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Irregular repeat accumulate (IRA) codes build on top of the ideas of RA codes. IRA replaces the outer code in RA code with a low density generator matrix code. [1] IRA codes first repeats information bits different times, and then accumulates subsets of these repeated bits to generate parity bits.
In coding theory, the repetition code is one of the most basic linear error-correcting codes. In order to transmit a message over a noisy channel that may corrupt the transmission in a few places, the idea of the repetition code is to just repeat the message several times. The hope is that the channel corrupts only a minority of these repetitions.
Selective Repeat ARQ; Sequential decoding; Serial concatenated convolutional codes; Shaping codes; Slepian–Wolf coding; Snake-in-the-box; Soft-decision decoder; Soft-in soft-out decoder; Sparse graph code; Srivastava code; Stop-and-wait ARQ; Summation check
If the number of errors within a code word exceeds the error-correcting code's capability, it fails to recover the original code word. Interleaving alleviates this problem by shuffling source symbols across several code words, thereby creating a more uniform distribution of errors. [ 21 ]
The previous statements are also valid MATLAB expressions if the third one is executed before the others (numerical comparisons may be false because of round-off errors). If the system is overdetermined – so that A has more rows than columns – the pseudoinverse A + (in MATLAB and GNU Octave languages: pinv(A) ) can replace the inverse A − ...
If the channel quality is bad, and not all transmission errors can be corrected, the receiver will detect this situation using the error-detection code, then the received coded data block is rejected and a re-transmission is requested by the receiver, similar to ARQ.
This LDPC code fragment represents a three-bit message encoded as six bits. Redundancy is used, here, to increase the chance of recovering from channel errors. This is a (6, 3) linear code, with n = 6 and k = 3. Again ignoring lines going out of the picture, the parity-check matrix representing this graph fragment is
Formally, a parity check matrix H of a linear code C is a generator matrix of the dual code, C ⊥. This means that a codeword c is in C if and only if the matrix-vector product Hc ⊤ = 0 (some authors [1] would write this in an equivalent form, cH ⊤ = 0.) The rows of a parity check matrix are the coefficients of the parity check equations. [2]