Erasure resilient checksum codes
In real time media transmission over internet (such as VOIP), the sender may need to add after every k media packets some additional redundant packets (relevant to the last k media packets). The redundant packets are computed such that the receiver can recover the lost media packets if a sufficient number of total packets are survived.
(4, 2) erasure resilient code:
- Packet size is at least 2 bits and is divisible by 2
- Information is in two packets
- Transmitted are 4 packets, two of which are information and two others are redundant (the code is systematic)
- It is sufficient to receive any of two out of four transmitted packets to recover the two information packets (it is an MDS code)
- Note that with Reed Solomon, with two two-bit symbols (packets) you can add only one redundant symbol, since the total length of the codeword cannot exceed _{}symbols
Redundant messages are computed as follows:
Let
- _{}be the first information packet, where _{} and _{} are the first and second half of the packet a
- _{}be the second information packet, where _{} and _{} are the first and second half of the packet b
The redundant packets are the following:
- _{}
- _{}
- where the operation + is binary XOR
The diagram for decoding, for any possible two survivals is given in an excel file
(5, 2) erasure resilient code:
- Packet size is at least 3 bits and is divisible by 3
- Information is in two packets
- Transmitted are 5 packets, two of which are information and three others are redundant (thus the code is systematic)
- It is sufficient to receive any of two out of five transmitted packets to recover the two information messages (thus it is an MDS code)
Redundant messages are computed as follows:
Let
- _{}be the first information packet, where _{}, _{} and _{} are the first, second and third equal portions of the packet a
- _{}the same for packet b
The three redundant packets are
- _{}
- _{}
- _{}
- where the operation + is binary XOR
The diagram for decoding, for any possible two survivals is given in an excel file
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