Abstract: In this invention, a new class of finite precision multilevel decoders for low-density parity-check (LDPC) codes is presented. These decoders are much lower in complexity compared to the standard belief propagation (BP) decoder. Messages utilized by these decoders are quantized to certain levels based on the number of bits allowed for representation in hardware. A message update function specifically defined as part of the invention, is used to determine the outgoing message at the variable node, and the simple min operation along with modulo 2 sum of signs is used at the check node. A general methodology is provided to obtain the multilevel decoders, which is based on reducing failures due to trapping sets and improving the guaranteed error-correction capability of a code. Hence these decoders improve the iterative decoding process on finite length graphs and have the potential to outperform the standard floating-point BP decoder in the error floor region.

Abstract: A string of K initial symbols is encoded with a code of the parity check type. The K initial symbols belong to a Galois field of order q strictly greater than 2. The code is defined by code characteristics representable by a graph (GRH) comprising N?K first nodes (NCi), each node satisfying a parity check equation defined on the Galois field of order q, N packets of intermediate nodes (NITi) and NI second nodes (NSSi), each intermediate node being linked to a single first node and to several second nodes by way of a connection scheme. The string of K initial symbols is encoded by using the said code characteristics and a string of N encoded symbols is obtained, respectively subdivided into NI sub-symbols belonging respectively to mathematical sets whose orders are less than q, according to a subdivision scheme representative of the connection scheme (H).

Abstract: In this invention, a new class of finite precision multilevel decoders for low-density parity-check (LDPC) codes is presented. These decoders are much lower in complexity compared to the standard belief propagation (BP) decoder. Messages utilized by these decoders are quantized to certain levels based on the number of bits allowed for representation in hardware. A message update function specifically defined as part of the invention, is used to determine the outgoing message at the variable node, and the simple min operation along with modulo 2 sum of signs is used at the check node. A general methodology is provided to obtain the multilevel decoders, which is based on reducing failures due to trapping sets and improving the guaranteed error-correction capability of a code. Hence these decoders improve the iterative decoding process on finite length graphs and have the potential to outperform the standard floating-point BP decoder in the error floor region.

Abstract: An encoder and a decoder employ an encoding scheme corresponding to a parity check matrix which is derivable from a bipartite protograph formed of variable nodes and check nodes, with each variable node corresponding to a codeword symbol position. The protograph has a plurality of groups of nodes, each group of nodes comprising both variable nodes and check nodes. Each of the check nodes in a group is of degree 2 and has connections to two variable nodes in the same group. The protograph also has a plurality of check nodes of degree n, where n is the number of said plurality of groups, wherein each of the plurality of check nodes has a connection to a variable node in each group such that the symbol positions in a codeword are interleaved between the groups of nodes.