FIR (Full Incremental Redundancy)

Full Incremental Redundancy (FIR) is a coding scheme used in digital communication systems to increase the reliability of data transmission over noisy channels. It is a type of Forward Error Correction (FEC) technique that adds redundancy to the transmitted data, so that errors can be detected and corrected at the receiving end.

In FIR coding, the data is transmitted in multiple bursts, with each burst containing a subset of the original data bits along with some redundant bits. The redundant bits are generated using a special encoding algorithm that is designed to provide maximum error detection and correction capability.

The FIR encoding process can be divided into two stages: the encoding stage and the transmission stage.

Encoding Stage:

During the encoding stage, the original data is divided into several subsets or "blocks". Each block contains a certain number of data bits, as well as some additional redundant bits that are generated using a special encoding algorithm. The encoding algorithm is designed to generate redundant bits that provide maximum error detection and correction capability.

The encoding algorithm used in FIR coding is typically based on a cyclic code, such as a Reed-Solomon code or a BCH (Bose-Chaudhuri-Hocquenghem) code. These codes are well suited for FEC because they provide strong error correction capabilities while requiring relatively few redundant bits.

Once the encoding algorithm has generated the redundant bits for each block of data, the blocks are transmitted over the channel one at a time.

Transmission Stage:

During the transmission stage, the encoded data is transmitted over the channel one block at a time. Each block is transmitted with a certain level of redundancy, which allows the receiver to detect and correct errors that occur during transmission.

The receiver first receives the data and performs a simple check to verify that the received block is not corrupted. This check is typically done using a cyclic redundancy check (CRC) code, which is a type of error detection code.

If the received block passes the CRC check, the receiver then attempts to decode the block using the same encoding algorithm that was used to encode the data. If the decoding is successful, the receiver has recovered the original data bits and can continue with the next block.

If the decoding fails, the receiver can use the redundant bits in the received block to attempt to correct errors that may have occurred during transmission. The exact method used to correct errors depends on the type of encoding algorithm used, but typically involves solving a set of linear equations or polynomial equations.

Once errors have been corrected (if possible), the receiver repeats the decoding process until it successfully recovers the original data bits. If the receiver is unable to correct errors in a block after a certain number of attempts, the block is considered lost and the receiver requests that the block be retransmitted.

Advantages and Disadvantages of FIR:

The main advantage of FIR coding is its ability to provide strong error correction capabilities with relatively few redundant bits. This makes it well suited for applications where bandwidth is limited, such as satellite communications or mobile networks.

Another advantage of FIR coding is its ability to provide incremental redundancy, which means that additional redundant bits can be added to a block of data if errors are detected during transmission. This allows the receiver to recover data even if a large number of errors occur during transmission.

However, FIR coding also has some disadvantages. One disadvantage is that it requires a relatively complex encoding and decoding algorithm, which can be computationally intensive. This can make it unsuitable for applications where low power consumption is important, such as battery-operated devices.

Another disadvantage of FIR coding is that it can introduce some delay in the transmission of data, as the receiver must wait for the entire block of data to be transmitted before attempting to decode it. This delay can be unacceptable in applications where real-time communication is required, such as voice or video calls.

Conclusion:

Full Incremental Red In conclusion, Full Incremental Redundancy (FIR) is a FEC technique used to improve the reliability of digital communication systems by adding redundancy to the transmitted data. FIR uses a cyclic code such as Reed-Solomon or BCH to generate redundant bits that provide strong error correction capabilities. The data is transmitted in multiple bursts, with each burst containing a subset of the original data bits along with some redundant bits. The receiver performs a CRC check on each received burst and attempts to decode it using the same encoding algorithm that was used to encode the data. If the decoding fails, the receiver uses the redundant bits to attempt to correct errors that may have occurred during transmission.

FIR offers several advantages such as its ability to provide strong error correction capabilities with relatively few redundant bits and its ability to provide incremental redundancy. However, FIR also has some disadvantages such as its computational complexity and the delay it introduces in the transmission of data. FIR is well suited for applications where bandwidth is limited and strong error correction capabilities are required, such as satellite communications or mobile networks.