Optimized bit mappings for spatially coupled LDPC codes over parallel binary erasure channels

Abstract

Abstract-In many practical communication systems, one binary encoder/decoder pair is used to communicate over a set of parallel channels. Examples of this setup include multi-carrier transmission, rate-compatible puncturing of turbo-like codes, and bit-interleaved coded modulation (BICM). A bit mapper is commonly employed to determine how the coded bits are allocated to the channels. In this paper, we study spatially coupled low-density parity check codes over parallel channels and optimize the bit mapper using BICM as the driving example. For simplicity, the parallel bit channels that arise in BICM are replaced by independent binary erasure channels (BECs). For two parallel BECs modeled according to a 4-PAM constellation labeled by the binary reflected Gray code, the optimization results show that the decoding threshold can be improved over a uniform random bit mapper, or, alternatively, the spatial chain length of the code can be reduced for a given gap to capacity. It is also shown that for rate-loss free, circular (tail-biting) ensembles, a decoding wave effect can be initiated using only an optimized bit mapper.

Improving the Decoding Threshold of Tailbiting Spatially Coupled LDPC Codes by Energy Shaping

“…In particular, we estimate the MAP threshold of the uncoupled ensemble by performing an EXIT analysis of the TE SC-LDPC code ensemble for very large N and by setting γ MAP = γ TE . Table I for the case of (d v , d c ) = (5,10). The table provides the thresholds for the different ensembles, for N = 128, N = 256, and N → ∞.…”

“…When the coupling length is moderate or small, the termination (which is necessary to trigger the decoding wave) entails a non negligible rate loss. The rate loss can be avoided by resorting to tailbiting (TB) SC-LDPC codes [5]- [7] at the cost of a (potentially large) threshold degradation. In fact, the BP threshold of a TB SC-LDPC code ensemble is the same as the one of the underlying uncoupled code ensemble.…”

Optimization of Bit Mapping and Quantized Decoding for Off-the-Shelf Protograph LDPC Codes with Application to IEEE 802.3ca

“…In the following, we use the ideas of [8], [9] to formulate an optimization procedure that optimizes the assignment of the m bit channels to the n P,t transmitted VN types of a given protograph basematrix. This bit mapping can be expressed as a non-negative matrix A = [a 1 , .…”

Laterally connected spatially coupled code chains for transmission over unstable parallel channels

“…The problem of designing spatially coupled codes for parallel binary erasure channels has been addressed in [5], where a single spatially coupled code instance is followed by an optimized interleaver, which assigns the bits of a code word to the parallel sub-channels. The drawback of that approach is that the number of bits assigned to each sub-channel is not This work was conducted while K. Mahdaviani was visiting Bell Labs funded by a scholarship of the DAAD-RisePro programme.…”