In this paper, a method to design regular (2, dc)LDPC codes over GF(q) with both good waterfall and error floor properties is presented, based on the algebraic properties of their binary image. First, the algebraic properties of rows of the parity check matrix H associated with a code are characterized and optimized to improve the waterfall. Then the algebraic properties of cycles and stopping ...

In this paper, we investigate the error correction capability of column-weight-three LDPC codes when decoded using the Gallager A algorithm. We prove that the necessary condition for a code to correct k ≥ 5 errors is to avoid cycles of length up to 2k in its Tanner graph. As a consequence of this result, we show that given any α > 0,∃N such that ∀n > N , no code in the ensemble of column-weight...

Trapping sets have been identified as one of the main factors causing error floors of low-density parity-check (LDPC) codes at high SNR values. By adding several new rows to the original parity-check matrix, a novel method is proposed to eliminate small trapping sets in the LDPC code’s Tanner graph. Based on this parity-check matrix extension, we design new codes with low error floors from the ...

A cycle search algorithm based on a message-passing in a Tanner graph is proposed for designing good LDPC codes. By applying the message-passing algorithm with a message alphabet composed of only two messages to a cycle search, we can perform a cycle search with less computational complexity than tree-based search algorithms. Also, the proposed algorithm can be easily implemented by using an ex...

We investigate the application of the sum-product algorithm to the decoding of a q-ary Block-Coded Modulation (BCM) scheme which is based on extending the parity check equations of a binary block code to q-ary symbols. This is achieved by decomposing the code into a sub-code with an acyclic Tanner graph and its cosets which. are represented by a trellis diagram. The combination of these two cyc...

BACKGROUND Body composition and resting energy expenditure (REE) have not been examined longitudinally during puberty. OBJECTIVE The purpose of this longitudinal study was to examine the influence of pubertal maturation on REE relative to body composition in African American and white children. DESIGN The study included 92 white and 64 African American children (mean age at baseline: 8.3 an...

In this paper, we extend our work on iterative softinput soft-output (SISO) decoding of high density parity check (HDPC) codes. Edge-local complementation (ELC) is a graph operation which can be used to give structural diversity during decoding with the sum-product algorithm (SPA). We describe the specific subgraphs required for ELC to not increase the weight of the Tanner graph beyond a specif...

We present a method for maximumlikelihood decoding of the (48; 24; 12) quadratic residue code. This method is based on projecting the code onto a subcode with an acyclic Tanner graph, and representing the set of coset leaders by a trellis diagram. This results in a two level coset decoding which can be considered a systematic generalization of the Wagner rule. We show that unlike the code does ...

We present a method for maximumlikelihood decoding of the quadratic residue code This method is based on projecting the code onto a subcode with an acyclic Tanner graph and representing the set of coset leaders by a trellis diagram This results in a two level coset decoding which can be considered a systematic generalization of the Wagner rule We show that unlike the Golay code the code does no...