NB-LDPC matrix alist format

Introduction

Several NB-LDPC matrices are proposed in order to evaluate and compare the performance of NB-LDPC decoder. Matrices are described using the 'alist' format . The 'alist' format is modified for NB matrices using the q-ary 'alist' format .

The matrix element are given as the power of the primitive element. GF(64) constructed using the irreductive polynomial Q[X] = X6 + X + 1. Similarly, GF(256) is defined thanks to the irreducible polynomial Q[X] = X8 + X4 + X3 + X2 + 1. The binary representation of the finite field can be obtained using the following matlab function build_GF.m NB-LDPC matrices can be represented in many way. In the matrices of this web site, the KN format is used. The advantage of the BeiDou format is that it is standardized.

Header common to all format

First line

  • N: the number of symbol (number of columns in the parity check matrix)
  • M: the number of Parity (number of lines in the parity check matrix)
  • GF: the code order q=2^m

    • Second line (sometime skipped)

  • d_v: maximum variable node degree
  • d_c: maximum check node degree

    • Third line

    d_v of each variable node

    fourth line

    d_c of each check node

    KN format

    Format used the university of Kaiserslautern http://www.uni-kl.de/channel-codes/channel-codes-database/non-binary-ldpc/
  • N lines (skipped in the c codes), where each line defines the CNs connected to a VN.
  • CNs numbered from 1 to M.
  • The CN number is followed by the coefficient associated to connection defined as the power of the primitive element alpha
  • one empty line
  • M lines, where each line defines the VNs connected to a CN.
  • VNs numbered from 1to N.
  • The CN number is followed by the coefficient associated to connection defined as the power of the primitive element alpha

    • BeiDou format

    Beidou Navigation Satellite System (BDS) defines NB-LDPC codes in its B1C open service signal [1], B2a signal [2] and B2b signal [3]
  • M lines, where each line defines the VNs connected to a CN. VNs numbered from 0 to N-1.
  • one empty line.
  • M lines, where the multiplicative element associated to each connection is given by the decimal value of the vector representation of GF symbol