Master the Art of Drawing Trellis Diagrams

Master the Art of Drawing Trellis Diagrams

Table of Contents:

1. Introduction
2. Understanding Turnings Diagram
3. Components of a Turnings Diagram 3.1 Constraint Length 3.2 Connection Polynomials 3.3 Encoder Connection
4. Drawing the Turnings Diagram 4.1 Mapping Input Bits to Output Bits 4.2 Generating the Next State Table 4.3 Creating the Output Table 4.4 Constructing the State Transition Diagram
5. Using the Turnings Diagram for Encoding
6. Conclusion

Understanding Turnings Diagram

The turnings diagram is a graphical representation of a convolutional encoder. It helps in visualizing the connection between the input and output bits of the encoder. By understanding the structure of the turnings diagram, one can easily encode data using a convolutional encoder.

Components of a Turnings Diagram

A turnings diagram consists of several components that play a crucial role in the encoding process. These include the constraint length, connection polynomials, and the encoder connection.

Constraint Length: The constraint length refers to the number of memory elements in the encoder. It determines the complexity and performance of the encoder. A higher constraint length indicates more memory elements and potentially better error correction capabilities.

Connection Polynomials: The connection polynomials define the connections between the memory elements in the encoder. They determine how the input bits are combined to generate the output bits. These polynomials are represented as binary numbers.

Encoder Connection: The encoder connection represents the connections between the memory elements and the input and output lines. It shows how each memory element is connected to the input and output lines, creating a feedback loop within the encoder.

Drawing the Turnings Diagram

To draw a turnings diagram, we need to perform several steps. These include mapping the input bits to output bits, generating the next state table, creating the output table, and constructing the state transition diagram.

Mapping Input Bits to Output Bits: Each input bit in the turnings diagram corresponds to two output bits. By examining the connection polynomials and the encoder connection, we can determine the output bits for each input bit.

Generating the Next State Table: The next state table shows the transition from the current state to the next state based on the input bits. It helps in understanding the state changes within the encoder.

Creating the Output Table: The output table determines the output bits produced by the encoder for each combination of input bits and current state. It is crucial in determining the encoded data.

Constructing the State Transition Diagram: The state transition diagram is a visual representation of the next state and output tables. It helps in understanding the flow of data within the encoder and decoding process.

Using the Turnings Diagram for Encoding

The turnings diagram is primarily used for encoding data using a convolutional encoder. By following the connections and mapping the input bits to output bits, we can easily encode data. The turnings diagram provides a visual representation of the encoding process, making it easier to understand and implement.

Conclusion

The turnings diagram is a powerful tool for understanding and encoding data using a convolutional encoder. By following the steps outlined in this article, one can easily draw a turnings diagram and use it for encoding data. Understanding the components and structure of the turnings diagram is crucial for efficient encoding and error correction.