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A prefix-free code is a code in which no codeword appears as the initial segment (prefix) of any other codeword. For every pair of distinct codewords, neither may begin with the other as a prefix.

Conditions: Defined relative to concatenation of binary strings.; For every pair of distinct codewords $c_a$, $c_b$, neither $c_a$ is a prefix of $c_b$ nor $c_b$ is a prefix of $c_a$.

A prefix-free code is a code in which no codeword appears as the initial segment (prefix) of any other codeword. For every pair of distinct codewords, neither may begin with the other as a prefix.

Conditions: Defined relative to concatenation of binary strings.; For every pair of distinct codewords $c_a$, $c_b$, neither $c_a$ is a prefix of $c_b$ nor $c_b$ is a prefix of $c_a$.

A non-prefix-free code causes ambiguity because a received bit string can be segmented in more than one way into valid codewords. For Code 3, the received string 00 can be parsed as two copies of the codeword 0 (giving $x_1x_1$) or as one copy of the codeword 00 (giving $x_3$).

Conditions: Occurs when at least one codeword is a prefix of another codeword.; Illustrated here for concatenated received strings under Code 3.

A non-prefix-free code causes ambiguity because a received bit string can be segmented in more than one way into valid codewords. For Code 3, the received string 00 can be parsed as two copies of the codeword 0 (giving $x_1x_1$) or as one copy of the codeword 00 (giving $x_3$).

Conditions: Occurs when at least one codeword is a prefix of another codeword.; Illustrated here for concatenated received strings under Code 3.

Code 3 fails the prefix-free condition because specific codewords act as prefixes for other codewords within the same code. Specifically, the codeword 0 assigned to $x_1$ is a prefix of the codeword 00 assigned to $x_3$, and the codeword 1 assigned to $x_2$ is a prefix of the codeword 11 assigned to $x_4$.

Conditions: Use the Code 3 column of the displayed table.; Apply the prefix-free definition: no codeword is a prefix of another.

Code 3 fails the prefix-free condition because specific codewords act as prefixes for other codewords within the same code. Specifically, the codeword 0 assigned to $x_1$ is a prefix of the codeword 00 assigned to $x_3$, and the codeword 1 assigned to $x_2$ is a prefix of the codeword 11 assigned to $x_4$.

Conditions: Use the Code 3 column of the displayed table.; Apply the prefix-free definition: no codeword is a prefix of another.

An optimal code is defined as a code that is both instantaneous and has the minimum length measure L for the given source. The slide identifies Huffman codes as examples of optimum codes.

Conditions: Requires instantaneousness (prefix-freeness).; Requires minimum L for the given source, where L is not further defined in this clip.

An optimal code is defined as a code that is both instantaneous and has the minimum length measure L for the given source. The slide identifies Huffman codes as examples of optimum codes.

Conditions: Requires instantaneousness (prefix-freeness).; Requires minimum L for the given source, where L is not further defined in this clip.

A uniquely decodable code is a code where every encoded message sequence has only one valid decomposition into codewords. The video emphasizes that prefix-freeness guarantees this property, but the converse is not required; a code can be uniquely decodable without being prefix-free.

Conditions: Concerns decoding of concatenated codeword sequences at the receiver.; The video does not state a formal symbolic definition beyond the examples and prose.

A uniquely decodable code is a code where every encoded message sequence has only one valid decomposition into codewords. The video emphasizes that prefix-freeness guarantees this property, but the converse is not required; a code can be uniquely decodable without being prefix-free.

Conditions: Concerns decoding of concatenated codeword sequences at the receiver.; The video does not state a formal symbolic definition beyond the examples and prose.

A distinct code is a code in which every source symbol is assigned a codeword different from the codewords assigned to all other symbols. No two symbols share the same binary string.

Conditions: Applies to a fixed code mapping symbols to codewords.; Requires pairwise inequality among all codewords in that code.

A distinct code is a code in which every source symbol is assigned a codeword different from the codewords assigned to all other symbols. No two symbols share the same binary string.

Conditions: Applies to a fixed code mapping symbols to codewords.; Requires pairwise inequality among all codewords in that code.