Reduced-complexity collaborative decoding of interleaved Reed-Solomon and Gabidulin codes

Abstract

An alternative method for collaborative decoding of interleaved Reed-Solomon codes as well as Gabidulin codes for the case of high interleaving degree is proposed. As an example of application, simulation results are presented for a concatenated coding scheme using polar codes as inner codes.

Simultaneous Partial Inverses and Decoding Interleaved Reed–Solomon Codes

“…The bound (8) can also be used with random error values. For t ≤ L, rank(E) is then likely to equal t, in which case (8) reduces to (5); for t = n − k − 1 ≤ L, (8) (by (117)) yields the same bound as (6) with γ = 1, which agrees with the bounds in [17], [19], where different decoding algorithms are used.…”

Coding for combined block-symbol error correction

“…Hence, when m ≥ d − 1, the decoding failure probability of the algorithm in Fig. 2 is bounded from above, up to a multiplicative factor 1 + o(1), by For m ≥ d − 1, this bound is (considerably) better than those given in [3] and [20], and is comparable to that in [29], [30] when m is much larger than d.…”

“…In [3], Bleichenbacher et al identified a threshold, (m/(m+1))(d−1), on the number of block errors, below which the decoding failure probability approaches 0 as d goes to infinity and n/q goes to 0. A better bound on the decoding error probability was obtained by Kurzweil et al [20] and by Schmidt et al [29], [30]. See also Brown et al [5], Coppersmith and Sudan [6], Justesen et al [16], Krachkovsky and Lee [19], and Wachter-Zeh et al [34].…”

An efficient length- and rate-preserving concatenation of polar and repetition codes

“…When used together with an improved polar decoder, the beneficial effects of both approaches are combined. Furthermore, the proposed scheme can itself be used as an inner code in other concatenation approaches -at least if inner and outer decoding are performed separately there like in [6]. In this case, the coding gain in error performance is preserved.…”

“…To this end, we propose a modified polar code construction by means of a serial concatenated scheme with the polar code used as an inner code. In contrast to many existing concatenation schemes based on polar codes as inner codes (as considered, e.g., in [5], [6], [7]), we focus here on coding schemes that do not change overall rate and block length, thus facilitating a pure trade-off of complexity and error performance. The approach is based on our prior attempt [1] where block codes of small dimension were chosen as outer codes.…”