Brian M. Kurkoski

Joint message-passing decoding of LDPC codes and partial-response channels

Ideas of message passing are applied to the problem of removing the effects of intersymbol interference (ISI) from partial-response channels. Both bit-based and state-based parallel message-passing algorithms are proposed. For a fixed number of iterations less than the block length, the bit-error rate of the state-based algorithm approaches a nonzero constant as the signal-to-noise ratio (SNR) approaches infinity. This limitation can be removed by using a precoder. It is well known that low-density parity-check (LDPC) codes can be decoded using a message-passing algorithm. Here, a single message-passing detector/decoder matched to the combination of a partial-response channel and an LDPC code is investigated.

Exact probability of erasure and a decoding algorithm for convolutional codes on the binary erasure channel

Analytic expressions for the exact probability of erasure for systematic, rate- 1/2 convolutional codes used to communicate over the binary erasure channel and decoded using the soft-input, soft-output (SISO) and a posteriori probability (APP) algorithms are given. An alternative forward-backward algorithm which produces the same result as the SISO algorithm is also given. This low-complexity implementation, based upon lookup tables, is of interest for systems which use convolutional codes, such as turbo codes.

Analysis of convolutional codes on the erasure channel

This paper describes the analysis of convolutional codes on the erasure channel. We compare the maximum likelihood (ML) sequence decision and the maximum a posteriori (MAP) symbol decision for codes, which are transmitted over the erasure channel. When a codeword from a linear error correcting code with elements from the field GF is transmitted over a q-ary erasure channel, the symbol error rate of the maximum likelihood (ML) sequence decision is the same as that of the symbol maximum a posteriori (MAP) probability decision. When decoding convolutional codes transmitted over an AWGN channel, it is widely known that the probability of symbol error for the Viterbi algorithm (which is a sequence ML decoder) is generally higher than that for the more complex BCJR algorithm (which is a symbol MAP decoder).

On BCJR state metric quantization for turbo equalization

Vector quantization of the BCJR and Viterbi algorithms state metrics for detection of finite-state channels is considered. An estimate is given for the gain associated with vector quantization, over conventional implementations. This is expressed using the volume of the recurrent region, and the maximum state metric difference, which are both intrinsic properties of the channel detector. One application of this gain is the complexity evaluation of a previously proposed lookup-table BCJR implementation. The BCJR algorithm is of interest in turbo equalization used for communication over intersymbol-interference and finite-state Markov channels

Turbo Equalization With Single-Parity Check Codes and Unequal Error Protection Codes

The performance of turbo equalization with interleaved single-parity check codes on partial-response channels is evaluated. Single-parity check codes are weak codes, but are shown to have modest performance gain. The proposed system achieves gains of 3.5, 3.4, 2.7, and 2.4 dB with code rates of 19/20,24/25,49/50, and 63/64, respectively, at a BER of 10-5. The complexity of the proposed decoder is significantly lower than that of turbo equalization using standard low-density parity-check codes. These single-parity check codes are modified to be unequal error protection codes, designed to decrease the probability that Viterbi error events span Reed-Solomon symbol boundaries, resulting in a decrease of the sector error rate. Once such code gains an additional 0.1 dB over a single-parity check code of the same code rate of 24/25

A viable system for tracing illegal users of video

Typical uses of watermarks include copyright protection and disabling unauthorized access to content. Especially, copyright protection watermarks embed some information in the data to identify the copyright holder or content provider, while receiver-identifying watermarking, commonly referred to as fingerprinting, embeds information to identify the receiver of that copy of the content. Thus, if an unauthorized copy of the content is recovered, extracting the fingerprint will show who the initial receiver was [1][2]. In this paper we generalize our previous work [3] of a video fingerprinting system to identify the source of illegal copies. This includes a logo embedding technique, generalization of the distribution system and detailed investigation of the robustness against collusion attacks.

Precoders for message-passing detection of partial-response channels

Parallel message-passing detectors for partial-response channels have the property that a bit is estimated using channel symbols in a window of size W centered upon that bit. Distinct input sequences that produce the same output sequence result in undesirable failure of window decoders, but preceding can eliminate this input-to-output mapping ambiguity. For a class of partial-response channels, we show necessary and sufficient conditions on a precoder to unambiguously map input sequences to output sequences.