9 research outputs found
Information-Distilling Quantizers
Let and be dependent random variables. This paper considers the
problem of designing a scalar quantizer for to maximize the mutual
information between the quantizer's output and , and develops fundamental
properties and bounds for this form of quantization, which is connected to the
log-loss distortion criterion. The main focus is the regime of low ,
where it is shown that, if is binary, a constant fraction of the mutual
information can always be preserved using
quantization levels, and there exist distributions for which this many
quantization levels are necessary. Furthermore, for larger finite alphabets , it is established that an -fraction of the
mutual information can be preserved using roughly quantization levels
Mutual Information-Maximizing Quantized Belief Propagation Decoding of Regular LDPC Codes
In mutual information-maximizing lookup table (MIM-LUT) decoding of
low-density parity-check (LDPC) codes, table lookup operations are used to
replace arithmetic operations. In practice, large tables need to be decomposed
into small tables to save the memory consumption, at the cost of degraded error
performance. In this paper, we propose a method, called mutual
information-maximizing quantized belief propagation (MIM-QBP) decoding, to
remove the lookup tables used for MIM-LUT decoding. Our method leads to a very
efficient decoder, namely the MIM-QBP decoder, which can be implemented based
only on simple mappings and fixed-point additions. Simulation results show that
the MIM-QBP decoder can always considerably outperform the state-of-the-art
MIM-LUT decoder, mainly because it can avoid the performance loss due to table
decomposition. Furthermore, the MIM-QBP decoder with only 3 bits per message
can outperform the floating-point belief propagation (BP) decoder at high
signal-to-noise ratio (SNR) regions when testing on high-rate codes with a
maximum of 10-30 iterations