List Decoding of Short Codes for Communication over Unknown Fading Channels

In this paper, the advantages of list decoding for short packet transmission over fading channels with an unknown state are illustrated. The principle is applied to polar codes (under successive cancellation list decoding) and to general short binary linear block codes (under ordered-statistics decoding). The proposed decoders assume neither a-priori knowledge of the channel coefficients, nor of their statistics. The scheme relies on short pilot fields that are used only to derive an initial channel estimate. The channel estimate is required to be accurate enough to enable a good list construction, i.e., the construction of a list that contains, with high probability, the transmitted codeword. The final decision on the message is obtained by applying a list. This allows one to use very few pilots, thus reducing the the Rayleigh block-fading channel and compared to finite-length performance bounds. The proposed technique provides (in the short block length regime) gains of 1 dB with respect to a traditional pilot-aided transmission scheme

Short Packets over Block-Memoryless Fading Channels: Pilot-Assisted or Noncoherent Transmission?

We present nonasymptotic upper and lower bounds on the maximum coding rate achievable when transmitting shortpackets over a Rician memoryless block-fading channel for a given requirement on the packet error probability.We focus on the practically relevant scenario in which there is no a priori channel state information available at the transmitter and at the receiver. An upper bound built upon the min-max converse is compared to two lower bounds: the first one relies on a noncoherent transmission strategy in which the fading channel is not estimated explicitly at the receiver; the second one employs pilot-assisted transmission (PAT) followed by maximum-likelihood channel estimation and scaled mismatched nearest-neighbor decoding at the receiver. Our bounds are tight enough to unveil the optimum number ofdiversity branches that a packet should span so that the energy per bit required to achieve a target packet error probability is minimized, for a given constraint on the code rate and the packet size. Furthermore, the bounds reveal that noncoherent transmission is more energy efficient than PAT, even when the number of pilot symbols and their power is optimized. For example, in Rayleigh fading, for the case when a coded packet of 168 symbols is transmitted using a channel code of rate 0.48 bits/channel use, over a block-fading channel with block size equal to 8 symbols, PAT requires an additional 1.2 dB of energy per information bit to achieve a packet error probability of 10\u1000003 compared to a suitably designed noncoherent transmission scheme. Finally, we devise a PAT scheme based on punctured tail-biting quasi-cyclic codes and ordered statistics decoding, whose performance is close (1 dB gap at 10^-3 packet error probability) to the ones predicted by our PAT lower bound. This shows that the PAT lower bound provides useful guidelines on the design of actual PAT schemes

Successive Cancellation Inactivation Decoding for Modified Reed-Muller and eBCH Codes

A successive cancellation (SC) decoder with inactivations is proposed as an efficient implementation of SC list (SCL) decoding over the binary erasure channel. The proposed decoder assigns a dummy variable to an information bit whenever it is erased during SC decoding and continues with decoding. Inactivated bits are resolved using information gathered from decoding frozen bits. This decoder leverages the structure of the Hadamard matrix, but can be applied to any linear code by representing it as a polar code with dynamic frozen bits. SCL decoders are partially characterized using density evolution to compute the average number of inactivations required to achieve the maximum a-posteriori decoding performance. The proposed measure quantifies the performance vs. complexity trade-off and provides new insight into dynamics of the number of paths in SCL decoding. The technique is applied to analyze Reed-Muller (RM) codes with dynamic frozen bits. It is shown that these modified RM codes perform close to extended BCH codes

Successive Cancellation List Decoding of Product Codes with Reed-Muller Component Codes

This letter proposes successive cancellation list (SCL) decoding of product codes with Reed–Muller (RM) component codes. SCL decoding relies on a product code description based on the 2�x2 Hadamard kernel, which enables interpreting the code as an RM subcode. The focus is on a class of product codes considered in wireless communication systems, based on single parity-check and extended Hamming component codes. For short product codes, it is shown that SCL decoding with a moderate list size performs as well as (and, sometimes, outperforms) belief propagation (BP) decoding. Furthermore, by concatenating a short product code with a high-rate outer code, SCL decoding outperforms BP decoding by up to 1.4 dB

Ternary Quantized Polar Code Decoders: Analysis and Design

The performance of short polar codes under successive cancellation (SC) and SC list (SCL) decoding is analyzed for the case where the decoder messages are coarsely quantized. This setting is of particular interest for applications requiring low-complexity energy-efficient transceivers (e.g., internet-of-things or wireless sensor networks). We focus on the extreme case where the decoder messages are quantized with 3 levels. We show how under SCL decoding quantized log-likelihood ratios lead to a large inaccuracy in the calculation of path metrics, resulting in considerable performance losses with respect to an unquantized SCL decoder. We then introduce two novel techniques which improve the performance of SCL decoding with coarse quantization. The first technique consists of a modification of the final decision step of SCL decoding, where the selected codeword is the one maximizing the maximum-likelihood decoding metric within the final list. The second technique relies on statistical knowledge about the reliability of the bit estimates, obtained through a suitably modified density evolution analysis, to improve the list construction phase, yielding a higher probability of having the transmitted codeword in the list. The effectiveness of the two techniques is demonstrated through simulations

Low-Complexity Joint Channel Estimation and List Decoding of Short Codes

A pilot-assisted transmission (PAT) scheme is proposed for short blocklengths, where the pilots are used only to derive an initial channel estimate for the list construction step. The final decision of the message is obtained by applying a non-coherent decoding metric to the codewords composing the list. This allows one to use very few pilots, thus reducing the channel estimation overhead. The method is applied to anordered statistics decoder for communication over a Rayleigh block-fading channel. Gains of up to 1.2 dB as compared to traditional PAT schemes are demonstrated for short codes with QPSK signaling. The approach can be generalized to other list decoders, e.g., to list decoding of polar codes

List Decoding of Short Codes for Communication over Unknown Fading Channels

In this paper, the advantages of list decoding for short packet transmission over fading channels with an unknown state are illustrated. The principle is applied to polar codes (under successive cancellation list decoding) and to general short binary linear block codes (under ordered-statistics decoding). The proposed decoders assume neither a-priori knowledge of the channel coefficients, nor of their statistics. The scheme relies on short pilot fields that are used only to derive an initial channel estimate. The channel estimate is required to be accurate enough to enable a good list construction, i.e., the construction of a list that contains, with high probability, the transmitted codeword. The final decision on the message is obtained by applying a list. This allows one to use very few pilots, thus reducing the the Rayleigh block-fading channel and compared to finite-length performance bounds. The proposed technique provides (in the short block length regime) gains of 1 dB with respect to a traditional pilot-aided transmission scheme

Successive Cancellation Decoding of Single Parity-Check Product Codes: Analysis and Improved Decoding

A product code with single parity-check component codes can be described via the tools of a multi-kernel polar code, where the rows of the generator matrix are chosen according to the constraints imposed by the product code construction. Following this observation, successive cancellation decoding of such codes is introduced. In particular, the error probability of single parity-check product codes over binary memoryless symmetric channels under successive cancellation decoding is characterized. A bridge with the analysis of product codes introduced by Elias is also established for the binary erasure channel. Successive cancellation list decoding of single parity-check product codes is then described. For the provided example, simulations over the binary input additive white Gaussian channel show that successive cancellation list decoding outperforms belief propagation decoding applied to the code graph. Finally, the performance of the concatenation of a product code with a high-rate outer code is investigated via distance spectrum analysis. Examples of concatenations performing within 0.7 dB from the random coding union bound are provided

Prognostic Factors for Overall Survival in Patients With Metastatic Colorectal Carcinoma Treated With Vascular Endothelial Growth Factor-Targeting Agents

Objective: Angiogenesis represents a key element in the pathogenesis of malignancy. There are no robust data on prognostic factors for overall survival (OS) in patients with metastatic colorectal cancer treated with vascular endothelial growth factor (VEGF)-targeted therapy. The present study was conducted to establish a prognostic model for patients using an oxaliplatin-based or irinotecan-based chemotherapy plus bevacizumab in metastatic colorectal cancer. Methods: Baseline characteristics and outcomes on 170 patients treated with FOLFIRI or XELOX plus anti-VEGF therapy-naive metastatic colorectal cancer were collected from three Turkey cancer centers. Cox proportional hazards regression was used to identify independent prognostic factors for OS. Results: The median OS for the whole cohort was 19 months (95% CI, 14.3 to 23.6 months). Three of the seven adverse prognostic factors according to the Anatolian Society of Medical Oncology (ASMO) were independent predictors of short survival: serum lactate dehydrogenase (LDH) greater than the upper limit of normal (ULN; p<0.001); neutrophils greater than the ULN (p<0.0014); and progression free survival (PFS) less than 6 months (p=0.001). Conclusion: Serum LDH and neutrophil levels were the main prognostic factors in predicting survival, followed by PFS. This model validates incorporation of components of the ASMO model into patient care and clinical trials that use VEGF-targeting agents