RS-CC Reed-Solomon Convolutional Code

Reed-Solomon Convolutional Code (RS-CC) is a forward error correction (FEC) coding scheme that combines the advantages of Reed-Solomon (RS) codes and convolutional codes. It is particularly well-suited for applications that require robust error correction, such as satellite communication, wireless communication, and storage systems.

To understand RS-CC, let's first briefly discuss Reed-Solomon codes and convolutional codes:

Reed-Solomon Codes:

Reed-Solomon codes are block-based error correction codes that operate on a block of symbols. The input message is divided into blocks, and each block is treated as a polynomial of a certain degree. These polynomials are evaluated at specific points to generate codewords. Reed-Solomon codes can correct a specified number of symbol errors and detect a greater number of errors. They provide excellent error correction capabilities, particularly for burst errors.

Convolutional Codes:

Convolutional codes are different from block codes in that they operate on a continuous stream of input symbols. The encoding process involves sliding a fixed-length window (called the memory length) over the input stream and producing output symbols based on the current window state. Convolutional codes have memory, and the output symbols depend on the current and previous input symbols. The decoder uses the Viterbi algorithm or other decoding techniques to correct errors.

Now, let's dive into RS-CC and how it combines the strengths of both Reed-Solomon and convolutional codes:

Encoding:

In RS-CC, the input data stream is first divided into blocks of symbols. Each block is treated as a polynomial, similar to Reed-Solomon codes. However, instead of evaluating the polynomial at specific points, convolutional encoding is performed.

The input symbols are fed into a shift register, which has a memory length defined by the encoder. The shift register operates on the input symbols and produces output symbols based on the current and previous input symbols. The generated symbols are then combined with the original Reed-Solomon codewords. This combination allows the RS-CC to inherit the powerful error correction capability of Reed-Solomon codes.

Decoding:

Decoding RS-CC is a two-step process:

Reed-Solomon decoding and convolutional decoding.

a. Reed-Solomon Decoding: The received codeword is divided into blocks, and each block is processed by the Reed-Solomon decoder. The Reed-Solomon decoder corrects errors and erasures in the received symbols, producing a modified codeword.

b. Convolutional Decoding: The modified codeword is then processed by the convolutional decoder, which uses the Viterbi algorithm or other decoding techniques. The decoder tries to find the most likely sequence of transmitted symbols by considering the current and previous received symbols. The decoded output is the reconstructed data stream.

The combination of Reed-Solomon decoding and convolutional decoding allows RS-CC to correct both burst errors (handled by Reed-Solomon codes) and random errors (handled by convolutional codes). This makes RS-CC highly effective in combating a wide range of error patterns.

Overall, RS-CC is a powerful FEC coding scheme that provides robust error correction capabilities by combining the strengths of Reed-Solomon codes and convolutional codes. It finds extensive use in various applications where reliable data transmission and storage are critical.