Low Density Parity Check (LDPC) codes are state-of-art error correcting codes, included in several standards for broadcast transmissions. Iterative softdecision decoding algorithms for LDPC codes reach excellent error correction capability; their performance, however, is strongly affected by finite-precision issues in the representation of inner variables. Great attention has been paid, in recent literature, to the topic of quantization for LDPC decoders, but mostly focusing on binary modulations and analyzing finite precision effects in a disaggregrated manner, i.e., considering separately each block of the receiver. Modern telecommunication standards, instead, often adopt high order modulation schemes, e.g. M-QAM, with the aim to achieve large spectral efficiency. This puts additional quantization problems, that have been poorly debated in previous literature. This paper discusses the choice of suitable quantization characteristics for both the decoder messages and the received samples in LDPC-coded systems using M-QAM schemes. The analysis involves also the demapper block, that provides initial likelihood values for the decoder, by relating its quantization strategy with that of the decoder. A signal label for a signal in a 2m-ary modulation scheme is simply the m-bit pattern assigned to the signal. A mapping strategy refers to the grouping of bits within a codeword, where each mbit group is used to select a 2m-ary signal in accordance with the signal labels. The most obvious mapping strategy is to use each group of m consecutive bits to select a signal. . We will call this the consecutive-bit (CB) mapping strategy. An alternative strategy is the bit-reliability (BR) mapping strategy which will be described below. A new demapper version, based on approximate expressions, is also presented, that introduces a slight deviation from the ideal case but yields a low complexity hardware implementation.
Kiran, U. and Ugendar, V.
"Mapper and Demapper for LDPC-Coded Systems,"
International Journal of Electronics and Electical Engineering: Vol. 1
, Article 7.
Available at: https://www.interscience.in/ijeee/vol1/iss2/7