ADAMs, Osteoclastogenesis and Bone Destruction in the Loosening of the Totally Replaced Hip

Total hip replacement is the golden standard treatment for severe osteoarthritis refractory for conservative treatment. Aseptic loosening and osteolysis are the major long-term complications after total hip replacement. Foreign body giant cells and osteoclasts are locally formed around aseptically loosening implants from precursor cells by cell fusion. When the foreign body response is fully developed, it mediates inflammatory and destructive host responses, such as collagen degradation. In the present study, it was hypothesized that the wear debris and foreign body inflammation are the forces driving local osteoclast formation, peri-implant bone resorption and enhanced tissue remodeling. Therefore the object was to characterize the eventual expression and the role of fusion molecules, ADAMs (an abbreviation for A Disintegrin And Metalloproteinase, ADAM9 and ADAM12) in the fusion of progenitor cells into multinuclear giant cells. For generation of such cells, activated macrophages trying to respond to foreign debris play an important role. Matured osteoclasts together with activated macrophages mediate bone destruction by secreting protons and proteinases, including matrix metalloproteinases (MMPs) and cathepsin K. Thus this study also assessed collagen degradation and its relationship to some of the key collagenolytic proteinases in the aggressive synovial membrane-like interface tissue around aseptically loosened hip replacement implants. ADAMs were found in the interface tissues of revision total hip replacement patients. Increased expression of ADAMs at both transcriptional and translational levels was found in synovial membrane-like interface tissue of revision total hip replacement (THR) samples compared with that in primary THR samples. These studies also demonstrate that multinucleate cell formation from monocytes by stimulation with macrophage-colony stimiulating factor (M-CSF) and receptor activator of nuclear factor kappa B ligand (RANKL) is characterized by time dependent changes of the proportion of ADAMs positive cells. This was observed both in the interface membrane in patients and in two different in vitro models. In addition to an already established MCS-F and RANKL driven model, a new virally (parainfluenza 2) driven model (of human salivary adenocarcinoma (HSY) cells or green monkey kidney (GMK) cells) was developed to study various fusion molecules and their role in cell fusion in general. In interface membranes, collagen was highly degraded and collagen degradation significantly correlated with the number of local cells containing collagenolytic enzymes, particularly cathepsin K. As a conclusion, fusion molecules ADAM9 and ADAM12 seem to be dynamically involved in cell-cell fusion processes and multinucleate cell formation. The highly significant correlation between collagen degradation and collagenolytic enzymes, particularly cathepsin K, indicates that the local acidity of the interface membrane in the pathologic bone and soft tissue destruction. This study provides profound knowledge about cell fusion and mechanism responsible for aseptic loosening as well as increases knowledge helpful for prevention and treatment.

Distributed Scheduling for Multi-Hop Wireless Networks

We study the performance of greedy scheduling in multihop wireless networks where the objective is aggregate utility maximization. Following standard approaches, we consider the dual of the original optimization problem. Optimal scheduling requires selecting independent sets of maximum aggregate price, but this problem is known to be NP-hard. We propose and evaluate a simple greedy heuristic. We suggest how the greedy heuristic can be implemented in a distributed manner. We evaluate an analytical bound in detail, for the special case of a line graph and also provide a loose bound on the greedy heuristic for the case of an arbitrary graph.

Effect of waiting time on health outcomes and service utilization : A prospective randomized study on patients admitted to hospital for hip or knee replacement

Although the principle of equal access to medically justified treatment has been promoted by official health policies in many Western health care systems, practices do not completely meet policy targets. Waiting times for elective surgery vary between patient groups and regions, and growing problems in the availability of services threaten equal access to treatment. Waiting times have come to the attention of decision-makers, and several policy initiatives have been introduced to ensure the availability of care within a reasonable time. In Finland, for example, the treatment guarantee came into force in 2005. However, no consensus exists on optimal waiting time for different patient groups. The purpose of this multi-centre randomized controlled trial was to analyse health-related quality of life, pain and physical function in total hip or knee replacement patients during the waiting time and to evaluate whether the waiting time is associated with patients health outcomes at admission. This study also assessed whether the length of waiting time is associated with social and health services utilization in patients awaiting total hip or knee replacement. In addition, patients health-related quality of life was compared with that of the general population. Consecutive patients with a need for a primary total hip or knee replacement due to osteoarthritis were placed on the waiting list between August 2002 and November 2003. Patients were randomly assigned to a short waiting time (maximum 3 months) or a non-fixed waiting time (waiting time not fixed in advance, instead the patient followed the hospitals routine practice). Patients health-related quality of life was measured upon being placed on the waiting list and again at hospital admission using the generic 15D instrument. Pain and physical function were evaluated using the self-report Harris Hip Score for hip patients and a scale modified from the Knee Society Clinical Rating System for knee patients. Utilization measures were the use of home health care, rehabilitation and social services, physician visits and inpatient care. Health and social services use was low in both waiting time groups. The most common services used while waiting were rehabilitation services and informal care, including unpaid care provided by relatives, neighbours and volunteers. Although patients suffered from clear restrictions in usual activities and physical functioning, they seemed primarily to lean on informal care and personal networks instead of professional care. While longer waiting time did not result in poorer health-related quality of life at admission and use of services during the waiting time was similar to that at the time of placement on the list, there is likely to be higher costs of waiting by people who wait longer simply because they are using services for a longer period. In economic terms, this would represent a negative impact of waiting. Only a few reports have been published of the health-related quality of life of patients awaiting total hip or knee replacement. These findings demonstrate that, in addition to physical dimensions of health, patients suffered from restrictions in psychological well-being such as depression, distress and reduced vitality. This raises the question of how to support patients who suffer from psychological distress during the waiting time and how to develop strategies to improve patients initiatives to reduce symptoms and the burden of waiting. Key words: waiting time, total hip replacement, total knee replacement, health-related quality of life, randomized controlled trial, outcome assessment, social service, utilization of health services

Meta-analysis identifies 13 new loci associated with waist-hip ratio and reveals sexual dimorphism in the genetic basis of fat distribution

Waist-hip ratio (WHR) is a measure of body fat distribution and a predictor of metabolic consequences independent of overall adiposity. WHR is heritable, but few genetic variants influencing this trait have been identified. We conducted a meta-analysis of 32 genome-wide association studies for WHR adjusted for body mass index (comprising up to 77,167 participants), following up 16 loci in an additional 29 studies (comprising up to 113,636 subjects). We identified 13 new loci in or near RSPO3, VEGFA, TBX15-WARS2, NFE2L3, GRB14, DNM3-PIGC, ITPR2-SSPN, LY86, HOXC13, ADAMTS9, ZNRF3-KREMEN1, NISCH-STAB1 and CPEB4 (P = 1.9 × 10−9 to P = 1.8 × 10−40) and the known signal at LYPLAL1. Seven of these loci exhibited marked sexual dimorphism, all with a stronger effect on WHR in women than men (P for sex difference = 1.9 × 10−3 to P = 1.2 × 10−13). These findings provide evidence for multiple loci that modulate body fat distribution independent of overall adiposity and reveal strong gene-by-sex interactions.

Liveweight prediction from hip height, condition score, fetal age and breed in tropical female cattle

Hip height, body condition, subcutaneous fat, eye muscle area, percentage Bos taurus, fetal age and diet digestibility data were collected at 17 372 assessments on 2181 Brahman and tropical composite (average 28% Brahman) female cattle aged between 0.5 and 7.5 years of age at five sites across Queensland. The study validated the subtraction of previously published estimates of gravid uterine weight to correct liveweight to the non-pregnant status. Hip height and liveweight were linearly related (Brahman: P<0.001, R-2 = 58%; tropical composite P<0.001, R-2 = 67%). Liveweight varied by 12-14% per body condition score (5-point scale) as cows differed from moderate condition (P<0.01). Parallel effects were also found due to subcutaneous rump fat depth and eye muscle area, which were highly correlated with each other and body condition score (r = 0.7-0.8). Liveweight differed from average by 1.65-1.66% per mm of rump fat depth and 0.71-0.76% per cm(2) of eye muscle area (P<0.01). Estimated dry matter digestibility of pasture consumed had no consistent effect in predicting liveweight and was therefore excluded from final models. A method developed to estimate full liveweight of post-weaning age female beef cattle from the other measures taken predicted liveweight to within 10 and 23% of that recorded for 65 and 95% of cases, respectively. For a 95% chance of predicted group average liveweight (body condition score used) being within 5, 4, 3, 2 and 1% of actual group average liveweight required 23, 36, 62, 137 and 521 females, respectively, if precision and accuracy of measurements matches that used in the research. Non-pregnant Bos taurus female cattle were calculated to be 10-40% heavier than Brahmans at the same hip height and body condition, indicating a substantial conformational difference. The liveweight prediction method was applied to a validation population of 83 unrelated groups of cattle weighed in extensive commercial situations on 119 days over 18 months (20 917 assessments). Liveweight prediction in the validation population exceeded average recorded liveweight for weigh groups by an average of 19 kg (similar to 6%) demonstrating the difficulty of achieving accurate and precise animal measurements under extensive commercial grazing conditions.

Impact of malnutrition on 12-month mortality following acute hip fracture

Background Studies investigating the relationship between malnutrition and post-discharge mortality following acute hip fracture yield conflicting results. This study aimed to determine whether malnutrition independently predicted 12-month post-fracture mortality after adjusting for clinically relevant covariates. Methods An ethics approved, prospective, consecutive audit was undertaken for all surgically treated hip fracture inpatients admitted to a dedicated orthogeriatric unit (November 2010–October 2011). The 12-month mortality data were obtained by a dual search of the mortality registry and Queensland Health database. Malnutrition was evaluated using the Subjective Global Assessment. Demographic (age, gender, admission residence) and clinical covariates included fracture type, time to surgery, anaesthesia type, type of surgery, post-surgery time to mobilize and post-operative complications (delirium, pulmonary and deep vein thrombosis, cardiac complications, infections). The Charlson Comorbidity Index was retrospectively applied. All diagnoses were confirmed by the treating orthogeriatrician. Results A total of 322 of 346 patients were available for audit. Increased age (P = 0.004), admission from residential care (P < 0.001), Charlson Comorbidity Index (P = 0.007), malnutrition (P < 0.001), time to mobilize >48 h (P < 0.001), delirium (P = 0.003), pulmonary embolism (P = 0.029) and cardiovascular complication (P = 0.04) were associated with 12-month mortality. Logistic regression analysis demonstrated that malnutrition (odds ratio (OR) 2.4 (95% confidence interval (CI) 1.3–4.7, P = 0.007)), in addition to admission from residential care (OR 2.6 (95% CI 1.3–5.3, P = 0.005)) and pulmonary embolism (OR 11.0 (95% CI 1.5–78.7, P = 0.017)), independently predicted 12-month mortality. Conclusions Findings substantiate malnutrition as an independent predictor of 12-month mortality in a representative sample of hip fracture inpatients. Effective strategies to identify and treat malnutrition in hip fracture should be prioritized.

Dislocation after total hip replacement: there is no such thing as a safe zone for socket placement with the posterior approach

Introduction Malorientation of the socket contributes to instability after hip arthroplasty but the optimal orientation of the cup in relation to the pelvis has not been unequivocally described. Large radiological studies are few and problems occur with film standardisation, measurement methodology used and alternative definitions of describing acetabular orientation. Methods A cohort of 1,578 patients from a single institution is studied where all patient data was collected prospectively. Risk factors for patients undergoing surgery are analysed. Radiological data was compared between a series of non-dislocating hips and dislocating cases matched 2:1 by operation type, age and diagnosis. Results The overall dislocation rate for all 1,578 cases was 3.23% but the rate varied according to the type of surgery performed. The rate in uncomplicated primary cases was 2.4% which increased to 9.3% for second stage implantation for a two stage procedure for infection. There was no significant difference in the variability of the dislocating and non-dislocating groups for either inclination (p = 0.393) or anteversion (p = 0.661). Conclusions A “safe zone” for socket orientation to avoid dislocation could not be defined. The cause of dislocation is multifactorial, re-establishing the anatomic centre of rotation, balancing soft tissues and avoidance of impingement around the hip are important considerations.

Primary total hip arthroplasty for primary osteoarthritis in Finland : A national register based analysis

The first aim of the current study was to evaluate the survival of total hip arthroplasty (THA) in patients aged 55 years and older on a nation-wide level. The second aim was to evaluate, on a nation wide-basis, the geographical variation of the incidence of primary THA for primary OA and also to identify those variables that are possibly associated with this variation. The third aim was to evaluate the effects of hospital volume: on the length of stay, on the numbers of re-admissions and on the numbers of complications of THR on population-based level in Finland. The survival of implants was analysed based on data from the Finnish Arthroplasty Register. The incidence and hospital volume data were obtained from the Hospital Discharge Register. Cementless total hip replacements had a significantly reduced risk of revision for aseptic loosening compared with cemented hip replacements. When revision for any reason was the end point in the survival analyses, there were no significant differences found between the groups. Adjusted incidence ratios of THA varied from 1.9- to 3.0-fold during the study period. Neither the average income within a region nor the morbidity index was associated with the incidence of THA. For the four categories of volume of total hip replacements performed per hospital, the length of the surgical treatment period was shorter for the highest volume group than for the lowest volume group. The odds ratio for dislocations was significantly lower in the high volume group than in the low volume group. In patients who were 55 years of age or older, the survival of cementless total hip replacements was as good as that of the cemented replacements. However, multiple wear-related revisions of the cementless cups indicate that excessive polyethylene wear was a major clinical problem with modular cementless cups. The variation in the long-term rates of survival for different cemented stems was considerable. Cementless proximal porous-coated stems were found to be a good option for elderly patients. When hip surgery was performed on with a large repertoire, the indications to perform THAs due to primary OA were tight. Socio-economic status of the patient had no apparent effect on THA rate. Specialization of hip replacements in high volume hospitals should reduce costs by significantly shortening the length of stay, and may reduce the dislocation rate.

Total hip arthroplasty in young patients : with special references to patients under 55 years of age and to patients with developmental dysplasia of the hip

There is an ongoing controversy as to which methods in total hip arthroplasty (THA) could provide young patients with best long-term results. THA is an especially demanding operation in patients with severely dysplastic hips. The optimal surgical treatment for these patients also remains controversial. The aim of this study was to evaluate the long-term survival of THA in young patients (<55 years at the time of the primary operation) on a nation-wide level, and to analyze the long-term clinical and radio-graphical outcome of uncemented THA in patients with severely dysplastic joints. Survival of 4661 primary THAs performed for primary osteoarthritis (OA), 2557 primary THAs per-formed for rheumatoid arthritis (RA), and modern uncemented THA designs performed for primary OA in young patients, were analysed from the Finnish Arthroplasty Register. A total of 68 THAs were per-formed in 56 consecutive patients with high congenital hip dislocation between 1989-1994, and 68 THAs were performed in 59 consecutive patients with severely dysplastic hips and a previous Schanz osteotomy of the femur between 1988-1995 at the Orton Orthopaedic Hospital, Helsinki, Finland. These patients underwent a detailed physical and radiographical evaluation at a mean of 12.3 years and 13.0 years postoperatively, respectively. The risk of stem revision due to aseptic loosening in young patients with primary OA was higher for cemented stems than for proximally porous-coated or HA-coated uncemented stems implanted over the 1991-2001 period. There was no difference in the risk of revision between all-poly cemented-cups and press-fit porous-coated uncemented cups implanted during the same period, when the end point was defined as any revision (including exchange of liner). All uncemented stem designs studied in young patients with primary OA had >90% survival rates at 10 years. The Biomet Bi-Metric stem had a 95% (95% CI 93-97) survival rate even at 15 years. When the end point was defined as any revision, 10 year survival rates of all uncemented cup designs except the Harris-Galante II decreased to <80%. In young patients with RA, the risk of stem revision due to aseptic loosening was higher with cemented stems than with proximally porous-coated uncemented stems. In contrast, the risk of cup revision was higher for all uncemented cup concepts than for all-poly cemented cups with any type of cup revision as the end point. The Harris hip score increased significantly (p<0.001) both in patients with high con-genital hip dislocation and in patients with severely dysplastic hips and a previous Schanz osteotomy, treated with uncemented THA. There was a negative Trendelenburg sign in 92% and in 88% of hips, respectively. There were 12 (18%) and 15 (22%) perioperative complications. The rate of survival for the CDH femoral components, with revision due to aseptic loosening as the end point, was 98% (95% CI 97-100) at 10 years in patients with high hip dislocation and 92% (95% CI, 86-99) at 14 years in patients with a previous Schanz osteotomy. The rate of survival for press-fit, porous-coated acetabular components, with revision due to aseptic loosening as the end point, was 95% (95% CI 89-100) at 10 years in patients with high hip dislocation, and 98% (95% CI 89-100) in patients with a previous Schanz osteotomy. When revision of the cup for any reason was defined as the end point, 10 year sur-vival rates declined to 88% (95% CI 81-95) and to 69% (95% CI, 56-82), respectively. For young patients with primary OA, uncemented proximally circumferentially porous- and HA-coated stems are the implants of choice. However, survival rates of modern uncemented cups are no better than that of all-poly cemented cups. Uncemented proximally circumferentially porous-coated stems and cemented all-poly cups are currently the implants of choice for young patients with RA. Uncemented THA, with placement of the cup at the level of the true acetabulum, distal advancement of the greater trochanter and femoral shortening osteotomy provided patients with high congenital hip dislocation good long-term outcomes. Most of the patients with severely dysplastic hips and a previous Schanz osteotomy can be successfully treated with the same method. However, the subtrochanteric segmental shortening with angular correction gives better leg length correction for the patients with a previous low-seated unilateral Schanz osteotomy.

Surveillance of Surgical Site Infections following Major Hip and Knee Surgery in Finland

Background and aims. Since 1999, hospitals in the Finnish Hospital Infection Program (SIRO) have reported data on surgical site infections (SSI) following major hip and knee surgery. The purpose of this study was to obtain detailed information to support prevention efforts by analyzing SIRO data on SSIs, to evaluate possible factors affecting the surveillance results, and to assess the disease burden of postoperative prosthetic joint infections in Finland. Methods. Procedures under surveillance included total hip (THA) and total knee arthroplasties (TKA), and the open reduction and internal fixation (ORIF) of femur fractures. Hospitals prospectively collected data using common definitions and written protocol, and also performed postdischarge surveillance. In the validation study, a blinded retrospective chart review was performed and infection control nurses were interviewed. Patient charts of deep incisional and organ/space SSIs were reviewed, and data from three sources (SIRO, the Finnish Arthroplasty Register, and the Finnish Patient Insurance Centre) were linked for capture-recapture analyses. Results. During 1999-2002, the overall SSI rate was 3.3% after 11,812 orthopedic procedures (median length of stay, eight days). Of all SSIs, 56% were detected after discharge. The majority of deep incisional and organ/space SSIs (65/108, 60%) were detected on readmission. Positive and negative predictive values, sensitivity, and specificity for SIRO surveillance were 94% (95% CI, 89-99%), 99% (99-100%), 75% (56-93%), and 100% (97-100%), respectively. Of the 9,831 total joint replacements performed during 2001-2004, 7.2% (THA 5.2% and TKA 9.9%) of the implants were inserted in a simultaneous bilateral operation. Patients who underwent bilateral operations were younger, healthier, and more often males than those who underwent unilateral procedures. The rates of deep SSIs or mortality did not differ between bi- and uni-lateral THAs or TKAs. Four deep SSIs were reported following bilateral operations (antimicrobial prophylaxis administered 48-218 minutes before incision). In the three registers, altogether 129 prosthetic joint infections were identified after 13,482 THA and TKA during 1999-2004. After correction with the positive predictive value of SIRO (91%), a log-linear model provided an estimated overall prosthetic joint infection rate of 1.6% after THA and 1.3% after TKA. The sensitivity of the SIRO surveillance ranged from 36% to 57%. According to the estimation, nearly 200 prosthetic joint infections could occur in Finland each year (the average from 1999 to 2004) after THA and TKA. Conclusions. Postdischarge surveillance had a major impact on SSI rates after major hip and knee surgery. A minority of deep incisional and organ/space SSIs would be missed, however, if postdischarge surveillance by questionnaire was not performed. According to the validation study, most SSIs reported to SIRO were true infections. Some SSIs were missed, revealing some weakness in case finding. Variation in diagnostic practices may also affect SSI rates. No differences were found in deep SSI rates or mortality between bi- and unilateral THA and TKA. However, patient materials between these two groups differed. Bilateral operations require specific attention paid to their antimicrobial prophylaxis as well as to data management in the surveillance database. The true disease burden of prosthetic joint infections may be heavier than the rates from national nosocomial surveillance systems usually suggest.

Delay Optimal Scheduling in a Two-Hop Vehicular Relay Network

We study a scheduling problem in a wireless network where vehicles are used as store-and-forward relays, a situation that might arise, for example, in practical rural communication networks. A fixed source node wants to transfer a file to a fixed destination node, located beyond its communication range. In the absence of any infrastructure connecting the two nodes, we consider the possibility of communication using vehicles passing by. Vehicles arrive at the source node at renewal instants and are known to travel towards the destination node with average speed v sampled from a given probability distribution. Th source node communicates data packets (or fragments) of the file to the destination node using these vehicles as relays. We assume that the vehicles communicate with the source node and the destination node only, and hence, every packet communication involves two hops. In this setup, we study the source node's sequential decision problem of transferring packets of the file to vehicles as they pass by, with the objective of minimizing delay in the network. We study both the finite file size case and the infinite file size case. In the finite file size case, we aim to minimize the expected file transfer delay, i.e. expected value of the maximum of the packet sojourn times. In the infinite file size case, we study the average packet delay minimization problem as well as the optimal tradeoff achievable between the average queueing delay at the source node buffer and the average transit delay in the relay vehicle.

Total Hip and Knee Arthoplasty for Osteoarthritis : Factors Related to the Early Outcome of Surgery

Some perioperative clinical factors related to the primary cemented arthroplasty operation for osteoarthritis of the hip or knee joint are studied and discussed in this thesis. In a randomized, double-blind study, 39 patients were divided into two groups: one receiving tranexamic acid and the other not receiving it. Tranexamic acid was given in a dose of 10 mg/kg before the operation and twice thereafter, at 8-hour intervals. Total blood loss was smaller in the tranexamic acid group than in the control group. No thromboembolic complications were noticed. In a prospective, randomized study, 58 patients with hip arthroplasty and 39 patients with knee arthroplasty were divided into groups with postoperative closed-suction drainage and without drainage. There was no difference in healing of the wounds, postoperative blood transfusions, complications or range of motion. As a result of this study, the use of drains is no longer recommended. In a randomised study the effectiveness of a femoral nerve block (25 patients) was compared with other methods of pain control (24 patients) on the first postoperative day after total knee arthroplasty. The femoral block consisted of a single injection administered at patients´ bedside during the surgeon´s hospital rounds. Femoral block patients reported less pain and required half of the amount of oxycodone. Additional femoral block or continued epidural analgesia was required more frequently by the control group patients. Pain management with femoral blocks resulted in less work for nursing staff. In a retrospective study of 422 total hip and knee arthroplasty cases the C-reactive protein levels and clinical course were examined. After hip and knee arthroplasty the maximal C-reactive protein values are seen on the second and third postoperative days, after which the level decreases rapidly. There is no difference between patients with cemented or uncemented prostheses. Major postoperative complications may cause a further increase in C-reactive protein levels at one and two weeks. In-hospital and outpatient postoperative control radiographs of 200 hip and knee arthroplasties were reviewed retrospectively. If postoperative radiographs are of good quality, there seems to be no need for early repetitive radiographs. The quality and safety of follow-up is not compromised by limiting follow-up radiographs to those with clinical indications. Exposure of the patients and the staff to radiation is reduced. Reading of the radiographs by only the treating orthopaedic surgeon is enough. These factors may seem separate from each other, but linking them together may help the treating orthopaedic surgeon to adequate patient care strategy. Notable savings can be achieved.

DMT of Multi-hop Cooperative Networks-Part II: Layered and Multi-Antenna Networks

We consider single-source, single-sink (ss-ss) multi-hop relay networks, with slow-fading Rayleigh links. This two part paper aims at giving explicit protocols and codes to achieve the optimal diversity-multiplexing tradeoff (DMT) of two classes of multi-hop networks: K-parallel-path (KPP) networks and Layered networks. While single-antenna KPP networks were the focus of the first part, we consider layered and multi-antenna networks in this second part. We prove that a linear DMT between the maximum diversity d(max). and the maximum multiplexing gain of 1 is achievable for single-antenna fully-connected layered networks under the half-duplex constraint. This is shown to be equal to the optimal DMT if the number of relaying layers is less than 4. For the multiple-antenna case, we provide an achievable DMT, which is significantly better than known lower bounds for half duplex networks. Along the way, we compute the DMT of parallel MIMO channels in terms of the DMT of the component channel. For arbitrary ss-ss single-antenna directed acyclic networks with full-duplex relays, we prove that a linear tradeoff between maximum diversity and maximum multiplexing gain is achievable using an amplify-and-forward (AF) protocol. Explicit short-block-length codes are provided for all the proposed protocols. Two key implications of the results in the two-part paper are that the half-duplex constraint does not necessarily entail rate loss by a factor of two as previously believed and that simple AN protocols are often sufficient to attain the best possible DMT.

DMT of Multi-hop Cooperative Networks-Part I: K-Parallel-Path Networks

We consider single-source, single-sink multi-hop relay networks, with slow-fading Rayleigh fading links and single-antenna relay nodes operating under the half-duplex constraint. While two hop relay networks have been studied in great detail in terms of the diversity-multiplexing tradeoff (DMT), few results are available for more general networks. In this two-part paper, we identify two families of networks that are multi-hop generalizations of the two hop network: K-Parallel-Path (KPP) networks and Layered networks. In the first part, we initially consider KPP networks, which can be viewed as the union of K node-disjoint parallel paths, each of length > 1. The results are then generalized to KPP(I) networks, which permit interference between paths and to KPP(D) networks, which possess a direct link from source to sink. We characterize the optimal DMT of KPP(D) networks with K >= 4, and KPP(I) networks with K >= 3. Along the way, we derive lower bounds for the DMT of triangular channel matrices, which are useful in DMT computation of various protocols. As a special case, the DMT of two-hop relay network without direct link is obtained. Two key implications of the results in the two-part paper are that the half-duplex constraint does not necessarily entail rate loss by a factor of two, as previously believed and that, simple AF protocols are often sufficient to attain the best possible DMT.