Concatenated tree codes: a low-complexity, high-performance approach

Abstract

This paper is concerned with a family of concatenated tree (CT) codes. CT codes are special low-density paritycheck (LDPC) codes consisting of several trees with large spans. They can also be regarded as special turbo codes with hybrid recursive/nonrecursive parts and multiple constituent codes. CT codes are decodable by the belief-propagation algorithm. They combine many advantages of LDPC and turbo codes, such as low decoding cost, fast convergence speed, and good performance.

Low rate turbo-Hadamard codes

“…The error floor performance improves consistently with , but the waterfall range performance stops improving for . Similar behavior has also been observed for other related turbo-type codes (such as CT codes [21]). …”

“…Therefore, the minimum Hamming weight, and so the asymptotic performance, of a turbo-Hadamard code is independent of the choice of . This property is also similar to that of concatenated tree codes [21] where each trellis section also carries multiple information bits. For a standard turbo code [13], the situation is different since each trellis section carries only one information bit.…”

“…This process is then repeated iteratively. For the first iteration and after the first iteration The principle is very similar to the concatenated tree (CT) decoder discussed in [21].…”

“…The global iterative decoder structure is illustrated in Fig. 7 [21]. It consists of looped local decoders, each responsible for one component code.…”

“…a) In evaluating in (24), we decompose into where (resp., ) is the vector obtained by replacing the parity (resp., information) entries in by zeros. In a turbo-type decoder, is not updated [13], [21] in all iterations. Thus we can use a reduced input FHT to update and then add it to a stored to obtain .…”