815 14 12 ------------- ------------- ------------- ------------- ------------- ------------- ------------- ------------- ------------- ------------- ------------- ------------- 0.000000 0 0.100402 12 0.240964 12 0.409639 13 0.606426 14 0.803213 14 0.991968 14 1.228916 15 13 ------------- ------------- ------------- ------------- ------------- ------------- ------------- ------------- ------------- ------------- ------------- ------------- ------------- 0.000000 0 0.092369 13 0.240964 14 0.401606 14 0.590361 15 0.771084 15 1.000000 16 14 ------------- ------------- ------------- ------------- ------------- ------------- ------------- ------------- ------------- ------------- ------------- ------------- ------------- ------------- 0.000000 0 0.104418 14 0.261044 15 0.409639 15 0.590361 15 0.815261 16 15 ------------- ------------- ------------- ------------- ------------- ------------- ------------- ------------- ------------- ------------- ------------- ------------- ------------- ------------- ------------- 0.000000 0 0.108434 15 0.257028 15 0.401606 16 0.614458 16 16 ------------- ------------- ------------- ------------- ------------- ------------- ------------- ------------- ------------- ------------- ------------- ------------- ------------- ------------- ------------- ------------- 0.000000 0 0.100402 16 0.236948 16 0.409639 17 17 ------------- ------------- ------------- ------------- ------------- ------------- ------------- ------------- ------------- ------------- ------------- ------------- ------------- ------------- ------------- ------------- ------------- 0.000000 0 0.092369 17 0.244980 18 18 ------------- ------------- ------------- ------------- ------------- ------------- ------------- ------------- ------------- ------------- ------------- ------------- ------------- ------------- ------------- ------------- ------------- ------------- 0.000000 0 0.104418 18 19 ------------- ------------- ------------- ------------- ------------- ------------- ------------- ------------- ------------- ------------- ------------- ------------- ------------- ------------- ------------- ------------- ------------- ------------- ------------- 0.000000 0 Code tree: 19 17 19 cost 0.244980 18 17 18 cost 0.092369 17 15 19 cost 0.614458 16 15 16 cost 0.108434 15 10 19 cost 1.726908 14 13 14 cost 0.092369 13 12 14 cost 0.240964 12 10 14 cost 0.598394 11 10 11 cost 0.104418 10 0 19 cost 4.361446 9 7 9 cost 0.236948 8 7 8 cost 0.092369 7 5 9 cost 0.582329 6 5 6 cost 0.100402 5 0 9 cost 1.634538 4 3 4 cost 0.108434 3 0 4 cost 0.566265 2 0 2 cost 0.216867 1 0 1 cost 0.084337 0 Codes & prob*# of bits 0 00000 0.200803 1 00001 0.220884 2 0001 0.192771 3 0010 0.208835 4 0011 0.224900 5 0100 0.160643 6 0101 0.240964 7 01100 0.240964 8 01101 0.220884 9 0111 0.208835 10 1000 0.240964 11 1001 0.176707 12 1010 0.224900 13 10110 0.220884 14 10111 0.240964 15 1100 0.224900 16 1101 0.208835 17 11100 0.240964 18 11101 0.220884 19 1111 0.240964 Expected bits per symbol 4.361446