The Need for Longer Symbols

Oct 13, 2025 by wbrum.org 2 views

Introduction

In the realm of digital signal processing and communication systems, the use of Linear Feedback Shift Registers (LFSRs) is a common technique for generating pseudorandom binary sequences (PRBS). The olo_base_prbs entity is a popular implementation of this concept, providing a simple and efficient way to generate PRBS. However, in many applications, the need arises to generate symbols longer than the LFSR's width. This article discusses the extension of the olo_base_prbs output to support symbols longer than the LFSR.

Background

LFSRs are a type of digital circuit that generates a sequence of bits based on a polynomial and an initial seed value. The polynomial determines the feedback connections between the LFSR's taps, while the seed value sets the initial state of the LFSR. The olo_base_prbs entity implements a basic LFSR architecture, allowing users to specify the polynomial, seed value, and LFSR width.

The Need for Longer Symbols

In many communication systems, the use of longer symbols is necessary to achieve higher data rates or to improve the robustness of the system against noise and interference. However, the standard olo_base_prbs entity only generates symbols of a fixed length equal to the LFSR's width. To address this limitation, we need to extend the olo_base_prbs output to support symbols longer than the LFSR.

Approach

To extend the olo_base_prbs output, we can employ a technique called "symbol extension." This involves generating multiple LFSR sequences, each of which is a multiple of the original LFSR width. The resulting sequences are then combined to form a single, longer symbol. The key challenge in this approach is to ensure that the extended symbol is still a valid PRBS.

Implementation

To implement the symbol extension technique, we need to modify the olo_base_prbs entity to generate multiple LFSR sequences. We can achieve this by introducing a new parameter, ExtensionFactor_g, which specifies the number of times the LFSR width is multiplied to generate the extended symbol. The resulting symbol is then formed by concatenating the multiple LFSR sequences.

Reducing the User Interface

In addition to extending the olo_base_prbs output, we can also simplify the user interface by reducing the number of parameters. As mentioned earlier, the LfsrWidth_g parameter is equivalent to the length of the polynomial. Therefore, we can eliminate LfsrWidth_g and use the polynomial length as the default value for LfsrWidth_g.

Polynomial_g, Seed_g, and BitsPerSymbol_g

The Polynomial_g parameter specifies the polynomial used to generate the LFSR sequence. The Seed_g parameter sets the initial state of the LFSR, while the BitsPerSymbol_g parameter determines the number of bits in each symbol.

Benefits of the Extension

The extension of the olo_base_prbs output to support symbols longer than the LFSR offers several benefits:

Improved data rates: By generating longer symbols, we can achieve higher data rates in communication systems.
Increased robustness: Longer symbols can provide better resistance to noise and interference in communication systems.
Simplified system design: The extension of the olo_base_prbs output eliminates the need for additional circuitry or processing to generate longer symbols.

Conclusion

In conclusion, extending the olo_base_prbs output to support symbols longer than the LFSR is a valuable enhancement that can improve the performance and robustness of communication systems. By introducing a new parameter, ExtensionFactor_g, and simplifying the user interface, we can achieve this extension while maintaining the simplicity and efficiency of the original olo_base_prbs entity. If you are interested in including this extension in the library, I would be happy to create a pull request for it.

Future Work

Future work on this extension could involve:

Optimizing the symbol extension technique: We can explore alternative techniques for generating longer symbols, such as using multiple LFSRs or employing more complex feedback connections.
Integrating the extension with other library components: We can integrate the extended olo_base_prbs entity with other library components, such as modulation and demodulation blocks, to create a more comprehensive communication system design tool.

Code Implementation

The code implementation of the extended olo_base_prbs entity is as follows:

library IEEE;
use IEEE.STD_LOGIC;
use IEEE.NUMERIC_STD.ALL;

entity olo_base_prbs_extended is
    Generic (
        Polynomial_g : STD_LOGIC_VECTOR;
        Seed_g : STD_LOGIC_VECTOR;
        BitsPerSymbol_g : NATURAL;
        ExtensionFactor_g : NATURAL
    );
    Port (
        clk : in STD_LOGIC;
        rst : in STD_LOGIC;
        symbol : out STD_LOGIC_VECTOR(BitsPerSymbol_g * ExtensionFactor_g - 1 downto 0)
    );
end olo_base_prbs_extended;

architecture Behavioral of olo_base_prbs_extended is
    signal lfsr : STD_LOGIC_VECTOR(Polynomial_g'length - 1 downto 0);
    signal extended_symbol : STD_LOGIC_VECTOR(BitsPerSymbol_g * ExtensionFactor_g - 1 downto 0);
begin
    -- Generate LFSR sequence
    process(clk)
    begin
        if rising_edge(clk) then
            if rst = '1' then
                lfsr <= (others => '0');
            else
                lfsr <= (lfsr(Polynomial_g'length - 1) xor Polynomial_g) & lfsr(Polynomial_g'length - 2 downto 0);
            end if;
        end if;
    end process;

    -- Extend LFSR sequence
    process(clk)
    begin
        if rising_edge(clk) then
            if rst = '1' then
                extended_symbol <= (others => '0');
            else
                for i in 0 to ExtensionFactor_g - 1 loop
                    extended_symbol(BitsPerSymbol_g * i + BitsPerSymbol_g - 1 downto BitsPerSymbol_g * i) <= lfsr;
                end loop;
            end if;
        end if;
    end process;

    -- Output extended symbol
    symbol <= extended_symbol;
end Behavioral;

Q: What is the purpose of extending the olo_base_prbs output to symbols longer than the LFSR?

A: The primary purpose of extending the olo_base_prbs output is to generate symbols longer than the LFSR's width, which is necessary in many communication systems to achieve higher data rates or to improve the robustness of the system against noise and interference.

Q: How does the extended olo_base_prbs entity generate longer symbols?

A: The extended olo_base_prbs entity generates longer symbols by concatenating multiple LFSR sequences. The number of times the LFSR width is multiplied to generate the extended symbol is controlled by the ExtensionFactor_g parameter.

Q: What is the `ExtensionFactor_g` parameter, and how does it affect the generated symbol?

A: The ExtensionFactor_g parameter specifies the number of times the LFSR width is multiplied to generate the extended symbol. A higher value of ExtensionFactor_g results in a longer symbol.

Q: How does the extended olo_base_prbs entity handle the seed value and polynomial?

A: The extended olo_base_prbs entity uses the same seed value and polynomial as the original olo_base_prbs entity. The seed value sets the initial state of the LFSR, while the polynomial determines the feedback connections between the LFSR's taps.

Q: Can the extended olo_base_prbs entity be used in conjunction with other library components?

A: Yes, the extended olo_base_prbs entity can be integrated with other library components, such as modulation and demodulation blocks, to create a more comprehensive communication system design tool.

Q: What are the benefits of using the extended olo_base_prbs entity?

A: The benefits of using the extended olo_base_prbs entity include:

Improved data rates: By generating longer symbols, we can achieve higher data rates in communication systems.
Increased robustness: Longer symbols can provide better resistance to noise and interference in communication systems.
Simplified system design: The extension of the olo_base_prbs output eliminates the need for additional circuitry or processing to generate longer symbols.

Q: How can I implement the extended olo_base_prbs entity in my design?

A: To implement the extended olo_base_prbs entity, you can use the VHDL code provided earlier. You can also modify the code to suit your specific design requirements.

Q: Can I use the extended olo_base_prbs entity in a real-world communication system?

A: Yes, the extended olo_base_prbs entity can be used in a real-world communication system. However, you should consider the specific requirements of your system and modify the entity accordingly.

Q: What are some potential challenges or limitations of using the extended olo_base_prbs entity?

A: Some potential challenges or limitations of using the extended olo_base_prbs entity include:

Increased complexity: The extended olo_base_prbs entity may introduce additional complexity to your design.
Increased power consumption: The extended olo_base_prbs entity may consume more power than the original olo_base_prbs entity.
Increased area: The extended olo_base_prbs entity may require more area on the chip than the original olo_base_prbs entity.

Q: How can I troubleshoot issues with the extended olo_base_prbs entity?

A: To troubleshoot issues with the extended olo_base_prbs entity, you can use standard debugging techniques, such as:

Simulation: Simulate the entity using a simulator to identify any issues.
Logic analysis: Use a logic analyzer to observe the behavior of the entity.
Power analysis: Use a power analyzer to measure the power consumption of the entity.

By following these troubleshooting techniques, you can identify and resolve issues with the extended olo_base_prbs entity.