11.1 Turbo Code Structure and Encoding
4 min read•august 7, 2024
are powerful error-correction codes that use of . They're known for their excellent performance, approaching the Shannon limit in many cases.
The turbo encoder structure consists of RSC encoders, an , and optional . These components work together to generate systematic and , creating a robust code that can correct errors effectively during decoding.
Turbo Encoder Components
Core Encoding Elements
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- Recursive systematic convolutional (RSC) encoders form the core of the turbo encoder
- RSC encoders are a type of convolutional encoder that incorporates feedback and produces both systematic and parity bits
- Typically, two or more RSC encoders are used in parallel to generate the turbo code
- The feedback in RSC encoders introduces memory into the encoding process, enabling better error correction performance
- Interleaver is a critical component that permutes the input bits before feeding them to the second RSC encoder
- Interleaving helps to decorrelate the inputs to the two RSC encoders, making the code more robust to burst errors
- Common interleaver types include block interleavers and pseudo-random interleavers
- The choice of interleaver can significantly impact the performance of the turbo code
- Puncturing is an optional process that selectively removes some of the encoded bits to increase the
- Puncturing allows for flexible code rates without changing the encoder structure
- A puncturing pattern determines which bits are removed from the encoded sequence
- Puncturing trades off error correction capability for higher data rates
Output Bit Types
- are the original input bits that are directly passed through to the output of the turbo encoder
- One of the RSC encoders (usually the first) is configured to output the systematic bits unchanged
- Including systematic bits in the output helps the decoder's convergence during iterative decoding
- Systematic bits provide a direct representation of the input data in the encoded sequence
- Parity bits are the redundant bits generated by the RSC encoders based on the input sequence
- Each RSC encoder generates its own set of parity bits
- Parity bits are used by the decoder to detect and correct errors in the received sequence
- The number of parity bits generated depends on the code rate and the puncturing pattern (if used)
Turbo Code Characteristics
Code Structure and Concatenation
- Turbo codes are parallel concatenated codes, meaning they consist of multiple constituent codes (RSC encoders) operating in parallel
- The input bits are encoded by each RSC encoder separately, and their outputs are combined to form the turbo codeword
- Parallel concatenation allows for efficient encoding and decoding while achieving excellent error correction performance
- The constituent RSC encoders are typically identical, but they can also be different for some turbo code designs
- Code rate of a turbo code is the ratio of the number of input bits to the number of output bits
- The code rate determines the amount of redundancy introduced by the encoding process
- Typical code rates for turbo codes are 1/2 and 1/3, but higher or lower rates can be achieved through puncturing or repetition
- Lower code rates provide better error correction but reduce the effective data throughput
Trellis Termination
- is a technique used to ensure that the turbo encoder reaches a known state at the end of the encoding process
- Trellis termination is necessary because the RSC encoders have memory and their final states depend on the input sequence
- Without trellis termination, the decoder would not know the starting and ending states, leading to degraded performance
- Trellis termination is typically achieved by appending a few additional bits to the input sequence to force the encoders into a known state (e.g., all-zero state)
Turbo Encoder Structure
Turbo Encoder Block Diagram
- The turbo encoder block diagram illustrates the arrangement and interconnection of the main components
- The input bits are fed into the first RSC encoder and the interleaver
- The interleaved bits are then encoded by the second RSC encoder
- The systematic bits (from the first RSC encoder) and the parity bits (from both RSC encoders) are multiplexed to form the output codeword
- Optional puncturing can be applied to the parity bits to achieve the desired code rate
- The trellis termination bits, if used, are appended to the input sequence and encoded by both RSC encoders
- The specific structure and parameters of the turbo encoder (e.g., number of RSC encoders, interleaver design, puncturing pattern) can vary depending on the application and performance requirements
Key Terms to Review (22)
Asymptotic Performance: Asymptotic performance refers to the behavior of algorithms or codes as their input size approaches infinity. It provides a way to analyze the efficiency and effectiveness of coding schemes by focusing on how they perform in large-scale scenarios, often expressed in terms of complexity classes such as big O notation. This concept is crucial in understanding how well systems like Turbo Codes and the McEliece Cryptosystem can handle increasing amounts of data or computational demands.
Code Rate: Code rate is a crucial metric in coding theory that represents the efficiency of a code by quantifying the ratio of the number of information bits to the total number of bits transmitted. A higher code rate indicates a more efficient code, but it may also mean less error correction capability. Understanding code rate helps in evaluating different coding techniques, their performance, and their application in various communication systems.
Component code: A component code is a type of error-correcting code that is used as a building block in more complex coding schemes, such as turbo codes. These codes are designed to encode data in a way that allows for the detection and correction of errors that may occur during data transmission. In the context of turbo codes, component codes are typically used in tandem, working together to enhance the overall error-correction capability and improve performance in noisy environments.
Convolutional Codes: Convolutional codes are a type of error-correcting code that are generated by passing data sequences through a linear finite state machine, producing encoded output as a function of the current input and previous inputs. This coding technique is essential for ensuring data integrity in communication systems and is deeply connected to several aspects of coding theory, including the use of generator and parity check matrices, systematic encoding techniques, and various decoding algorithms.
Free distance: Free distance is a key concept in coding theory that refers to the minimum number of errors that can occur in a codeword before it becomes indistinguishable from another codeword. It is crucial for determining the error-correcting capability of a code, as a higher free distance generally indicates better performance in detecting and correcting errors during data transmission.
Gallager's Bound: Gallager's Bound is a theoretical limit that describes the performance of error-correcting codes, specifically focusing on how well a code can correct errors in data transmission. This bound helps to determine the trade-offs between the code rate and the probability of decoding errors, influencing the design and efficiency of coding schemes, particularly in turbo codes.
Interleaver: An interleaver is a device or algorithm used to rearrange the order of symbols in a data stream, effectively spreading out bursts of errors to improve error correction. This technique enhances the performance of coding schemes, particularly in scenarios with burst errors, allowing for better error detection and correction during transmission. By dispersing consecutive bits across a wider time frame, interleavers help maintain data integrity even when faced with noisy environments.
Map algorithm: A map algorithm is a computational technique used in the context of Turbo Codes to efficiently handle the mapping of input data to encoded output. This algorithm takes advantage of iterative processing and combines multiple decoding processes to improve error correction capabilities. By utilizing a structured approach, it allows for significant performance gains in terms of decoding speed and accuracy when working with coded data.
Maximum likelihood decoding: Maximum likelihood decoding is a statistical approach used to determine the most likely transmitted codeword from a received signal in the presence of noise. This method relies on calculating the likelihood of various possible codewords and selecting the one that maximizes this likelihood, thus making it an essential concept in error correction and decoding schemes for different types of codes, including convolutional and turbo codes.
Parallel concatenation: Parallel concatenation is a method used in coding theory where multiple encoders operate simultaneously on the same input data to create a single encoded output. This technique enhances error correction capabilities by combining the strengths of different encoders, making the resulting code more robust against noise during transmission. In the context of turbo codes, parallel concatenation involves linking multiple convolutional encoders with an interleaver, allowing for improved performance in noisy environments.
Parity bits: Parity bits are binary digits added to a string of data to ensure that the total number of 1-bits is even or odd, providing a simple method for error detection in data transmission. They play a crucial role in encoding schemes like turbo codes, where they help verify the integrity of the transmitted information and enable the detection of single-bit errors.
Puncturing: Puncturing is a technique used in coding theory to selectively remove bits from a codeword, effectively reducing its length while maintaining its essential error-correcting properties. This process allows for more efficient use of bandwidth and resources, making it particularly useful in communication systems where bandwidth is limited. It creates a trade-off by simplifying the code while aiming to keep its performance intact, especially in contexts like turbo codes and performance optimization.
Recursive structure: A recursive structure is a concept in which an object or a process is defined in terms of itself, allowing for the repeated application of rules or methods. This idea is crucial in various fields, as it enables the creation of complex systems through simple building blocks, facilitating efficient solutions to problems by breaking them down into smaller, manageable parts. In the context of encoding, recursive structures are especially important for understanding how data can be organized and processed effectively.
Recursive systematic convolutional (rsc) encoders: Recursive systematic convolutional (RSC) encoders are a type of error-correcting code that use convolutional encoding techniques while maintaining a systematic form. This means that the input bits are preserved as part of the output, allowing for easier decoding. The recursive aspect refers to the feedback mechanism in the encoder structure, enabling improved performance in terms of error correction and data throughput, making them essential in advanced coding schemes like turbo codes.
Satellite Communication: Satellite communication refers to the use of satellite technology to send and receive information over long distances, allowing for a wide range of data transmission services, including television broadcasting, internet access, and telephone communications. This technology relies on satellites positioned in orbit around the Earth to relay signals between ground stations, which enhances the ability to reach remote areas and facilitates global connectivity.
Serial concatenation: Serial concatenation is a method of combining multiple codes in a sequential manner, where the output of one coding scheme is used as the input for another. This technique allows for enhanced error correction capabilities by taking advantage of the strengths of different coding algorithms, making it particularly useful in Turbo Code structures. It ensures that data is robustly encoded, improving reliability in communication systems.
Shannon's Theorem: Shannon's Theorem, formulated by Claude Shannon, defines the maximum data transmission rate over a noisy communication channel without error, known as the channel capacity. This theorem highlights the critical balance between data rate, bandwidth, and noise, showing how efficient coding techniques can approach this theoretical limit. Understanding this concept is essential for various coding techniques that aim to minimize errors and optimize data transfer in digital communication systems.
Soft decision decoding: Soft decision decoding is a technique used in error correction coding where the decoder considers not just the received bits but also the confidence level associated with each bit. This approach allows for more nuanced interpretations of the received signals, which can lead to better error correction performance compared to hard decision decoding, where bits are simply treated as either 0 or 1. By leveraging probabilistic information from the received signal, soft decision decoding is crucial for improving the efficiency and reliability of various coding schemes, especially in convolutional codes and turbo codes.
Systematic bits: Systematic bits are the original data bits that are directly transmitted in a coded message without any modification. In coding schemes, particularly in turbo codes, these bits are crucial because they represent the actual information being sent, making it easier for the receiver to decode and understand the intended message. The relationship between systematic bits and redundancy is key as it ensures that while some bits provide error correction information, others convey the essential data.
Trellis termination: Trellis termination refers to a method used in decoding convolutional codes, specifically within the framework of turbo codes. This technique ensures that the trellis structure representing the code has a defined ending state, allowing for effective and accurate decoding by reducing the complexity of the decoding process. Proper termination of the trellis is crucial for improving error performance and managing the computational load during the decoding stage.
Turbo Codes: Turbo codes are a class of error correction codes that use two or more convolutional codes in parallel, combined with an interleaver, to achieve near Shannon limit performance on communication channels. They revolutionized coding theory by enabling significant improvements in error correction capabilities, making them widely used in modern digital communication systems.
Wireless communications: Wireless communications refer to the transfer of information between two or more points that are not connected by an electrical conductor. This technology allows for the transmission of data over distances without physical cables, utilizing radio waves, microwaves, and infrared signals. Wireless communications are crucial for mobile devices and have paved the way for advanced encoding techniques to ensure reliable data transmission, especially in environments with potential interference.