Variable length binary codes Codeword length .
Average number of code letters (bits) per source symbol ( average length of a codeword):
, for binary code: . If then,
By proper selection of codeword lengths, the minimum distance of one bit from absolute minimum (4.2.2) can be achieved.
Distance from this absolute minimum can be further reduced (minimized) by encoding of sequences of source messages (the L -th extension of a source). Average codeword length of the L -th extension:
but
and Then,
The longer is sequence of encoded source messages, the shorter is distance between and . The assumed distance can be always reached by encoding sequences long enough.
Binary source probability assignment: . Find average length of binary codeword when encoding: a) original source, b) its second extension.
For the given assignment: [bit/message of X ].
When coding original source: ,
[bit/message of X ]; d =0.19 [bit/message of X ].
When coding sequences of L =2 messages:
,
,
,
.
Then, [bit/message of ] and [bit/message of X ]; d =0.03 [bit/message of X ].
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