Block Diagram for Convolutional Code. The major elements of the convolutional coding technique include the shift register that acts as temporary storage and whose stored bits undergo shifting using a sliding window, a logic circuit that performs modulo-2 …

For example, one convolutional code can be generated by several different generator matrices and each generator matrix can be realized by different encoder, e.g., controllable and observable encoders. Use combinatorial logic to implement block codes.

Oct 4, 2010 · We now describe two views of the convolutional encoder, which we will find useful in better understanding convolutional codes and in implementing the encoding and decod- ing procedures.

Block codes, Cyclic codes, Convolutional codes, and Turbo codes. r parity bits or check bits are added to each block (total length n = k + r). In Maximum-likelihood decoding, we compare the received vector with all possible transmitted codes and choose that which is closest in Hamming distance (i.e., which is differs in the fewest bits).

We’ll focus on a specific convolutional code in this lecture, study its encoding and view the code through a few diferent perspectives. The encoder takes a binary information sequence b1, b2, . . . , bk ∈ {0, 1} and generates the encoded sequence p1, p2, . . . , pn ∈ {0, 1}.

Theorem 1 Any convolutional code C ⊆ Fn((D)) is the image of a convolutional mapping with a transfer function matrix that is a delay free generator matrix. Proof: Suppose C is the image of F k ((D)) under the mapping corresponding to G(D) ∈ F(D) k×n .

Remark: A convolutional code’s error-correction capability improves by increasing the number of the encoder states. Remark: 𝑚tailing bits are needed to force the encoder back to the all-zero state.

Convolutional codes are linear codes that have additional structure in the generator matrix. These encoding operations can be viewed as digital ltering, or convolution, operations.

• A generator matrix for a convolutional code is catastrophic if there exists an infinite weight input u(D) which results in a finite weight output v(D) • A convolutional encoder is catastrophic ()its state diagram has a zero-weight cycle other than the self-loop around the all-zeros state 19/23

Convolutional codes are applied in applications that require good performance with low implementation cost. They operate on data stream, not static block. Assume a three bit message is to transmitted. To clear the encoder two zero-bits are appended after message. Thus 5 bits are inserted into encoder and 10 bits produced.