Module arithmetic

Expand description

LDPC decoder arithmetic.

This module contains the trait DecoderArithmetic, which defines generic arithmetic rules used by a belief propagation LDPC decoder, and implementors of that trait. The LDCP decoders, such as the flooding schedule Decoder, are generic over the DecoderArithmetic trait, so it can be used to obtain monomorphized implementations for different arithemtic rules.

§References

Most of the arithmetic rules implemented here are taken from:

[1] Jon Hamkins, Performance of Low-Density Parity-Check Coded Modulation, IPN Progress Report 42-184, February 15, 2011.

Another good resource is this book:

[2] Sarah J. Johnson, Iterative Error Correction: Turbo, Low-Density Parity-Check and Repeat-Accumulate Codes. Cambridge University Press. June 2012.

Other references:

[3] C. Jones, et al. “Approximate-MIN* Constraint Node Updating for LDPC Code Decoding.” In Proceedings of MILCOM 2003 (Boston, Massachusetts), 1-157-1-162. Piscataway, NJ: IEEE, October 2003.

Structs§

Aminstarf32: LDPC decoder arithmetic with $f and the A-Min*-BP described in [3].
Aminstarf64: LDPC decoder arithmetic with $f and the A-Min*-BP described in [3].
Aminstari8: LDPC decoder arithmetic with 8-bit quantization and the A-Min*-BP described in [3].
Aminstari8Deg1Clip: LDPC decoder arithmetic with 8-bit quantization and the A-Min*-BP described in [3].
Aminstari8Jones: LDPC decoder arithmetic with 8-bit quantization and the A-Min*-BP described in [3].
Aminstari8JonesDeg1Clip: LDPC decoder arithmetic with 8-bit quantization and the A-Min*-BP described in [3].
Aminstari8JonesPartialHardLimit: LDPC decoder arithmetic with 8-bit quantization and the A-Min*-BP described in [3].
Aminstari8JonesPartialHardLimitDeg1Clip: LDPC decoder arithmetic with 8-bit quantization and the A-Min*-BP described in [3].
Aminstari8PartialHardLimit: LDPC decoder arithmetic with 8-bit quantization and the A-Min*-BP described in [3].
Aminstari8PartialHardLimitDeg1Clip: LDPC decoder arithmetic with 8-bit quantization and the A-Min*-BP described in [3].
Minstarapproxf32: LDPC decoder arithmetic with $f and the following approximation to the min* function:
Minstarapproxf64: LDPC decoder arithmetic with $f and the following approximation to the min* function:
Minstarapproxi8: LDPC decoder arithmetic with 8-bit quantization and an approximation to the min* function.
Minstarapproxi8Deg1Clip: LDPC decoder arithmetic with 8-bit quantization and an approximation to the min* function.
Minstarapproxi8Jones: LDPC decoder arithmetic with 8-bit quantization and an approximation to the min* function.
Minstarapproxi8JonesDeg1Clip: LDPC decoder arithmetic with 8-bit quantization and an approximation to the min* function.
Minstarapproxi8JonesPartialHardLimit: LDPC decoder arithmetic with 8-bit quantization and an approximation to the min* function.
Minstarapproxi8JonesPartialHardLimitDeg1Clip: LDPC decoder arithmetic with 8-bit quantization and an approximation to the min* function.
Minstarapproxi8PartialHardLimit: LDPC decoder arithmetic with 8-bit quantization and an approximation to the min* function.
Minstarapproxi8PartialHardLimitDeg1Clip: LDPC decoder arithmetic with 8-bit quantization and an approximation to the min* function.
Phif32: LDPC decoder arithmetic with $f and phi(x) involution.
Phif64: LDPC decoder arithmetic with $f and phi(x) involution.
Tanhf32: LDPC decoder arithmetic with $f and 2 * atanh(\Prod tanh(x/2) rule.
Tanhf64: LDPC decoder arithmetic with $f and 2 * atanh(\Prod tanh(x/2) rule.

Traits§

DecoderArithmetic: LDPC decoder arithmetic.