FPGA Implementation of Orthogonal Code Convolution for Efficient Digital Communication

FPGA Implementation of Orthogonal Code Convolution for Efficient Digital Communication

*Raghvendra Dubey & P. Lakshmi Sarojini Department of Electronics & Communication Engineering

Swarnandhra College of Engineering and Technology, Seetharampuram, Narsapur (A.P.), INDIA

Abstract

In digital communication system, convolution coding is preferred for the channel coding as it facilitates a better error correction as comparison to block coding which does not require memory. Among other techniques such as Cyclic Redundancy and Solomon Codes; orthogonal coding is one of the codes which can detect errors and correct corrupted data in an efficient way. In this paper, FPGA implementation of orthogonal code convolution is presented by employing Xilinx and Modelsim softwares. It is found that the orthogonal code implementation improved the error detection upto 99.9%. With this method, the transmitter does not have to send the parity bit since the parity bit is known to be always zero. Therefore, if there is a transmission error, the receiver will be able to detect it by generating a parity bit at the receiving end.

Keywords: Code Convolution, Orthogonal Codes, Antipodal Codes, FPGA.

1. Introduction

   Information and communication technology has brought enormous changes to our life and turned out to be one of the basic building blocks of modern society. Day by day, there is an increasing demand of network capacity due to the use of internet and real time transmission of voice and picture. To fulfil these requirements data transmission at high bit rates is essential for various aspects such as video, high-quality audio and mobile integrated service digital network (ISDN). However, the data transmitted at high bit rates over mobile radio channels, leads to inter symbol interference (ISI). The significant factors which cause the reliability of digital data communication are the transmission medium i.e. cable or air, sources of noise and some others like electromagnetic interface, crosstalk and distance. To overcome this problem, error correction coding

   is a solution for the best possible communication. The main advantage of using coding is the efficiency of the channels use becomes higher as comparison to the case when code is not used. Therefore, error detection and correction techniques are needed which can detect errors such as the Cyclic Redundancy Check and others which can detect as well as correct errors such as Solomon Codes [1-3]. The CRC check includes table driven CRC calculation and loop driven CRC calculation however, this application describes the implementation of the CRC-16 polynomial. Further, there are several formats for the implementation of CRC such as CRC-CCITT, CRC-32 or other polynomials. The CRC generation has many advantages over simple sum techniques or parity check. CRC error correction gives the detection of single, double and bundled bit errors and useful where large data packages are transmitted. ReedSolomon (RS) codes are non- binary cyclic error-correcting codes which described a systematic way of building codes that could detect and correct multiple random symbol errors. This coding has found its applications from deep-space communication to consumer electronics (CDs, DVDs, Blu-ray Discs). Among these methods, orthogonal code is one of the codes which can detect errors and correct corrupted data in an efficiently with increased quantity of data transmitted [4]. This coding is binary valued and with equal number of 1s and 0s. All orthogonal codes can generate zero parity bits as n-bit orthogonal code has n/2 1s and n/2 0s. In simple there are n/2 positions where 1s and 0s differ and hence, each antipodal code can also generate a zero parity bit [5]. It is noted that with this method, the transmitter does not have to send the parity bit since the parity bit is known to be always zero. Therefore, if there is a transmission error, the receiver will be able to detect it by generating a parity bit at the receiving end.

   In this paper, the FPGA implementation of orthogonal code convolution is presented by employing Xilinx and Modelsim softwares; in section second and third, the theory of orthogonal coding and design approach are presented. The simulated results and analysis are discussed in section fourth. Finally, section fifth concludes the paper.

2. Theory of Orthogonal Coding

   Orthogonal codes are consists of equal number of 1s and 0s e.g. n-bit orthogonal code consist n/2 1s and n/2 0. Meaning, there are n/2 positions where 1s and 0s differ. In this way, all orthogonal codes generate zero parity bits. An illustration of 16-bit orthogonal code is shown in figure 1.

   Figure 1. A 16-bit orthogonal code has 16 orthogonal codes and 16-antipodal codes for a total of 32 bi-orthogonal codes.

   It is comprised of 16-orthogonal codes and 16- antipodal codes (just the inverse of orthogonal

   Figure 2. Encoding and Decoding Process.

   This is governed by the correlation process, where

   codes) for a total of 32 bi-orthogonal codes as

   a pair of n-bit codes

   x1, x2 , x3 , . . . xn

   and

   depicted in figure 2. The advantage with this

   y1, y2, y3, . . . yn is compared to yield, autocorrelation

   approach is that transmitter does not need to send the parity bit as parity bit is known to be always zero. In this way, if error exists during, the receiver can detect by generating a parity bit at the receiving

   value which is given as

   n

   R(x, y)

   i 1

   n

   xi yi 4 1

   (2)

   end. In orthogonal coding, a k-bit data set is

   mapped into a unique n-bit before transmission.

   Where R(x, y) = autocorrelation function, n= code

   Here, we have considered a 5-bit data set which is

   length, and

   dth =threshold midway. For reliable

   can be represented by a unique 16-bit orthogonal code and transmitted without the parity bit. After receiving the data, it is decoded based on code correlation by setting a threshold midway between two orthogonal codes. The threshold midway is represented as

   detection, an additional 1-bit offset is added to equation (2).

   Further, we can estimate the average number of errors which can be corrected by combining equation (1) and equating (2), and can be represented as

   n

   dth 4

   (1)

   t n R(x, y) n 1

   4

   (3)

   Where n is the code length and dth is the threshold midway between two orthogonal codes. According to above equation, for 16-bit orthogonal coding, threshold midway is 4 between two orthogonal codes. This approach offers a decision process, where the incoming impaired orthogonal code is examined for correlation with the neighbouring codes for a possible match. It is noted that the acceptance criterion for a valid code is that an n-bit comparison must yield a good autocorrelation value; otherwise, a false detection will occur.

   Here, t is the number of errors which can be

   corrected by means of an n-bit orthogonal code.

3. Design Approach

   Our design approach is based on the comparison between the received code and all the orthogonal code combinations stored in a look up table; which has two major components such as a transmitter and a receiver. The first component (transmitter) consists of two blocks such as encoder and shift register which is shown in figure 3.

   Figure 3. Block diagram of the 5-bit data transmitter.

   Here, encoder encodes a k-bit data set to n=2k-1 bits of the orthogonal code and the shift register transforms this code to a serial data in order transmit these. In our cse of 5-bit data, it can be encoded to 16-bit (24) orthogonal code according to the lookup table shown in figure 3. Further, the generated orthogonal code can be serially transmitted by using a shift register with the rising edge of the clock.

   Figure 4. Block diagram of Receiver.

   The second component (receiver) consists of two major blocks such as serial to parallel converter and decoder as shown in figure 4. Here, the incoming serial bits are converted into n-bit parallel codes and compared with all the codes in the lookup table for error detection. This is processed by counting the number of ones in the signal resulting from

   XOR operation between the received code and each combination of the orthogonal codes in the lookup table. Further, counter is used to count the number of ones in the resulting n-bit signal and also searches for the minimum count. However, a value rather than zero shows an error in the received code. The orthogonal code in the lookup table which is associated with the minimum count is the closest match for the corrupted received code. The matched orthogonal code in the lookup table is the corrected code, which is then decoded to k-bit data. The receiver is able to correct up to (n/4)-1 bits in the received impaired code. Signal (REQ), goes high when the minimum count is associated with more than one combination of orthogonal code.

   1. Encoder Simulation

      We have done RTL simulation of encoder to ensure the proper working of stand alone module. The encoder reset, using the reset signal reset. This resets the encoder to the default value 0000000000000000. The encoder is then enabled

      using the signal data_rdy. This signal is HIGH when the data is ready.

      Figure 5. Simulated result of encoder.

      The input data is encoded to 16-bit orthogonal code with the rising edge of the clock signal. The 16-bit orthogonal code is outputted through a signal

      data_out. The signal data_out_rdy is using to indicate the availability of output data. This signal is HIGH when the output data is ready. For example, the 5-bit data 00001 is encoded to 0101010101010101 16-bit orthogonal code, this is shown in figure 5.

   2. Parallel to Serial Shift Register Simulation

      The shift register reset, using the reset signal

      reset. This resets the shift register to the default value 0000000000000000. The shift register is then enabled using the signal data_rdy.

      Figure 6. Simulated result of parallel to serial shift register.

      This signal is HIGH when the data is ready. The parallel input data is loaded into a temporary register shft_reg. The simulated result of parallel to serial shift register is shown in figure 6. The shift register transmits the bits serially using a signal

      data_out with the rising edge of the clock signal. The signal data_out_rdy is used to indicate the availability of output data. This signal is HIGH when the output data is ready

   3. Transmitter Simulation

      After simulating encoder and parallel to shift register, the transmitter is simulated and results are shown in figure 7. The transmitter reset, using the reset signal reset. This resets the transmitter to the default value 00000. The encoder encodes a k-bit data set to n=2k-1 bits of the orthogonal code and the shift register transforms this code to a serial data in order to be transmitted. The transmitter is then enabled using the signal data_rdy. This signal is HIGH when the data is ready. For example, the 5- bit data 00001 is encoded to 0101010101010101 16-bit orthogonal code. The generated orthogonal code is then transmitted serially using a shift register with the rising edge of the clock. The bits are outputted through a signal

      data_out. The signal data_out_rdy is using to indicate the availability of output data. This signal is HIGH when the output data is ready.

      Figure 7. Simulated result of Transmitter

   4. Serial to Parallel Shift Register Simulation

      The sub module of receiver, serial to parallel shift register is simulated and shown in figure 8. The shift register reset, using the reset signal

      reset. This resets the shift register to the default value 0000000000000000. The shift register is then enabled using the signal data_rdy. This signal is HIGH when the data is ready. The input data bits are serially loaded into a temporary register shft_reg with the rising edge of the clock signal. After the final input bit is clocked in the signal cnt is greater than 10000.

      Figure 8. Simulated result of serial to parallel shift register.

      When the cnt value is greater than 10000 the data in temporary register is available at the output signal data_out. The signal data_out_rdy is using to indicate the availability of output data. This signal is HIGH when the output data is ready.

   5. Counter Simulation

      The simulated result of counter module is shown in figure 9. The counter reset, using the reset signal reset. This resets the counter to the default value 00000. The counter is then enabled using the signal data_rdy. This signal is HIGH when the data is ready. The counter counts the number of 1s present in the given 16-bit data and produces the count value at the signal cnt_out. The signal

      cnt_rdy is using to indicate the availability of output data. This signal is HIGH when the output data is ready.

      Figure 9. Simulated result of Counter.

   6. Receiver Simulation

      The receiver is simulated with its components such as serial to parallel converter and counter; and results are shown in figure 10. The receiver reset, using the reset signal reset. This resets the receiver to the default value 00000. The receiver is then enabled using the signal data_rdy. This signal is HIGH when the data is ready. The 16-bit code at the signal data is compared with all the

      codes in the lookup table for error detection. This is done by counting the number of ones in the signal resulting from XOR operation between the received code and each combination of the orthogonal codes in the lookup table. A counter is used to count the number of ones in the resulting 16-bit signal and also searches for the minimum count. However a value rather than zero shows an error in the received code. The orthogonal code in the lookup table which is associated with the minimum count is the closest match for the corrupted received code. The matched orthogonal code in the lookup table is the corrected code, which is then decoded to 5-bit data which is available at signal data_out. The signal

      data_out_rdy is using to indicate the availability of output data. This signal is HIGH when the output data is ready.

      For example, if the 16-bit data is 0101010101010101, is XORed with each combination of 16-bit orthogonal codes in the lookup table. The resulting 16-bit data is given as an input to counter. The counter counts the number of 1s in each 16-bit XORed output. The minimum count value is 00000 for the orthogonal code is 0101010101010101. Therefore the associated 5- bit data is 00001. Another example, if the 16-bit data is 0101010101011101, is XORed with each combination of 16-bit orthogonal codes in the lookup table. The resulting 16-bit data is given as an input to counter. The counter counts the number of 1s in each 16-bit XORed output. The minimum count value is 00001 for the orthogonal code is 0101010101010101. Therefore the associated 5- bit data is 00001.

      Figure 10. Simulated result of receiver.

4. Results and Discussion

   In previous section, module by module simulation is done. Finally transmitter and receiver modules are combined and simulated. figure 11 shows the RTL schematic of transmitter and receiver.

   Figure 11. RTL Schematic of transmitter and receiver.

   The Transmitter and Receiver reset, using the reset signal reset. This resets the Transmitter and Receiver to the default value 0000. The receiver is then enabled using the signal data_rdy. This signal is HIGH when the data is ready. For example, the input data value 00001 labeled as

   data has been encoded to the associated orthogonal code 0101010101010101 labeled as p_data. The signal p_data_rdy is used to enable the transmission of the serial bits p_data of the orthogonal code with every rising edge of the clock.

   Upon reception, the incoming serial data is converted into 16-bit parallel code p_data1. Counter is used to count the number of 1s after XOR operation between the received code and all combinations of orthogonal code in the lookup table. The signal cnt gives the minimum count of ones among them. The orthogonal code p_data associated with the minimum count is the closest match for the received code, which is then decoded to the final data given by signal data_out.

   Figure 12. First Case: Simulated result of Transmitter and Receiver.

   We have considered five cases to observe the output from above simulation. In first case, the received code has a match in the lookup table. As shown in figure 12, the received code is p_data1 = 0101010101010101, the value of minimum count is 00000 and hence the received code is not corrupted. The code is then decoded to the

   corresponding final data 00001 which is given by signal data_out.

   Figure 13. Second Case: Simulated result of Transmitter and Receiver.

   In second case, the received code has no match in the lookup table. As shown in figure 13, the received code is p_data11 =0101010101011101, the value of minimum count is 00001, which reveals an error. The corresponding orthogonal code is 0101010101010101 which is the closest match for the received code given by the minimum count, and the decoded final data is 00001 which is given by signal data_out. In this case the single bit error is detected and corrected by the receiver.

   Figure 14. Third Case: Simulated result of Transmitter and Receiver.

   In third case, the received code has no match in the lookup table. As shown in figure 14, the received code is p_data11 = 0101010100011101, the value of minimum count is 00002, which reveals an error. The corresponding orthogonal code is 0101010101010101 which is the closest match for the received code given by the minimum count, and the decoded final data is 00001 which is

   given by signal data_out. In this case the two bit errors are detected and corrected by the receiver.

   Figure 15. Fourth Case: Simulated result of Transmitter and Receiver.

   In fourth case, the received code has no match in the lookup table. As shown in figure 15, the received code is p_data11 = 0101010100011111, the value of minimum count is 00003, which reveals an error. The corresponding orthogonal code is 0101010101010101 which is the closest match for the received code given by the minimum count, and the decoded final data is 00001 which is given by signal data_out. In this case the three bit errors are detected and corrected by the receiver.

   In fifth case, there is more than one possibility of closest match in the lookup table. As shown in figure 16, the received code is p_data11 = 0101011100011111. The value of minimum count is associated with more than one orthogonal code and thus it is not possible to determine the closest match in the lookup table for the received code.

   Figure 16. Fifth Case: Simulated result of Transmitter and Receiver.

   In summary, 5-bit data is encoded into 16-bit

   1. Saleh Faruque, Error Control Coding Based on Orthogonal Codes, Wireless Proceedings, Vol. 2, pp. 608-615, 2004.

   2. Naima Kaabouch, Aparna Dhirde, and Saleh Faruque, Improvement of the Orthogonal Code Convolution Capabilities Using FPGA Implementation, IEEE Proceedings, Nov. 2007, pp.337-341.

   orthogonal code which has 25 32 combinations

   of orthogonal code. Therefore, out of 65,536 possible combinations of 16-bit received code the receiver will not able to detect error in those codes which are one of the combinations of orthogonal code. The detection percentage for 16-bit orthogonal code is estimated to be 99.95% which is able to correct three bit error.

5. Conclusion

In present paper, FPGA implementation of orthogonal code convolution is presented to ensure the efficient digital communication. This work involved the implementation of various modules of the transmitter and receiver using VHDL. A fully synthesizable HDL code was written to ensure that the design was feasible. This orthogonal code implementation has improved the error detection upto 99.9% for 16-bit coding. It is noted that with this method, the transmitter does not have to send the parity bit since the parity bit is known to be always zero. Therefore, if there is a transmission error, the receiver will be able to detect it by generating a parity bit at the receiving end. Finally, this work has the future scope of further improvement in orthogonal coding for large digital data processing.

References

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