Concatenated code[1]
Also known as Serially concatenated code.
Description
A combination of two codes, an inner code \(C\) and an outer code \(C^\prime\), where the coordinates used for the inner code consist of the message subspace of the outer code.
Rate
There exist bounds on distance and rate of concatenated codes with a fixed outer and random inner code [2,3].
Decoding
Generalized minimum-distance decoder [4].
Parent
Children
- Irregular repeat-accumulate (IRA) code — IRA codes can be interpreted as serial concatenated codes [5].
- Tensor-product code — Tensor-product codes can be viewed as serial concatenated codes [6].
- Binary balanced spherical code — A binary balanced spherical code can be thought of as a concatenation of a constant-weight binary outer code with a shifted and scaled BPSK-like inner code.
- Polyphase code — A polyphase code can be thought of as a concatenation of a \(q\)-ary outer code with a PSK inner code.
Cousins
- Concatenated quantum code
- Hsu-Anastasopoulos LDPC (HA-LDPC) code — HA-LDPC codes are a concatenation of an LDPC and an LDGM code.
- Generalized RS (GRS) code — Concatenations of GRS codes with random linear codes almost surely attain the GV bound [7].
References
- [1]
- G. D. Forney, Jr (1966). Concatenated Codes. MIT Press, Cambridge, MA.
- [2]
- A. Barg, J. Justesen, and C. Thommesen, “Concatenated codes with fixed inner code and random outer code”, IEEE Transactions on Information Theory 47, 361 (2001) DOI
- [3]
- D. Doron, J. Mosheiff, and M. Wootters, “When Do Low-Rate Concatenated Codes Approach The Gilbert-Varshamov Bound?”, (2024) arXiv:2405.08584
- [4]
- G. Forney, “Generalized minimum distance decoding”, IEEE Transactions on Information Theory 12, 125 (1966) DOI
- [5]
- S. Benedetto et al., “Serial concatenation of interleaved codes: performance analysis, design, and iterative decoding”, IEEE Transactions on Information Theory 44, 909 (1998) DOI
- [6]
- A. Barg and G. Zemor, “Concatenated Codes: Serial and Parallel”, IEEE Transactions on Information Theory 51, 1625 (2005) DOI
- [7]
- C. Thommesen, “The existence of binary linear concatenated codes with Reed - Solomon outer codes which asymptotically meet the Gilbert- Varshamov bound”, IEEE Transactions on Information Theory 29, 850 (1983) DOI
Page edit log
- Victor V. Albert (2022-03-22) — most recent
Cite as:
“Concatenated code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/concatenated