BCC (Block Convolutional Code)
Block Convolutional Codes (BCCs) are a type of error-correcting codes used in communication systems to correct errors that may occur during transmission. They are a variation of convolutional codes that encode input data into blocks rather than into a stream. BCCs are commonly used in applications where the transmitted data needs to be highly reliable, such as satellite communication, wireless communication, and digital television.
In this article, we will provide an in-depth explanation of BCCs, including their definition, encoding and decoding process, and their properties and advantages.
Definition of BCC
A Block Convolutional Code (BCC) is a type of error-correcting code that operates on blocks of input data rather than a continuous stream. A BCC takes a block of k binary digits as input and produces an encoded block of n binary digits as output. The input block is encoded using a convolutional encoder, which produces a set of parity check bits that are appended to the input data to form the encoded block.
BCCs are similar to convolutional codes in that they use a shift register to generate a set of parity check bits based on the input data. However, while convolutional codes operate on a continuous stream of input data, BCCs operate on blocks of input data. This makes them more suitable for applications where the input data is naturally partitioned into blocks, such as in digital communications systems.
Encoding Process of BCC
The encoding process of a BCC involves two main steps: convolutional encoding and block encoding.
Convolutional Encoding
The first step in the encoding process of a BCC is convolutional encoding. Convolutional encoding involves using a shift register and a set of modulo-2 adders to generate a set of parity check bits based on the input data. The shift register is initialized to an all-zero state, and the input data is shifted into the shift register one bit at a time. At each clock cycle, the contents of the shift register are combined using modulo-2 addition to produce a set of parity check bits.
The parity check bits are then appended to the input data to form the encoded block. The number of parity check bits generated depends on the configuration of the shift register and the number of clock cycles used.
Block Encoding
The second step in the encoding process of a BCC is block encoding. Block encoding involves dividing the input data into blocks of k bits and encoding each block separately using the convolutional encoder. The encoded blocks are then concatenated to form the output block of n bits.
Decoding Process of BCC
The decoding process of a BCC involves two main steps: block decoding and convolutional decoding.
Block Decoding
The first step in the decoding process of a BCC is block decoding. Block decoding involves dividing the received block of n bits into blocks of k+n bits and decoding each block separately. If the number of errors in a block is less than or equal to the error correction capability of the code, the errors can be corrected by a suitable decoding algorithm.
Convolutional Decoding
The second step in the decoding process of a BCC is convolutional decoding. Convolutional decoding involves using a maximum likelihood (ML) decoding algorithm to correct errors in the encoded data. The ML decoding algorithm involves finding the most likely transmitted sequence given the received data and the encoding scheme. The decoding algorithm works by comparing the received data with all possible transmitted sequences and selecting the most likely one based on the probability of error.
The convolutional decoding algorithm used for BCCs is often a variant of the Viterbi algorithm, which is an efficient algorithm that searches for the most likely transmitted sequence by maintaining a set of candidate paths through the trellis diagram of the code. The Viterbi algorithm works by assigning a metric to each candidate path based on the likelihood of the received data given the path. The algorithm then selects the path with the highest metric as the most likely transmitted sequence.
Properties and Advantages of BCC
BCCs have several properties and advantages that make them suitable for use in digital communication systems.
High Error Correction Capability
BCCs have a high error correction capability, which means they can correct a large number of errors in the transmitted data. The error correction capability of a BCC depends on the length of the block, the number of parity check bits, and the decoding algorithm used.
Efficient Decoding Algorithm
BCCs can be decoded efficiently using the Viterbi algorithm, which is a computationally efficient algorithm that can search for the most likely transmitted sequence in real-time. The Viterbi algorithm is able to correct errors in the transmitted data with a high degree of accuracy and is suitable for use in applications where the data needs to be transmitted in real-time.
Robustness to Burst Errors
BCCs are also robust to burst errors, which are errors that occur in a contiguous sequence of bits. This makes BCCs suitable for use in applications where the transmitted data is subject to noise or interference, such as in satellite communication or wireless communication.
Easy Implementation
BCCs are relatively easy to implement and can be implemented using simple logic circuits. This makes them suitable for use in applications where low power consumption and low cost are important factors.
Conclusion
In conclusion, Block Convolutional Codes (BCCs) are a type of error-correcting code that operate on blocks of input data. BCCs use a convolutional encoder to generate a set of parity check bits based on the input data, and the encoded blocks are then concatenated to form the output block. BCCs can be decoded efficiently using the Viterbi algorithm, which is able to correct errors in the transmitted data with a high degree of accuracy. BCCs have several properties and advantages that make them suitable for use in digital communication systems, including their high error correction capability, robustness to burst errors, and ease of implementation.